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  • 1.
    Ahlinder, Jon
    et al.
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Nordgaard, Anders
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. 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 attacks2015Inngår i: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 29, nr 5, s. 267-276Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 2.
    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 (Annet vitenskapelig)
    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.

  • 3.
    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 (Annet vitenskapelig)
    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.

  • 4.
    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-normality2013Inngår i: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, nr 1, s. 81-99Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 5.
    Aitken, Colin
    et al.
    School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom.
    Nordgaard, Anders
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Swedish Police Auhtority, National Forensic Centre (NFC).
    Taroni, Franco
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    Biedermann, Alex
    School of Criminal Justice, Université de Lausanne, Lausanne, Switzerland.
    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. 122:272018Inngår i: Frontiers in Genetics, ISSN 1664-8021, E-ISSN 1664-8021, Vol. 9, artikkel-id 224Artikkel i tidsskrift (Fagfellevurdert)
  • 6.
    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 insulinpump2010Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    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.

  • 7.
    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?2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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.

  • 8.
    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 Projects2016Inngår i: Journal of Nursing Care Quality, ISSN 1057-3631, E-ISSN 1550-5065, Vol. 31, nr 1, s. E1-E8Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 9.
    Andersson Naesseth, Christian
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Nowcasting using Microblog Data2012Independent thesis Basic level (degree of Bachelor), 10,5 poäng / 16 hpOppgave
    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.

  • 10.
    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 Carlo2019Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 67, nr 16, s. 4177-4188Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 11.
    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 Carlo2014Inngår i: 2014 IEEE Information Theory Workshop, 2014, s. 431-435Konferansepaper (Fagfellevurdert)
    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.

  • 12.
    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 Methods2015Inngår 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. 1292-1301Konferansepaper (Fagfellevurdert)
    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.

  • 13.
    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 Models2014Inngår i: Advances in Neural Information Processing Systems, 2014, s. 1862-1870Konferansepaper (Fagfellevurdert)
    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.

  • 14.
    Andersson, Niklas
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Hansson, Josef
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Metodik för detektering av vägåtgärder via tillståndsdata2010Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    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.

  • 15.
    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 Laboratory2014Konferansepaper (Annet vitenskapelig)
    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.

  • 16.
    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 flygtrafiksmodeller2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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 .

  • 17.
    Barakat, Arian
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    What makes an (audio)book popular?2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

  • 18.
    Barkhagen, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Risk-Neutral and Physical Estimation of Equity Market Volatility2013Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The overall purpose of the PhD project is to develop a framework for making optimal decisions on the equity derivatives markets. Making optimal decisions refers e.g. to how to optimally hedge an options portfolio or how to make optimal investments on the equity derivatives markets. The framework for making optimal decisions will be based on stochastic programming (SP) models, which means that it is necessary to generate high-quality scenarios of market prices at some future date as input to the models. This leads to a situation where the traditional methods, described in the literature, for modeling market prices do not provide scenarios of sufficiently high quality as input to the SP model. Thus, the main focus of this thesis is to develop methods that improve the estimation of option implied surfaces from a cross-section of observed option prices compared to the traditional methods described in the literature. The estimation is complicated by the fact that observed option prices contain a lot of noise and possibly also arbitrage. This means that in order to be able to estimate option implied surfaces which are free of arbitrage and of high quality, the noise in the input data has to be adequately handled by the estimation method.

    The first two papers of this thesis develop a non-parametric optimization based framework for the estimation of high-quality arbitrage-free option implied surfaces. The first paper covers the estimation of the risk-neutral density (RND) surface and the second paper the local volatility surface. Both methods provide smooth and realistic surfaces for market data. Estimation of the RND is a convex optimization problem, but the result is sensitive to the parameter choice. When the local volatility is estimated the parameter choice is much easier but the optimization problem is non-convex, even though the algorithm does not seem to get stuck in local optima. The SP models used to make optimal decisions on the equity derivatives markets also need generated scenarios for the underlying stock prices or index levels as input. The third paper of this thesis deals with the estimation and evaluation of existing equity market models. The third paper gives preliminary results which show that, out of the compared models, a GARCH(1,1) model with Poisson jumps provides a better fit compared to more complex models with stochastic volatility for the Swedish OMXS30 index.

    Delarbeid
    1. Non-parametric estimation of the option implied risk-neutral density surface
    Åpne denne publikasjonen i ny fane eller vindu >>Non-parametric estimation of the option implied risk-neutral density surface
    (engelsk)Manuskript (preprint) (Annet vitenskapelig)
    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.

