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  • 1.
    Abrahamsson, Olle
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    On Aggregation and Dynamics of Opinions in Complex Networks2024Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [sv]

    Avhandlingen studerar två problem definierade på komplexa nätverk, varav det första utforskar en tänkbar utökning av strukturell balansteori och det andra behandlar konvergensfrågor inom opinionsdynamik.

    I avhandlingens första hälft diskuteras möjliga definitioner på villkor för strukturell balans i ett nätverk med preferensordningar som nodattribut. Huvudresultatet är att för fallet med tre alternativ (A, B, C) så kan de (3!)3 = 216 möjliga konfigurationerna av trianglar reduceras till 10 ekvivalensklasser, vilka används som mått på en triangels balans som ett steg mot möjliga utökningar av strukturell balansteori. Vi härleder även en generell formel för antalet ekvivalensklasser för preferensordningar med n alternativ. Slutligen analyseras en empirisk datamängd och dess empiriska sannolikhetsfördelning av triangel-ekvivalensklasser jämförs med en nollhypotes i vilken preferenser tilldelas noderna slumpmässigt.

    Den andra hälften av avhandlingen rör en opinionsdynamikmodell där varje agent agerar slumpmässigt enligt en Bernoullifördelning vars sannolikhet uppdateras vid varje diskret tidssteg, och vi bevisar att denna modell konvergerar nästan säkert till konsensus. Vi ger också en detaljerad kritik av ett påstått bevis av detta resultat i litteraturen. Vi generaliserar resultatet genom att visa att antagandet om irreducibilitet i den ursprungliga modellen inte är nödvändigt. Vidare visar vi, som följdsats av det generaliserade resultatet, att den nästan säkra konvergensen till konsensus även håller om en agent är fullständigt envis och aldrig byter åsikt. I tillägg till detta visar vi att modellen, både i det ursprungliga och i det generaliserade fallet, konvergerar till konsensus även i r:te ordningens moment.  

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  • 2.
    Abrahamsson, Olle
    et al.
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Danev, Danyo
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Larsson, Erik G
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Strong Convergence of a Random Actions Model in Opinion Dynamics2024Ingår i: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, ISSN 2373-776X, Vol. 10, s. 147-161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in $r$th mean.

    Ladda ner fulltext (pdf)
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  • 3.
    Ahlinder, Jon
    et al.
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Nordgaard, Anders
    Swedish National Forensic Centre (NFC), Linköping, Sweden.
    Wiklund Lindström, Susanne
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Chemometrics comes to court: evidence evaluation of chem–bio threat agent attacks2015Ingår i: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 29, nr 5, s. 267-276Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Forensic statistics is a well-established scientific field whose purpose is to statistically analyze evidence in order to support legal decisions. It traditionally relies on methods that assume small numbers of independent variables and multiple samples. Unfortunately, such methods are less applicable when dealing with highly correlated multivariate data sets such as those generated by emerging high throughput analytical technologies. Chemometrics is a field that has a wealth of methods for the analysis of such complex data sets, so it would be desirable to combine the two fields in order to identify best practices for forensic statistics in the future. This paper provides a brief introduction to forensic statistics and describes how chemometrics could be integrated with its established methods to improve the evaluation of evidence in court.

    The paper describes how statistics and chemometrics can be integrated, by analyzing a previous know forensic data set composed of bacterial communities from fingerprints. The presented strategy can be applied in cases where chemical and biological threat agents have been illegally disposed.

  • 4.
    Ahlqvist, Max
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanik och hållfasthetslära. Linköpings universitet, Tekniska fakulteten. Epiroc Rock Drills AB, Sweden.
    Weddfelt, Kenneth
    Epiroc Rock Drills AB, Sweden.
    Norman, Viktor
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Konstruktionsmaterial. Linköpings universitet, Tekniska fakulteten.
    Leidermark, Daniel
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanik och hållfasthetslära. Linköpings universitet, Tekniska fakulteten.
    Probabilistic evaluation of the Step-Stress fatigue testing method considering cumulative damage2023Ingår i: Probabilistic Engineering Mechanics, ISSN 0266-8920, E-ISSN 1878-4275, Vol. 74, artikel-id 103535Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general testing and analysis framework for the Step-Stress fatigue testing method is identified, utilizing interval-censored data and maximum likelihood estimation in an effort to improve estimation of fatigue strength distribution parameters has been performed. The Step-Stress methods limitations are characterized, using a simple material model that considers cumulative damage to evaluate load history effects. In this way, the performance including cumulative damage was evaluated and quantified using a probabilistic approach with Monte-Carlo simulations, benchmarked against the Staircase method throughout the work. It was found that the Step-Stress method, even when cumulative damage occurs to a wide extent, outperforms the Staircase method, especially for small sample sizes. Furthermore, positive results reaches further than the increase performance in estimating fatigue strength distribution parameters, where improvements in secondary information, i.e. S-N data gained from failure specimens, are shown to be distributed more closely to the fatigue life region of interest.

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  • 5.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.

  • 6.
    Ahmad, M. Rauf
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Ohlson, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
    Some Tests of Covariance Matrices for High Dimensional Multivariate Data2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

  • 7.
    Ahmad, M. Rauf
    et al.
    Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
    von Rosen, Dietrich
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    A note on mean testing for high dimensional multivariate data under non-normality2013Ingår i: Statistica Neerlandica, ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, nr 1, s. 81-99Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.

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  • 8.
    Aitken, Colin
    et al.
    School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom.
    Nordgaard, Anders
    Swedish Police Authority, National Forensic Centre (NFC), Linköping, Sweden.
    Taroni, Franco
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    Biedermann, Alex
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    Commentary: Likelihood Ratio as Weight of Forensic Evidence: A Closer Look: A commentary on Likelihood Ratio as Weight of Forensic Evidence: A Closer Look by Lund, S. P., and Iyer, H. (2017). J. Res. Natl. Inst. Stand. Technol. 122:272018Ingår i: Frontiers in Genetics, E-ISSN 1664-8021, Vol. 9, artikel-id 224Artikel i tidskrift (Övrigt vetenskapligt)
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  • 9.
    Alenlöv, Johan
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Doucet, Arnaud
    Univ Oxford, England.
    Lindsten, Fredrik
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Pseudo-Marginal Hamiltonian Monte Carlo2021Ingår i: Journal of machine learning research, ISSN 1532-4435, E-ISSN 1533-7928, Vol. 22Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some auxiliary latent variables, or pseudo-marginal Metropolis-Hastings (MH) schemes. The latter mimic a MH algorithm targeting the marginal posterior of the parameters by approximating unbiasedly the intractable likelihood. However, in scenarios where the parameters and auxiliary variables are strongly correlated under the posterior and/or this posterior is multimodal, Gibbs sampling or Hamiltonian Monte Carlo (HMC) will perform poorly and the pseudo-marginal MH algorithm, as any other MH scheme, will be inefficient for high-dimensional parameters. We propose here an original MCMC algorithm, termed pseudo-marginal HMC, which combines the advantages of both HMC and pseudo-marginal schemes. Specifically, the PM-HMC method is controlled by a precision parameter N, controlling the approximation of the likelihood and, for any N, it samples the marginal posterior of the parameters. Additionally, as N tends to infinity, its sample trajectories and acceptance probability converge to those of an ideal, but intractable, HMC algorithm which would have access to the intractable likelihood and its gradient. We demonstrate through experiments that PM-HMC can outperform significantly both standard HMC and pseudo-marginal MH schemes.

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  • 10.
    Alhasan, Ahmed
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Generating Geospatial Trip DataUsing Deep Neural Networks2022Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Synthetic data provides a good alternative to real data when the latter is not sufficientor limited by privacy requirements. In spatio-temporal applications, generating syntheticdata is generally more complex due to the existence of both spatial and temporal dependencies.Recently, with the advent of deep generative modeling such as GenerativeAdversarial Networks (GAN), synthetic data generation has seen a lot of development andsuccess. This thesis uses a GAN model based on two Recurrent Neural Networks (RNN)as a generator and a discriminator to generate new trip data for transport vehicles, wherethe data is represented as a time series. This model is compared with a standalone RNNnetwork that does not have an adversarial counterpart. The result shows that the RNNmodel (without the adversarial counterpart) performed better than the GAN model dueto the difficulty that involves training and tuning GAN models.

    Ladda ner fulltext (pdf)
    Master Thesis
  • 11.
    Almroth, Henrik
    et al.
    Linköpings universitet, Medicinska fakulteten. Region Östergötland, Hjärtcentrum, Kardiologiska kliniken US. Linköpings universitet, Institutionen för hälsa, medicin och vård, Avdelningen för diagnostik och specialistmedicin.
    Karlsson, Lars O
    Linköpings universitet, Medicinska fakulteten. Linköpings universitet, Institutionen för hälsa, medicin och vård, Avdelningen för diagnostik och specialistmedicin. Region Östergötland, Hjärtcentrum, Kardiologiska kliniken US.
    Carlhäll, Carl-Johan
    Linköpings universitet, Institutionen för hälsa, medicin och vård, Avdelningen för diagnostik och specialistmedicin. Linköpings universitet, Medicinska fakulteten. Region Östergötland, Hjärtcentrum, Fysiologiska kliniken US.
    Charitakis, Emmanouil
    Linköpings universitet, Medicinska fakulteten. Linköpings universitet, Institutionen för hälsa, medicin och vård, Avdelningen för diagnostik och specialistmedicin. Region Östergötland, Hjärtcentrum, Kardiologiska kliniken US.
    Haemodynamic changes after atrial fibrillation initiation in patients eligible for catheter ablation: a randomized controlled study2023Ingår i: European Heart Journal Open, E-ISSN 2752-4191, Vol. 3, nr 6, artikel-id oead112Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    AbstractAims: Atrial fibrillation (AF) haemodynamics is less well studied due to challenges explained by the nature of AF. Until now, no randomized data are available. This study evaluates haemodynamic variables after AF induction in a randomized setting.

    Methods and results: Forty-two patients with AF who had been referred for ablation to the University Hospital, Linköping, Sweden, and had no arrhythmias during the 4-day screening period were randomized to AF induction vs. control (2:1). Atrial fibrillation was induced by burst pacing after baseline intracardiac pressure measurements. Pressure changes in the right and left atrium (RA and LA), right ventricle (RV), and systolic and diastolic blood pressures (SBP and DBP) were evaluated 30 min after AF induction compared with the control group. A total of 11 women and 31 men (median age 60) with similar baseline characteristics were included (intervention n = 27, control group n = 15). After 30 min in AF, the RV end-diastolic pressure (RVEDP) and RV systolic pressure (RVSP) significantly reduced compared with baseline and between randomization groups (RVEDP: P = 0.016; RVSP: P = 0.001). Atrial fibrillation induction increased DBP in the intervention group compared with the control group (P = 0.02), unlike reactions in SBP (P = 0.178). Right atrium and LA mean pressure (RAm and LAm) responses did not differ significantly between the groups (RAm: P = 0.307; LAm: P = 0.784).

    Conclusion: Induced AF increased DBP and decreased RVEDP and RVSP. Our results allow us to understand some paroxysmal AF haemodynamics, which provides a haemodynamic rationale to support rhythm regulatory strategies to improve symptoms and outcomes.

    Trial registration number clinicaltrialsgov: No NCT01553045. https://clinicaltrials.gov/ct2/show/NCT01553045?term=NCT01553045&rank=1.

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  • 12.
    Alnervik, Jonna
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Nord Andersson, Peter
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    En retrospektiv studie av vilka patientgrupper som erhåller insulinpump2010Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Målsättning

    Att utreda skillnader i tillgänglighet till insulinpump mellan olika patientgrupper samt vad som orsakar ett byte till insulinpump.

    Metod

    Data från 7224 individer med typ 1 diabetes vid tio olika vårdenheter analyserades för att utreda effekterna av njurfunktion, kön, långtidsblodsocker, insulindos, diabetesduration samt ålder. Jämförelsen mellan patientgrupper utfördes med logistisk regression som en tvärsnittsstudie och Cox-regression för att utreda vad som föregått ett byte till pump.

    Resultat

    Genom logistisk regression erhölls en bild av hur skillnader mellan patienter som använder insulinpump och patienter som inte gör det ser ut i dagsläget. Cox-regressionen tar med ett tidsperspektiv och ger på så sätt svar på vad som föregått ett byte till insulinpump. Dessa analyser gav liknande resultat gällande variabler konstanta över tiden. Kvinnor använder pump i större utsträckning än män och andelen pumpanvändare skiljer sig åt vid olika vårdenheter. I dagsläget visar sig hög ålder sänka sannolikheten att använda insulinpump, vilket bekräftas vid den tidsberoende studien som visade hur sannolikheten att byta till pump är avsevärt lägre vid hög ålder. Långtidsblodsockret har också tydlig effekt på sannolikheten att gå över till pump där ett högt långtidsblodsocker medför hög sannolikhet att byta till insulinpump.