    Emneord
    Risk-neutral density surface, Non-parametric estimation, Optimization, No-arbitrage constraints, Implied volatility surface, Local volatility
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-94357 (URN)
    Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
    2. Non-parametric estimation of local variance surfaces
    Åpne denne publikasjonen i ny fane eller vindu >>Non-parametric estimation of local variance surfaces
    (engelsk)Manuskript (preprint) (Annet vitenskapelig)
    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.

    Emneord
    Local volatility surface; Non-parametric estimation; Optimization; No-arbitrage conditions
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-94358 (URN)
    Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
    3. Statistical tests for selected equity market models
    Åpne denne publikasjonen i ny fane eller vindu >>Statistical tests for selected equity market models
    (engelsk)Manuskript (preprint) (Annet vitenskapelig)
    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.

    Emneord
    GARCH models, stochastic volatility models, Markov Chain Monte Carlo methods, statistical tests
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-94359 (URN)
    Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
  • 19.
    Barkhagen, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Statistical tests for selected equity market modelsManuskript (preprint) (Annet vitenskapelig)
    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.

  • 20.
    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 programming2016Inngår i: Quantitative finance (Print), ISSN 1469-7688, E-ISSN 1469-7696, Vol. 16, nr 2, s. 259-273Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 21.
    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) (Annet vitenskapelig)
    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.

  • 22.
    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) (Annet vitenskapelig)
    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.

  • 23.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Exact and approximate limit behaviour of the Yule trees cophenetic index2018Inngår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 303, s. 26-45Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 24.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model2019Inngår i: Applicationes Mathematicae, ISSN 1233-7234, E-ISSN 1730-6280Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 25.
    Bartoszek, Krzysztof
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Phylogenetic effective sample size2016Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, s. 371-386Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 26.
    Bartoszek, Krzysztof
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Quantifying the effects of anagenetic and cladogenetic evolution2014Inngår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 254, s. 42-57Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 27.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Simulating an infinite mean waiting time2019Inngår i: Mathematica Applicanda, ISSN 1730-2668, Vol. 47, nr 1, s. 93-102Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 28.
    Bartoszek, Krzysztof
    Gdansk University of Technology, Poland.
    The Bootstrap and Other Methods of Testing Phylogenetic Trees2007Inngår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2007, s. 103-108Konferansepaper (Fagfellevurdert)
    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.

  • 29.
    Bartoszek, Krzysztof
    Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Göteborg Sweden.
    The Laplace Motion in Phylogenetic Comparative Methods2012Inngår i: Proceedings of the 18th National Conference on Applications of Mathematics in Biology and Medicine, 2012, s. 25-30Konferansepaper (Fagfellevurdert)
    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.

  • 30.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Trait evolution with jumps: illusionary normality2017Inngår i: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine, 2017, s. 23-28Konferansepaper (Fagfellevurdert)
    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.

  • 31.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Bartoszek, Wojciech
    Gdansk University of Technology, Poland.
    On the Time Behaviour of Okazaki Fragments2006Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, nr 2, s. 500-509Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 32.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Uppsala Univ, Sweden.
    Domsta, Joachim
    State Univ Appl Sci Elblag, Poland.
    Pulka, Malgorzata
    Gdansk Univ Technol, Poland.
    Weak Stability of Centred Quadratic Stochastic Operators2019Inngår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, nr 4, s. 1813-1830Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 33.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology.
    Izydorek, Bartosz
    Gdansk University of Technology.
    Ratajczak, Tadeusz
    Gdansk University of Technology, Poland.
    Skokowski, Jaroslaw
    Medical University of Gdansk, Poland.
    Szwaracki, Karol
    Gdansk University of Technology, Poland.
    Tomczak, Wiktor
    Gdansk University of Technology, Poland.
    Neural Network Breast Cancer Relapse Time Prognosis2006Inngår i: ASO Summer School 2006 abstract book Ostrzyce 30.06-2.07. 2006 / [ed] J. Skokowski and K. Drucis, 2006, s. 8-10Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    This paper is a result of a project at the Faculty of Electronics, Telecommunication and Computer Science (Technical University of Gdansk). The aim of the project was to create a neural network to predict the relapsetime of breast cancer. The neural network was to be trained on data collected over the past 20 years by dr. Jarosław Skokowski. The data includes 439 patient records described by about 40 parameters. For our neuralnetwork we only considered 6 medically most significant parameters the number of nodes showing evidence of cancer, size of tumour (in mm.), age, bloom score, estrogen receptors and proestrogen receptors and the relapsetime as the outcome. Our neural network was created in the MATLAB environment.

  • 34.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Jones, Graham
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden / Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Oxelman, Bengt
    Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Sagitov, Serik
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Time to a single hybridization event in a group of species with unknown ancestral history2013Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 322, s. 1-6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments, and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.