    Slutsatser

    I dagsläget finns det skillnader i andelen insulinpumpanvändare mellan olika patientgrupper och skillnader finns även i de olika gruppernas benägenhet att byta från andra insulinbehandlingar till insulinpump. Beroende av patienters njurfunktion, kön, långtidsblodsocker, insulindos, diabetesduration och ålder har dessa olika sannolikheter att byta till insulinpump.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 13.
    Alsén, Simon
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Åkesson, Andreas
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Jämförelse av metoder för hantering av partiellt bortfall vid logistisk regressionsanalys2021Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Partiellt bortfall är en vanligt förekommande felkälla vid statistiska undersökningar. Med partiellt bortfall avses avsaknad av vissa variabelvärden för ett observationsobjekt, något som riskerar leda till förlust av statistisk styrka och skeva parameterskattningar. Ett stort antal metoder har utvecklats för att hantera denna problematik, och syftet med denna uppsats är att undersöka vilken effekt några av dessa metoder har på parameterskattningarna i en logistisk regressionsmodell, och huruvida dessa metoder är lämpliga att tillämpa på aktuellt datamaterial. De metoder som inkluderats i denna studie är complete case analysis, MICE och missForest.

    För ändamålet simuleras partiellt bortfall av olika omfattningar och under olika bortfallsmekanismer i ett verkligt datamaterial som består av 2987 observationer och fem variabler. Metoderna utvärderas sedan med avseende på normalized root mean squared error (NRMSE), samt genom att undersöka hur de regressionskoefficienter som skattats med de imputerade datamaterialen avviker från de regressionskoefficienter som skattats med det kompletta, observerade datamaterialet.

    missForest resulterar i lägst NRMSE. I den efterföljande logistiska regressionsanalysen resulterar dock MICE i betydligt lägre bias än missForest.

    Ladda ner fulltext (pdf)
    fulltext
  • 14.
    Amundsson, Martin
    Linköpings universitet, Institutionen för datavetenskap.
    Långtidscovid: symptomförlopp och mönster över tid: En explorativ analys av crowdsource-insamlat enkätdata2022Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Two years after the first recorded outbreak of Covid-19 its long-term effects are still not completely understood. An unknown proportion of all covid patients go on to develop post-acute covid syndrome and suffer long-term symptoms and health effects long after the initial infection subsides. Project Crowdsourcing Långtidscovid-Sverige sent out in summer of 2021 an open online survey and gathered respondents through crowdsourcing to gather info about people in Sweden with prolonged health effects lasting at least three months after confirmed or suspected Covid-19 infection.

    In this thesis an explorative analysis of the aforementioned survey is conducted with its initial focus placed onthe progression of symptoms. Descriptive statistics are provided for the survey sample; hierarchical clusteringon principal components is performed; and association rule mining as well as sequence rule mining is used toextract frequently co-occurring symptoms.

    Women stand for 85.2% of all respondents, possibly indicating a skewed gender distribution in the sample. The average age of a respondent is 50 years old, but ranges between 18 and 80 years of age. The number of reported symptoms tend to diminish over time and symptoms within the 'air passages' category diminish on average quicker than other categories.

    Hierarchical clustering with Ward’s criterion revealed 4 clusters with an average silhouette coefficient of 0.246. The resulting clusters are not well-separated from each other and have some overlap in their bordering regions, and should therefore be interpreted with caution. Broadly speaking, individuals from cluster 1, 3 and 4 are distinguished primarily by their total number of symptoms reported, meanwhile cluster 2 is characterized by individuals that experience many symptoms early on and fewer symptoms later on.

    The most prevalent symptom over the entire period is fatigue (90.2%), closely followed by worsening symptomsafter physical activity (87.1%), problems with concentration (82.3%), headaches (79.5%), and brain fog (77.9%). There are several strong associations between various symptoms, especially for symptoms within the same category. Most symptoms have a sequential correlation with themselves and have an increased tendency to occur several times.

    Ladda ner fulltext (pdf)
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  • 15.
    Anders, Erik
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Classification of Corporate Social Performance2021Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Over the past few years there has been an exponentially increasing attention in financetowards socially responsible investments which creates a need to determine whether acompany is socially responsible or not. The ESG ratings often used to do this are based onEnvironmental, Social and Governance related data about the companies and have manyflaws. This thesis proposes to instead model them by their controversies discussed in themedia. It tries to answer the question if it is possible to predict future controversies of acompany by its controversies and ESG indicators in the past and to isolate predictors whichinfluence these. This has not been done before and offers a new way of rating companieswithout falling for the biases of conventional ESG ratings. The chosen method to approachthis issue is the Zero Inflated Poisson Regression with Random Intercepts. A selectionof variables was determined by Lasso and projection predictive variable selection. Thismethod discovered new connections in the data between ESG indicators and the numberof controversies but also made it apparent that it is difficult to make predictions for futureyears. Nether the less the coefficients of the selected indicators can give a valuable insightinto the potential risk of an investment.

    Ladda ner fulltext (pdf)
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  • 16.
    Anderskär, Erika
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Thomasson, Frida
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Inkrementell responsanalys av Scandnavian Airlines medlemmar: Vilka kunder ska väljas vid riktad marknadsföring?2017Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Scandinavian Airlines has a large database containing their Eurobonus members. In order to analyze which customers they should target with direct marketing, such as emails, uplift models have been used. With a binary response variable that indicates whether the customer has bought or not, and a binary dummy variable that indicates if the customer has received the campaign or not conclusions can be drawn about which customers are persuadable. That means that the customers that buy when they receive a campaign and not if they don't are spotted. Analysis have been done with one campaign for Sweden and Scandinavia. The methods that have been used are logistic regression with Lasso and logistic regression with Penalized Net Information Value. The best method for predicting purchases is Lasso regression when comparing with a confusion matrix. The variable that best describes persuadable customers in logistic regression with PNIV is Flown (customers that have own with SAS within the last six months). In Lassoregression the variable that describes a persuadable customer in Sweden is membership level1 (the rst level of membership) and in Scandinavia customers that receive campaigns with delivery code 13 are persuadable, which is a form of dispatch.

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  • 17.
    Andersson Hagiwara, Magnus
    et al.
    University of Borås, Sweden.
    Andersson Gare, Boel
    Jönköping University, Sweden.
    Elg, Mattias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Logistik- och kvalitetsutveckling. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, HELIX Vinn Excellence Centre.
    Interrupted Time Series Versus Statistical Process Control in Quality Improvement Projects2016Ingår i: Journal of Nursing Care Quality, ISSN 1057-3631, E-ISSN 1550-5065, Vol. 31, nr 1, s. E1-E8Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    To measure the effect of quality improvement interventions, it is appropriate to use analysis methods that measure data over time. Examples of such methods include statistical process control analysis and interrupted time series with segmented regression analysis. This article compares the use of statistical process control analysis and interrupted time series with segmented regression analysis for evaluating the longitudinal effects of quality improvement interventions, using an example study on an evaluation of a computerized decision support system.

  • 18.
    Andersson, Henrik
    et al.
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Bakke Cato, Robin
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Stokastisk modellering och prognosticering inom livförsäkring: En dödlighetsundersökning på Länsförsäkringar Livs bestånd2023Självständigt arbete på avancerad nivå (masterexamen), 28 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Studier av livslängder och dödssannolikheter är avgörande för livförsäkring. Betalningar gällande livförsäkringar är helt beroende av om en individ lever eller ej, eller befinner sig i olika hälsotillstånd. För att kunna prissätta premier korrekt och avsätta reserver är det därför av stort intresse att modellera livslängden på ett så korrekt sätt som möjligt. Försäkringsbranschen använder idag historiskt beprövade och välfungerande modeller som går så långt bak i tiden som 200 år. Det finns modeller ännu längre bak i tiden, men de modeller som används idag är främst Gompertz (1826), Makeham (1860) och Lee-Carter (1992). Även om dessa modeller presterar bra är det alltid nödvändigt att undersöka om det kan finnas alternativa modeller som modellerar dödligheten bättre.

    I detta examensarbete tillämpas affina korträntemodeller för modellering av dödlighetsintensiteten som ligger till grund för flertalet intressanta aktuariella storheter. Då dessa modeller introducerar stokastisk dödlighet kan osäkerheten och beroendet över tid därmed beskrivas. De korträntemodeller som undersöks i arbetet och som är vanligt förekommande inom den finansiella teorin; är Ornstein-Uhlenbeck, Feller och Hull-White. Dessa modeller jämförs sedan mot varandra vad gäller modellerad dödlighetsintensitet samt förväntad återstående livslängd och ettårig dödssannolikhet. En aspekt av stokastisk dödlighetsmodellering som ej återfinns i befintlig litteratur men som undersöks i detta examensarbete är modellering av dödlighet över tid då detta är en av de mest väsentliga aspekterna inom det livförsäkringsmatematiska arbetet. Till sist i valideringssyfte utvärderas samtliga korträntemodeller genom back-testing. Den andra huvudsakliga delen av arbetet består i att generera resultat för samma storheter som ovan baserat på DUS-metoden för att på så sätt jämföra en kommersiell metod mot en mer teoretisk mindre beprövad sådan.

    Resultaten visar på en stor potential hos flera av korträntemodellerna kontra DUS både vad gäller modellering över åldrar och kalenderår. Däremot är inte resultaten helt felfria för enstaka kalenderår där stora spikar uppstår på grund av parametermässig felanpassning. Modelleringen av korträntemodellerna över tid var över förväntan då modellerna inte är konstruerade för att fånga avtagande trender. Detta är något som kan betraktas som en stor flexibilitet hos korträntemodellerna då de står sig väl mot Lee-Cartermodellen som används i DUS, både vad gäller ålders- och tidsmodellering av dödlighet.

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    Stokastisk modellering och prognosticering inom livförsäkring - Robin Bakke Cato - Henrik Andersson
  • 19.
    Andersson, Kasper
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    A Review of Gaussian Random Matrices2020Självständigt arbete på grundnivå (kandidatexamen), 14 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Medan många stöter på statistik och sannolikhetslära tidigt under sina universitetsstudier så är det sällan slumpmatristeori (RMT) dyker upp förän på forskarnivå. RMT handlar om att studera matriser där elementen följer någon sannolikhetsfördelning och den här uppsatsen presenterar den mest grundläggande teorin för slumpmatriser. Vi introducerar Gaussian ensembles, Wishart ensembles samt fördelningarna för dem tillhörande egenvärdena. Avslutningsvis så introducerar vi hur slumpmatriser kan användas i neruonnät och i PCA.

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  • 20.
    Andersson, Kasper
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Classification of Repeated Measurement Data Using Growth Curves and Neural Networks2022Självständigt arbete på avancerad nivå (masterexamen), 28 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Den här uppsatsen introducerar klassificeringsmetoder skapade för data av typen upprepade mätningar och sekventiell data. Den klassiska MANOVA modellen introduceras först som en grund för den mer allmäna tillväxtkurvemodellen(GMANOVA), som i sin tur används för att modellera upprepade mätningar på ett meningsfullt sätt. Under antagandet av normalfördelad data så härleds en binär klassificeringsmetod baserad på linjär diskriminantanalys, som tillsammans med maximum likelihood-skattningar från tillväxtkurvemodellen ger en binär klassificeringsregel för data av typen upprepade mätningarn.

    Vi fortsätter med att introducera läsaren för klassiska neurala nätverk och relevanta ämnen diskuteras. Vi generaliserar teorin kring neurala nätverk till typen "recurrent" neurala nätverk och LSTM som är designade för sekventiell data.

    Avslutningsvis så testas klassificeringsmetoderna på tre typer av data i totalt åtta olika fall.

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  • 21.
    Andersson Naesseth, Christian
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Nowcasting using Microblog Data2012Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The explosion of information and user generated content made publicly available through the internet has made it possible to develop new ways of inferring interesting phenomena automatically. Some interesting examples are the spread of a contagious disease, earth quake occurrences, rainfall rates, box office results, stock market fluctuations and many many more. To this end a mathematical framework, based on theory from machine learning, has been employed to show how frequencies of relevant keywords in user generated content can estimate daily rainfall rates of different regions in Sweden using microblog data.

    Microblog data are collected using a microblog crawler. Properties of the data and data collection methods are both discussed extensively. In this thesis three different model types are studied for regression, linear and nonlinear parametric models as well as a nonparametric Gaussian process model. Using cross-validation and optimization the relevant parameters of each model are estimated and the model is evaluated on independent test data. All three models show promising results for nowcasting rainfall rates.

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  • 22.
    Andersson Naesseth, Christian
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Lindsten, Fredrik
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Schon, Thomas B.
    Uppsala Univ, Sweden.
    High-Dimensional Filtering Using Nested Sequential Monte Carlo2019Ingår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 67, nr 16, s. 4177-4188Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without a good proposal distribution can perform poorly, in particular in high dimensions. We propose nested sequential Monte Carlo, a methodology that generalizes the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correctSMCalgorithm. This way, we can compute an "exact approximation" of, e. g., the locally optimal proposal, and extend the class of models forwhichwe can perform efficient inference using SMC. We showimproved accuracy over other state-of-the-art methods on several spatio-temporal state-space models.

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  • 23.
    Andersson Naesseth, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindsten, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Capacity estimation of two-dimensional channels using Sequential Monte Carlo2014Ingår i: 2014 IEEE Information Theory Workshop, 2014, s. 431-435Konferensbidrag (Refereegranskat)
    Abstract [en]

    We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D (1, ∞) run-length limited constrained channel, but the underlying idea is generally applicable. The proposed algorithm is profiled against a state-of-the-art method, yielding more than an order of magnitude improvement in estimation accuracy for a given computation time.