  • 35.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Krzeminski, Michal
    Gdansk University of Technology.
    Critical case stochastic phylogenetic tree model via the Laplace transform2014Inngår i: Demonstratio Matematicae, ISSN 0420-1213, Vol. 47, nr 2, s. 474-481Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both in uenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this we correct the proof of Liggett and Schinazi (2009) in the critical case.

  • 36.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Krzeminski, Michal
    Gdansk University of Technology.
    Skokowski, Jaroslaw
    Medical University of Gdansk.
    Survival time prognosis under a Markov model of cancer development2010Inngår i: Proceedings of the XVI National Conference Applications of Mathematics to Biology and Medicine, Krynica, Poland, September 14–18, 2010 / [ed] M. Ziółko, M. Bodnar and E. Kutafina, 2010, s. 6-11Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this study we look at a breast cancer data set of women from the Pomerania region collected in the year 1987- 1992 in the Medical University of Gdansk.We analyze the clinical risk factors in conjunction with a Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction (which was done on this data set in a previous study) via a simulation study.

  • 37.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Lio, Pietro
    Univ Cambridge, England.
    MODELLING TRAIT-DEPENDENT SPECIATION WITH APPROXIMATE BAYESIAN COMPUTATION2019Inngår i: ACTA PHYSICA POLONICA B PROCEEDINGS SUPPLEMENT, JAGIELLONIAN UNIV , 2019, Vol. 12, nr 1, s. 25-47Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The fields progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work, we present an R package, pcmabc, publicly available on CRAN, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

  • 38.
    Bartoszek, Krzysztof
    et al.
    Mathematical Statistics, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
    Liò, Pietro
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Sorathiya, Anil
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Influenza differentiation and evolution2010Inngår i: Acta Physica Polonica B Proceedings Supplement, 2010, Vol. 3, s. 417-452, artikkel-id 2Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The aim of the study is to do a very wide analysis of HA, NA and M influenza gene segments to find short nucleotide regions,which differentiate between strains (i.e. H1, H2, ... e.t.c.), hosts, geographic regions, time when sequence was found and combination of time and region using a simple methodology. Finding regions  differentiating between strains has as its goal the construction of a Luminex microarray which will allow quick and efficient strain recognition. Discovery for the other splitting factors could shed lighton structures significant for host specificity and on the history of influenza evolution. A large number of places in the HA, NA and M gene segments were found that can differentiate between hosts, regions, time and combination of time and region. Also very good differentiation between different Hx strains can be seen.We link one of our findings to a proposed stochastic model of creation of viral phylogenetic trees.

  • 39.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Pienaar, Jason
    Department of Genetics, University of Pretoria, Pretoria 0002, South Africa.
    Mostad, Petter
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Andersson, Staffan
    Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden.
    Hansen, Thomas F.
    CEES, Department of Biology, University of Oslo, Oslo, Norway.
    A phylogenetic comparative method for studying multivariate adaptation2012Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 314, s. 204-215Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Phylogenetic comparative methods have been limited in the way they model adaptation. Although some progress has been made, there are still no methods that can fully account for coadaptationbetween traits. Based on Ornstein-Uhlenbeck (OU) models of adaptive evolution, we present a method,with R implementation, in which multiple traits evolve both in response to each other and, as inprevious OU models, to fixed or randomly evolving predictor variables. We present the interpretation ofthe model parameters in terms of evolutionary and optimal regressions enabling the study of allometric and adaptive relationships between traits. To illustrate the method we reanalyze a data set of antlerand body-size evolution in deer (Cervidae).

  • 40.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pietro, Lio'
    Computer Laboratory , University of Cambridge, Cambridge, Un ited Kingdom.
    A novel algorithm to reconstruct phylogenies using gene sequences and expression data2014Inngår i: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III, 2014, Vol. 70, s. 8-12Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Phylogenies based on single loci should be viewed with caution and the best approach for obtaining robust trees is to examine numerous loci across the genome. It often happens that for the same set of species trees derived from different genes are in conflict between each other. There are several methods that combine information from different genes in order to infer the species tree. One novel approach is to use informationfrom different -omics. Here we describe a phylogenetic method based on an Ornstein–Uhlenbeck process that combines sequence and gene expression data. We test our method on genes belonging to the histidine biosynthetic operon. We found that the method provides interesting insights into selection pressures and adaptive hypotheses concerning gene expression levels.

  • 41.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Pulka, Malgorzata
    Department of Probability and Biomathematics, Gdánsk University of Technology, Gdánsk, Poland.
    Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait2013Inngår i: Proceedings of the 19th National Conference on Applications of Mathematics in Biology and Medicine / [ed] Katarzyna D. Lewandowska and Piotr Bogús, 2013, s. 19-24Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introducedand studied recently. In the present work we discuss biological interpretations that can be attributedto them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.