    Ladda ner fulltext (pdf)
    fulltext
  • 24.
    Andersson Naesseth, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Lindsten, Fredrik
    The University of Cambridge, Cambridge, United Kingdom.
    Schön, Thomas
    Uppsala University, Uppsala, Sweden.
    Nested Sequential Monte Carlo Methods2015Ingår i: Proceedings of The 32nd International Conference on Machine Learning / [ed] Francis Bach, David Blei, Journal of Machine Learning Research (Online) , 2015, Vol. 37, s. 1292-1301Konferensbidrag (Refereegranskat)
    Abstract [en]

    We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.

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  • 25.
    Andersson Naesseth, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindsten, Fredrik
    University of Cambridge, Cambridge, UK.
    Schön, Thomas
    Uppsala University, Uppsala, Sweden.
    Sequential Monte Carlo for Graphical Models2014Ingår i: Advances in Neural Information Processing Systems, 2014, s. 1862-1870Konferensbidrag (Refereegranskat)
    Abstract [en]

    We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

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  • 26.
    Andersson, Niklas
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Hansson, Josef
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Metodik för detektering av vägåtgärder via tillståndsdata2010Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The Swedish Transport Administration has, and manages, a database containing information of the status of road condition on all paved and governmental operated Swedish roads. The purpose of the database is to support the Pavement Management System (PMS). The PMS is used to identify sections of roads where there is a need for treatment, how to allocate resources and to get a general picture of the state of the road network condition. All major treatments should be reported which has not always been done.

    The road condition is measured using a number of indicators on e.g. the roads unevenness. Rut depth is an indicator of the roads transverse unevenness. When a treatment has been done the condition drastically changes, which is also reflected by these indicators.

    The purpose of this master thesis is to; by using existing indicators make predictions to find points in time when a road has been treated.

    We have created a SAS-program based on simple linear regression to analyze rut depth changes over time. The function of the program is to find levels changes in the rut depth trend. A drastic negative change means that a treatment has been made.

    The proportion of roads with an alleged date for the latest treatment earlier than the programs latest detected date was 37 percent. It turned out that there are differences in the proportions of possible treatments found by the software and actually reported roads between different regions. The regions North and Central have the highest proportion of differences. There are also differences between the road groups with various amount of traffic. The differences between the regions do not depend entirely on the fact that the proportion of heavily trafficked roads is greater for some regions.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 27.
    Ansell, Ricky
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Biologi. Linköpings universitet, Tekniska fakulteten. Polismyndigheten - Nationellt Forensiskt Centrum.
    Nordgaard, Anders
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten. Polismyndigheten - Nationellt Forensiskt Centrum.
    Hedell, Ronny
    Polismyndigheten - Nationellt Forensiskt Centrum.
    Interpretation of DNA Evidence: Implications of Thresholds Used in the Forensic Laboratory2014Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Evaluation of forensic evidence is a process lined with decisions and balancing, not infrequently with a substantial deal of subjectivity. Already at the crime scene a lot of decisions have to be made about search strategies, the amount of evidence and traces recovered, later prioritised and sent further to the forensic laboratory etc. Within the laboratory there must be several criteria (often in terms of numbers) on how much and what parts of the material should be analysed. In addition there is often a restricted timeframe for delivery of a statement to the commissioner, which in reality might influence on the work done. The path of DNA evidence from the recovery of a trace at the crime scene to the interpretation and evaluation made in court involves several decisions based on cut-offs of different kinds. These include quality assurance thresholds like limits of detection and quantitation, but also less strictly defined thresholds like upper limits on prevalence of alleles not observed in DNA databases. In a verbal scale of conclusions there are lower limits on likelihood ratios for DNA evidence above which the evidence can be said to strongly support, very strongly support, etc. a proposition about the source of the evidence. Such thresholds may be arbitrarily chosen or based on logical reasoning with probabilities. However, likelihood ratios for DNA evidence depend strongly on the population of potential donors, and this may not be understood among the end-users of such a verbal scale. Even apparently strong DNA evidence against a suspect may be reported on each side of a threshold in the scale depending on whether a close relative is part of the donor population or not. In this presentation we review the use of thresholds and cut-offs in DNA analysis and interpretation and investigate the sensitivity of the final evaluation to how such rules are defined. In particular we show what are the effects of cut-offs when multiple propositions about alternative sources of a trace cannot be avoided, e.g. when there are close relatives to the suspect with high propensities to have left the trace. Moreover, we discuss the possibility of including costs (in terms of time or money) for a decision-theoretic approach in which expected values of information could be analysed.

  • 28.
    Argillander, Joakim
    et al.
    Linköpings universitet, Institutionen för systemteknik, Informationskodning. Linköpings universitet, Tekniska fakulteten.
    Alarcon, Alvaro
    Linköpings universitet, Institutionen för systemteknik, Informationskodning. Linköpings universitet, Tekniska fakulteten.
    Xavier, Guilherme B.
    Linköpings universitet, Institutionen för systemteknik, Informationskodning. Linköpings universitet, Tekniska fakulteten.
    A tunable quantum random number generator based on a fiber-optical Sagnac interferometer2022Ingår i: Journal of Optics, ISSN 2040-8978, E-ISSN 2040-8986, Vol. 24, nr 6, artikel-id 064010Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Quantum random number generators (QRNGs) are based on naturally random measurementresults performed on individual quantum systems. Here, we demonstrate a branching-pathphotonic QRNG implemented using a Sagnac interferometer with a tunable splitting ratio. Thefine-tuning of the splitting ratio allows us to maximize the entropy of the generated sequence ofrandom numbers and effectively compensate for tolerances in the components. By producingsingle-photons from attenuated telecom laser pulses, and employing commercially-availablecomponents we are able to generate a sequence of more than 2 gigabytes of random numberswith an average entropy of 7.99 bits/byte directly from the raw measured data. Furthermore, oursequence passes randomness tests from both the NIST and Dieharder statistical test suites, thuscertifying its randomness. Our scheme shows an alternative design of QRNGs based on thedynamic adjustment of the uniformity of the produced random sequence, which is relevant forthe construction of modern generators that rely on independent real-time testing of itsperformance.

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  • 29.
    Arvid, Odencrants
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska högskolan.
    Dennis, Dahl
    Linköpings universitet, Institutionen för datavetenskap. Linköpings universitet, Tekniska högskolan.
    Utvärdering av Transportstyrelsens flygtrafiksmodeller2014Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The Swedish Transport Agency has for a long time collected data on a monthly basis for different variables that are used to make predictions, short projections as well as longer projections. They have used SAS for producing statistical models in air transport. The model with the largest value of coefficient of determination is the method that has been used for a long time. The Swedish Transport Agency felt it was time for an evaluation of their models and methods of how projections is estimated, they would also explore the possibilities to use different, completely new models for forecasting air travel. This Bachelor thesis examines how the Holt-Winters method does compare with SARIMA, error terms such as RMSE, MAPE, R2, AIC and BIC  will be compared between the methods. 

    The results which have been produced showing that there may be a risk that the Holt-Winters models adepts a bit too well in a few variables in which Holt-Winters method has been adapted. But overall the Holt-Winters method generates better forecasts .

    Ladda ner fulltext (pdf)
    UtvarderingavTransportstyrelsensflygtrafiksmodeller
  • 30.
    Asokan, Mowniesh
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    A study of forecasts in Financial Time Series using Machine Learning methods2022Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Forecasting financial time series is one of the most challenging problems in economics and business. Markets are highly complex due to non-linear factors in data and uncertainty. It moves up and down without any pattern. Based on historical univariate close prices from the S\&P 500, SSE, and FTSE 100 indexes, this thesis forecasts future values using two different approaches: one using a classical method, a Seasonal ARIMA model, and a hybrid ARIMA-GARCH model, while the other uses an LSTM neural network. Each method is used to perform at different forecast horizons. Experimental results have proven that the LSTM and Hybrid ARIMA-GARCH model performs better than the SARIMA model. To measure the model performance we used the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE).

    Ladda ner fulltext (pdf)
    A study of forecasts in Financial Time Series using Machine Learning methods
  • 31.
    Bacharach, Lucien
    et al.
    Univ Toulouse Isae Supaero, France.
    Fritsche, Carsten
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Orguner, Umut
    Middle East Tech Univ, Turkey.
    Chaumette, Eric
    Univ Toulouse Isae Supaero, France.
    A TIGHTER BAYESIAN CRAMER-RAO BOUND2019Ingår i: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2019, s. 5277-5281Konferensbidrag (Refereegranskat)
    Abstract [en]

    It has been shown lately that any "standard" Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a "tighter" form which upper bounds the "standard" form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region.

  • 32.
    Barakat, Arian
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    What makes an (audio)book popular?2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Audiobook reading has traditionally been used for educational purposes but has in recent times grown into a popular alternative to the more traditional means of consuming literature. In order to differentiate themselves from other players in the market, but also provide their users enjoyable literature, several audiobook companies have lately directed their efforts on producing own content. Creating highly rated content is, however, no easy task and one reoccurring challenge is how to make a bestselling story. In an attempt to identify latent features shared by successful audiobooks and evaluate proposed methods for literary quantification, this thesis employs an array of frameworks from the field of Statistics, Machine Learning and Natural Language Processing on data and literature provided by Storytel - Sweden’s largest audiobook company.

    We analyze and identify important features from a collection of 3077 Swedish books concerning their promotional and literary success. By considering features from the aspects Metadata, Theme, Plot, Style and Readability, we found that popular books are typically published as a book series, cover 1-3 central topics, write about, e.g., daughter-mother relationships and human closeness but that they also hold, on average, a higher proportion of verbs and a lower degree of short words. Despite successfully identifying these, but also other factors, we recognized that none of our models predicted “bestseller” adequately and that future work may desire to study additional factors, employ other models or even use different metrics to define and measure popularity.

    From our evaluation of the literary quantification methods, namely topic modeling and narrative approximation, we found that these methods are, in general, suitable for Swedish texts but that they require further improvement and experimentation to be successfully deployed for Swedish literature. For topic modeling, we recognized that the sole use of nouns provided more interpretable topics and that the inclusion of character names tended to pollute the topics. We also identified and discussed the possible problem of word inflections when modeling topics for more morphologically complex languages, and that additional preprocessing treatments such as word lemmatization or post-training text normalization may improve the quality and interpretability of topics. For the narrative approximation, we discovered that the method currently suffers from three shortcomings: (1) unreliable sentence segmentation, (2) unsatisfactory dictionary-based sentiment analysis and (3) the possible loss of sentiment information induced by translations. Despite only examining a handful of literary work, we further found that books written initially in Swedish had narratives that were more cross-language consistent compared to books written in English and then translated to Swedish.

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    what_makes_an_audiobook_popular
  • 33. Beställ onlineKöp publikationen >>
    Barkhagen, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Risk-Neutral and Physical Estimation of Equity Market Volatility2013Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Det övergripande syftet med doktorandprojektet är att utveckla ett ramverk för att fatta optimala beslut på aktiederivatmarknaderna. Att fatta optimala beslut syftar till exempel på hur man optimalt ska hedga en optionsportfölj, eller hur man ska göra optimala investeringar på aktiederivatmarknaderna. Ramverket för att fatta optimala beslut kommer att baseras på stokastisk programmerings-modeller (SP-modeller), vilket betyder att det är nödvändigt att generera högkvalitativa scenarier för marknadspriser för en framtida tidpunkt som indata till SP-modellen. Detta leder till en situation där de traditionella metoderna, som finns beskrivna i litteraturen, för att modellera marknadspriser inte ger scenarier av tillräckligt hög kvalitet för att fungera som indata till SP-modellen. Följaktligen är huvudfokus för denna avhandling att utveckla metoder som, jämfört med de traditionella metoderna som finns beskrivna i litteraturen, förbättrar estimeringen av ytor som impliceras av en given mängd observerade optionspriser. Estimeringen kompliceras av att observerade optionspriser innehåller mycket brus och möjligen också arbitrage. Det betyder att för att kunna estimera optionsimplicerade ytor som är arbitragefria och av hög kvalitet, så behöver estimeringsmetoden hantera bruset i indata på ett adekvat sätt.

    De första två artiklarna i avhandlingen utvecklar ett icke-parametriskt optimeringsbaserat ramverk för estimering av högkvalitativa och arbitragefria options-implicerade ytor. Den första artikeln behandlar estimeringen av den risk-neutrala täthetsytan (RND-ytan) och den andra artikeln estimeringen av den lokala volatilitetsytan. Båda metoderna ger upphov till jämna och realistiska ytor för marknadsdata. Estimeringen av RND-ytan är ett konvext optimeringsproblem men resultatet är känsligt för valet av parametrar. När den lokala volatilitetsytan estimeras är parametervalet mycket enklare men optimeringsproblemet är icke-konvext, även om algoritmen inte verkar fastna i lokala optima. SP-modellerna som används för att fatta optimala beslut på aktiederivatmarknaderna behöver också indata i form av genererade scenarier för de underliggande aktiepriserna eller indexnivåerna. Den tredje artikeln i avhandlingen behandlar estimering och evaluering av existerande modeller för aktiemarknaden. Den tredje artikeln tillhandahåller preliminära resultat som visar att, av de jämförda modellerna, ger en GARCH(1,1)-modell med Poissonhopp en bättre beskrivning av dynamiken för det svenska aktieindexet OMXS30 jämfört med mer komplicerade modeller som innehåller stokastisk volatilitet.