  • 42.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pulka, Malgorzta
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, s. 26-39Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 43.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pułka, Małgorzata
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Prevalence Problem in the Set of Quadratic StochasticOperators Acting on L12018Inngår i: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, nr 1, s. 159-173Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.

  • 44.
    Bartoszek, Krzysztof
    et al.
    Uppsala universitet, Tillämpad matematik och statistik.
    Sagitov, Serik
    A consistent estimator of the evolutionary rate2015Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, s. 69-78Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance sigma(2). In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.

  • 45.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Sagitov, Serik
    Chalmers University of Technology and the Unversity of Gothenburg, Sweden.
    Phylogenetic confidence intervals for the optimal trait value2015Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, nr 4, s. 1115-1132Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein–Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

  • 46.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Signerska, Justyna
    Gdansk University of Technology, Poland.
    Moments of the Distribution of Okazaki Fragments2006Inngår i: Rose–Hulman Undergraduate Mathematics Journal, Vol. 7, nr 2, s. 1-5Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper is a continuation of Bartoszek & Bartoszek (2006) who provide formulae for the probability distributions of the number of Okazaki fragments at time t during the process of DNA replication. Given the expressions for the moments of the probability distribution of the number of Okazaki fragments at time t in the recursive form, we evaluated formulae for the third and fourth moments, using Mathematica, and obtained results in explicit form. Having done this, we calculated the distribution’s skewness and kurtosis.

  • 47.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Stokowska, Anna
    University of Gothenburg.
    Performance of pseudo-likelihood estimator in modelling cells' proliferation with noisy measurements2010Inngår i: Conference proceedings from the 12th International Workshop for Young Mathematicians "Probability and Statistics", Krakow, Poland, 20th till 26th September 2009, 2010, s. 21-42Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Branching processes are widely used to describe cell development and proliferation. Currently parameter estimation is studied in mathematical models describing the dynamics of cell cultures where we can get very accurate measurements of cell counts. In vivo samples we will not have this accuracy, here the noise levels can be very significant. We will study a newly proposed pseudo-likelihood estimator of a multitype Bellman-Harris process modelling cell development and see how it performs under noisy measurements of cell counts.

  • 48.
    Bendtsen, Marcus
    Linköpings universitet, Institutionen för datavetenskap, Databas och informationsteknik. Linköpings universitet, Tekniska fakulteten.
    Gated Bayesian Networks2017Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    Bayesian networks have grown to become a dominant type of model within the domain of probabilistic graphical models. Not only do they empower users with a graphical means for describing the relationships among random variables, but they also allow for (potentially) fewer parameters to estimate, and enable more efficient inference. The random variables and the relationships among them decide the structure of the directed acyclic graph that represents the Bayesian network. It is the stasis over time of these two components that we question in this thesis.

    By introducing a new type of probabilistic graphical model, which we call gated Bayesian networks, we allow for the variables that we include in our model, and the relationships among them, to change overtime. We introduce algorithms that can learn gated Bayesian networks that use different variables at different times, required due to the process which we are modelling going through distinct phases. We evaluate the efficacy of these algorithms within the domain of algorithmic trading, showing how the learnt gated Bayesian networks can improve upon a passive approach to trading. We also introduce algorithms that detect changes in the relationships among the random variables, allowing us to create a model that consists of several Bayesian networks, thereby revealing changes and the structure by which these changes occur. The resulting models can be used to detect the currently most appropriate Bayesian network, and we show their use in real-world examples from both the domain of sports analytics and finance.

  • 49.
    Berberovic, Adnan
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi.
    Eriksson, Alexander
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi.
    A Multi-Factor Stock Market Model with Regime-Switches, Student's T Margins, and Copula Dependencies2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes.

  • 50.
    Berglund, Frida
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Oskarsson, Mayumi Setsu
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Modellering av spårvidd över bandel 119 inom Stambanan genom Övre Norrland: Kandidatuppsats i Statistik och dataanalys2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Trafikverket har varit de som ansvarar för underhållet på den svenska järnvägen sedan 2010. För att järnvägen ska vara säker för passagerare och övriga transporter behöver den hållas i gott skick genom regelbundet underhåll. Därför är det viktigt att kontrollera spårgeometriers kvalitet. Spårvidden är en utav de viktigaste mått som varken får vara för bred eller för smal.

    Syftet med denna rapport är att bygga en modell som kan användas för att simulera avvikelsen på normal spårvidd med avseende på spårgeometrier samt spårens egenskaper.

    Avikkelsen från normal spårvidd är en slumpvariabel som vi modellerat med en generaliserad linjär modell och en generaliserad additiv modell. De kan sedan användas för att simulera avvikelsen på normal spårvidd. I studien visas att GAM lyckas förklara en stor del av variationen i avvikelse på normal spårvidd med hjälp av information från spårgeometrier samt spårens egenskaper.

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