    Delarbeten
    1. Non-parametric estimation of the option implied risk-neutral density surface
    Öppna denna publikation i ny flik eller fönster >>Non-parametric estimation of the option implied risk-neutral density surface
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Accurate pricing of exotic or illiquid derivatives which is consistent with noisy market prices presents a major challenge. The pricing accuracy will crucially depend on using arbitrage free inputs to the pricing engine. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND), while satisfying no-arbitrage constraints. Our developed framework is a generalization of the RNDs implied by existing parametric models such as the Heston model. Thus, the method considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized making it possible to use general purpose optimization algorithms. The approach leads to an optimization model where it is possible to formulate the constraints as linear constraints making the resulting optimization problem convex. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. By perturbing input data with random errors we demonstrate that our method gives better results than the Heston model in terms of yielding stable RNDs.

    Nyckelord
    Risk-neutral density surface, Non-parametric estimation, Optimization, No-arbitrage constraints, Implied volatility surface, Local volatility
    Nationell ämneskategori
    Ekonomi och näringsliv Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-94357 (URN)
    Tillgänglig från: 2013-06-25 Skapad: 2013-06-25 Senast uppdaterad: 2023-12-28Bibliografiskt granskad
    2. Non-parametric estimation of local variance surfaces
    Öppna denna publikation i ny flik eller fönster >>Non-parametric estimation of local variance surfaces
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we develop a general optimization based framework for estimation of the option implied local variance surface. Given a specific level of consistency with observed market prices there exist an infinite number of possible surfaces. Instead of assuming shape constraints for the surface, as in many traditional methods, we seek the solution in the subset of realistic surfaces. We select local volatilities as variables in the optimization problem since it makes it easy to ensure absence of arbitrage, and realistic local volatilities imply realistic risk-neutral density- (RND), implied volatility- and price surfaces. The objective function combines a measure of consistency with market prices, and a weighted integral of the squared second derivatives of local volatility in the strike and the time-to-maturity direction. Derivatives prices in the optimization model are calculated efficiently with a finite difference scheme on a non-uniform grid. The framework has previously been successfully applied to the estimation of RND surfaces. Compared to when modeling the RND, it is for local volatility much easier to choose the parameters in the model. Modeling the RND produces a convex optimization problem which is not the case when modeling local volatility, but empirical tests indicate that the solution does not get stuck in local optima. We show that our method produces local volatility surfaces with very high quality and which are consistent with observed option quotes. Thus, unlike many methods described in the literature, our method does not produce a local volatility surface with irregular shape and many spikes or a non-smooth and multimodal RND for input data with a lot of noise.

    Nyckelord
    Local volatility surface; Non-parametric estimation; Optimization; No-arbitrage conditions
    Nationell ämneskategori
    Ekonomi och näringsliv Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-94358 (URN)
    Tillgänglig från: 2013-06-25 Skapad: 2013-06-25 Senast uppdaterad: 2023-12-28Bibliografiskt granskad
    3. Statistical tests for selected equity market models
    Öppna denna publikation i ny flik eller fönster >>Statistical tests for selected equity market models
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we evaluate which of four candidate equity market models that provide the best fit to observed closing data for the OMXS30 index from 30 September 1986 to 6 May 2013. The candidate models are two GARCH type models and two stochastic volatility models. The stochastic volatility models are estimated with the help of Markov Chain Monte Carlo methods. We provide the full derivations of the posterior distributions for the two stochastic volatility models, which to our knowledge have not been provided in the literature before. With the help of statistical tests we conclude that, out of the four candidate models, a GARCH model which includes jumps in the index level provides the best fit to the observed OMXS30 closing data.

    Nyckelord
    GARCH models, stochastic volatility models, Markov Chain Monte Carlo methods, statistical tests
    Nationell ämneskategori
    Ekonomi och näringsliv Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-94359 (URN)
    Tillgänglig från: 2013-06-25 Skapad: 2013-06-25 Senast uppdaterad: 2013-06-26Bibliografiskt granskad
    Ladda ner fulltext (pdf)
    Risk-Neutral and Physical Estimation of Equity Market Volatility
    Ladda ner (pdf)
    omslag
  • 34.
    Barkhagen, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Statistical tests for selected equity market modelsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we evaluate which of four candidate equity market models that provide the best fit to observed closing data for the OMXS30 index from 30 September 1986 to 6 May 2013. The candidate models are two GARCH type models and two stochastic volatility models. The stochastic volatility models are estimated with the help of Markov Chain Monte Carlo methods. We provide the full derivations of the posterior distributions for the two stochastic volatility models, which to our knowledge have not been provided in the literature before. With the help of statistical tests we conclude that, out of the four candidate models, a GARCH model which includes jumps in the index level provides the best fit to the observed OMXS30 closing data.

  • 35.
    Barkhagen, Mathias
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
    Blomvall, Jörgen
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
    Modeling and evaluation of the option book hedging problem using stochastic programming2016Ingår i: Quantitative finance (Print), ISSN 1469-7688, E-ISSN 1469-7696, Vol. 16, nr 2, s. 259-273Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Hedging of an option book in an incomplete market with transaction costs is an important problem in finance that many banks have to solve on a daily basis. In this paper, we develop a stochastic programming (SP) model for the hedging problem in a realistic setting, where all transactions take place at observed bid and ask prices. The SP model relies on a realistic modeling of the important risk factors for the application, the price of the underlying security and the volatility surface. The volatility surface is unobservable and must be estimated from a cross section of observed option quotes that contain noise and possibly arbitrage. In order to produce arbitrage-free volatility surfaces of high quality as input to the SP model, a novel non-parametric estimation method is used. The dimension of the volatility surface is infinite and in order to be able solve the problem numerically, we use discretization and principal component analysis to reduce the dimensions of the problem. Testing the model out-of-sample for options on the Swedish OMXS30 index, we show that the SP model is able to produce a hedge that has both a lower realized risk and cost compared with dynamic delta and delta-vega hedging strategies.

  • 36.
    Barkhagen, Mathias
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Blomvall, Jörgen
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Non-parametric estimation of local variance surfacesManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we develop a general optimization based framework for estimation of the option implied local variance surface. Given a specific level of consistency with observed market prices there exist an infinite number of possible surfaces. Instead of assuming shape constraints for the surface, as in many traditional methods, we seek the solution in the subset of realistic surfaces. We select local volatilities as variables in the optimization problem since it makes it easy to ensure absence of arbitrage, and realistic local volatilities imply realistic risk-neutral density- (RND), implied volatility- and price surfaces. The objective function combines a measure of consistency with market prices, and a weighted integral of the squared second derivatives of local volatility in the strike and the time-to-maturity direction. Derivatives prices in the optimization model are calculated efficiently with a finite difference scheme on a non-uniform grid. The framework has previously been successfully applied to the estimation of RND surfaces. Compared to when modeling the RND, it is for local volatility much easier to choose the parameters in the model. Modeling the RND produces a convex optimization problem which is not the case when modeling local volatility, but empirical tests indicate that the solution does not get stuck in local optima. We show that our method produces local volatility surfaces with very high quality and which are consistent with observed option quotes. Thus, unlike many methods described in the literature, our method does not produce a local volatility surface with irregular shape and many spikes or a non-smooth and multimodal RND for input data with a lot of noise.

  • 37.
    Barkhagen, Mathias
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Blomvall, Jörgen
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Non-parametric estimation of the option implied risk-neutral density surfaceManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Accurate pricing of exotic or illiquid derivatives which is consistent with noisy market prices presents a major challenge. The pricing accuracy will crucially depend on using arbitrage free inputs to the pricing engine. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND), while satisfying no-arbitrage constraints. Our developed framework is a generalization of the RNDs implied by existing parametric models such as the Heston model. Thus, the method considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized making it possible to use general purpose optimization algorithms. The approach leads to an optimization model where it is possible to formulate the constraints as linear constraints making the resulting optimization problem convex. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. By perturbing input data with random errors we demonstrate that our method gives better results than the Heston model in terms of yielding stable RNDs.

  • 38.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    A Central Limit Theorem for punctuated equilibrium2020Ingår i: Stochastic Models, ISSN 1532-6349, E-ISSN 1532-4214, Vol. 36, nr 3, s. 473-517Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated-the phenotype can jump. Such a jump could especially occur at speciation, i.e., dramatic change occurs that drives the species apart. Here we derive a Central Limit Theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to normality to hold, the variability in the occurrence of change has to disappear with time.

    Ladda ner fulltext (pdf)
    fulltext
  • 39.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Exact and approximate limit behaviour of the Yule trees cophenetic index2018Ingår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 303, s. 26-45Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a sub-martingale that converges almost surely and in L-2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction-type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution. We propose heuristic methods of simulating from these distributions and it may be observed that these algorithms result in reasonable tails. Therefore, we propose a way based on the quantiles of the derived distributions for hypothesis testing, whether an observed phylogenetic tree is consistent with the pure-birth process. Simulating a sample by the proposed heuristics is rapid, while exact simulation (simulating the tree and then calculating the index) is a time-consuming procedure. We conduct a power study to investigate how well the cophenetic indices detect deviations from the Yule tree and apply the methodology to empirical phylogenies.

    Ladda ner fulltext (pdf)
    fulltext
  • 40.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model2020Ingår i: Applicationes Mathematicae, ISSN 1233-7234, E-ISSN 1730-6280, Vol. 6, s. 29-44Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper builds on T. Martínez-Coronado, A. Mir, F. Rosselló and G. Valiente’s 2018 work, introducing a new balance index for trees. We show that this balance index, in the case of Aldous’s $(\beta \ge 0)$-model, converges weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.

  • 41.
    Bartoszek, Krzysztof
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Phylogenetic effective sample size2016Ingår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, s. 371-386Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper I address the question—how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

  • 42.
    Bartoszek, Krzysztof
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Quantifying the effects of anagenetic and cladogenetic evolution2014Ingår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 254, s. 42-57Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.

  • 43.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Revisiting the Nowosiółka skull with RMaCzek2023Ingår i: Mathematica Applicanda, ISSN 1730-2668, Vol. 50, nr 2, s. 255-266Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    One of the first fully quantitative distance matrix visualization methods was proposed by Jan Czekanowski at the beginning of the previous century. Recently, a software package, RMaCzek, was made available that allows for producing such diagrams in R. Here we reanalyze the original data that Czekanowski used for introducing his method, and in the accompanying code show how the user can specify their own custom distance functions in the package.

  • 44.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Simulating an infinite mean waiting time2019Ingår i: Mathematica Applicanda, ISSN 1730-2668, Vol. 47, nr 1, s. 93-102Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.

    Ladda ner fulltext (pdf)
    Simulating an infinite mean waiting time
  • 45.
    Bartoszek, Krzysztof
    Gdansk University of Technology, Poland.
    The Bootstrap and Other Methods of Testing Phylogenetic Trees2007Ingår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2007, s. 103-108Konferensbidrag (Refereegranskat)
    Abstract [en]

    The final step of a phylogenetic analysis is the test of the generated tree. This is not a easy task for which there is an obvious methodology because we do not know the full probabilistic model of evolution. A number of methods have been proposed but there is a wide debate concerning the interpretations of the results they produce.

  • 46.
    Bartoszek, Krzysztof
    Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Göteborg Sweden.
    The Laplace Motion in Phylogenetic Comparative Methods2012Ingår i: Proceedings of the 18th National Conference on Applications of Mathematics in Biology and Medicine, 2012, s. 25-30Konferensbidrag (Refereegranskat)
    Abstract [en]

    The majority of current phylogenetic comparative methods assume that the stochastic evolutionaryprocess is homogeneous over the phylogeny or offer relaxations of this in rather limited and usually parameter expensive ways. Here we make a preliminary investigation, bymeans of a numerical experiment, whether the Laplace motion process can offer an alternative approach.

  • 47.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Trait evolution with jumps: illusionary normality2017Ingår i: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine, 2017, s. 23-28Konferensbidrag (Refereegranskat)
    Abstract [en]

    Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous.This is despite biological intuition that evolution is rather punctuated thangradual. On the other hand, there has been a number of recent proposals of evolutionarymodels with jump components. However, as we are only beginning to understandthe behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptoticsof branching  OU processes with jumps is an even greater unknown. In thiswork we build up on a previous study concerning OU with jumps evolution on a pure birth tree.We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process.We furthermore, also use this work to illustrate the simulation and graphic generation possibilitiesof the mvSLOUCH package.

  • 48.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Bartoszek, Wojciech
    Gdansk University of Technology, Poland.
    On the Time Behaviour of Okazaki Fragments2006Ingår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, nr 2, s. 500-509Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

  • 49.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Domsta, Joachim
    State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.
    Pulka, Malgorzata
    Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.
    Weak Stability of Centred Quadratic Stochastic Operators2019Ingår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, nr 4, s. 1813-1830Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offsprings trait is equal to an additively perturbed arithmetic mean of the parents traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.

    Ladda ner fulltext (pdf)
    Weak Stability of Centred Quadratic Stochastic Operators
  • 50.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Erhardsson, Torkel
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    NORMAL APPROXIMATION FOR MIXTURES OF NORMAL DISTRIBUTIONS AND THE EVOLUTION OF PHENOTYPIC TRAITS2021Ingår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 53, nr 1, s. 162-188Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Explicit bounds are given for the Kolmogorov andWasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some sigma-algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the sigma-algebra. The proof is based on Steins method. As an application, we consider the Yule-Ornstein-Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

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