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  • 1.
    Ahmad, M. Rauf
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A two-sample test statistic for high-dimensional multivariate data under non-normality2011Report (Other academic)
    Abstract [en]

    Ahmad, Ohlson, and von Rosen (2011a) present asymptotic distribution of a one-sample test statistic under non-normality, when the data are high dimensional, i.e., when the dimension of the vector, p, may exceed the sample size, n. This paper extends the case to a two-sample statistic to test the difference of mean vectors of two independent multivariate distributions, again under high-dimensional set up. Using the asymptotic theory of U-statistics, and under mild assumptions on the traces of the unknown covariance matrices, the statistic is shown to follow an approximate normal distribution when n and p are large. However, no relationship between n and p is assumed. An extension to the paired case is given, which, being essentially a one-sample statistic, supplements the asymptotic results obtained in Ahmad, Ohlson, and von Rosen (2011a).

  • 2.
    Ahmad, M. Rauf
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality2011Report (Other academic)
    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.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    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 Data2011Report (Other academic)
    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.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden; University of Munich, Germany.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
    Tests for high-dimensional covariance matrices using the theory of U-statistics2015In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, no 13, p. 2619-2631Article in journal (Refereed)
    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. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p and#8811;n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

  • 5.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. Swedish University of Agriculture Science, Sweden.
    Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 7, p. 1387-1398Article in journal (Refereed)
    Abstract [en]

    Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp greater thangreater than n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.

  • 6.
    Ahmad, M. Rauf
    et al.
    Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A note on mean testing for high dimensional multivariate data under non-normality2013In: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, no 1, p. 81-99Article in journal (Refereed)
    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.

  • 7.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    A conditional perspective of weighted variance estimation of regression estimator2003Report (Other academic)
  • 8.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    A conditional perspective of weighted variance estimation of the optimal regression estimator2006In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 136, no 1, p. 221-234Article in journal (Refereed)
    Abstract [en]

    The estimation of the variance for the GREG (general regression) estimator by weighted residuals is widely accepted as a method which yields estimators with good conditional properties. Since the optimal (regression) estimator shares the properties of GREG estimators which are used in the construction of weighted variance estimators, we introduce the weighting procedure also for estimating the variance of the optimal estimator. This method of variance estimation was originally presented in a seemingly ad hoc manner, and we shall discuss it from a conditional point of view and also look at an alternative way of utilizing the weights. Examples that stress conditional behaviour of estimators are then given for elementary sampling designs such as simple random sampling, stratified simple random sampling and Poisson sampling, where for the latter design we have conducted a small simulation study. © 2004 Elsevier B.V. All rights reserved.

  • 9.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Alternative confidence intervals for the total of a skewed biological population2003Report (Other academic)
  • 10.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Alternative confidence intervals for the total of a skewed biological population2004In: Ecology, ISSN 0012-9658, E-ISSN 1939-9170, Vol. 85, no 11, p. 3166-3171Article in journal (Refereed)
    Abstract [en]

    In a 1999 Ecology article, T. G. Gregoire and O. Schabenberger addressed the problem of obtaining truly symmetric confidence intervals for the total of a positively skewed biological population under simple random sampling. Their simulation study revealed that the skewness induced a substantial positive correlation between the estimator of the total and the estimator of its variance. This caused the standard nominally symmetric t-based intervals, based on approximate normality of the estimator of the total, to be highly unbalanced, i.e., intervals much more often missed from below than from above. To better cope with this situation I suggest an alternative confidence interval procedure that takes into account and adjusts for the induced correlation. A simulation study based on one of the populations used by Gregoire and Schabenberger shows that the resulting adjusted intervals have more balanced noncoverage probabilities and often higher coverage probability than the standard intervals in cases of substantial correlation. I also provide an example of an unequal probability design using auxiliary information, where there is much less need for an adjustment.

  • 11.
    Andersson, Per Gösta
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Thorburn, Daniel
    An optimal calibration distance leading to optimal regression estimator2003Report (Other academic)
  • 12.
    Andersson, Per Gösta
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Thorburn, Daniel
    Department of Statistics Stockholm universitet.
    An Optimal Calibration Distance Leading to the Optimal Regresion Estimator2005In: Survey methodology, ISSN 0714-0045, Vol. 31, no 1, p. 95-99Article in journal (Refereed)
    Abstract [en]

    When there is auxiliary information in survey sampling, the design based optimal regression estimator of a finite population mean is known to be at least asymptocially more effective than the corresponding GREG estimator . We show that the optimal estimator can be seen as a calibration estimator.

  • 13.
    Andrushchenko, Zhanna
    et al.
    Department of Biometry and Engineering SLU.
    Ohlson, Martin
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    von Rosen, Dietrich
    Department of Biometry and Engineering SLU.
    Estimation of banded covariance matrices in a multivariate normal distribution2008Report (Other academic)
  • 14.
    Andrushchenko, Zhanna
    et al.
    Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Asymptotic distribution of the estimators of a harmonic component in a multivariate time series under m-dependence2011Report (Other academic)
    Abstract [en]

    Multivariate time series with definite harmonic structure is considered, in the special case when the marginal univariate time series are independent and asymptotically stationary to second order. The asymptotic distribution of the estimators of a harmonic component under $m$-dependence is found

  • 15.
    Aurzada, Frank
    et al.
    Technical University of Darmstadt, Germany .
    Dereich, Steffen
    University of Münster, Germany .
    Lifshits, Mikhail
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. St. Petersburg State University, Russia.
    Persistence probabilities for a Bridge of an integrated simple random walk2014In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 34, no 1, p. 1-22Article in journal (Refereed)
    Abstract [en]

    We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability n(-1/2) to stay positive. This question is motivated by random polymer models and proves a conjecture by Caravenna and Deuschel.

  • 16.
    Austin, Brian
    et al.
    Deparrment of Biological Sciences Heriot-Watt University.
    Dawyndt, Peter
    Lab. of Microbiology University of Ghent.
    Gyllenberg, Mats
    Dept. of mathematics University of Turku.
    Lund, Tatu
    Nokia Mobile Phones.
    Swings, Jean
    Lab. of microbiology Univesrity of Ghent.
    Thompson, Fabiano
    Lab. of microbiology University of Ghent.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Sliding window discretization: A new method for multiple band matching of bacterial genotyping fingerprints2004In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 66, no 6, p. 1575-1596Article in journal (Refereed)
    Abstract [en]

    Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods - such as the minimization of stochastic complexity - for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.

  • 17.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    More on Estimation of Banded and Banded Toeplitz Covariance Matrices2017Report (Other academic)
    Abstract [en]

    In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms.

    One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable method. We propose some new methods which preserves the positive definiteness and still give the correct structure.

    More specific we consider the problem of estimating parameters of a multivariate normal p–dimensional random vector for (i) a banded covariance structure reflecting m–dependence, and (ii) a banded Toeplitz covariance structure.

  • 18.
    Böörs, Mikael
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Wängberg, Tobias
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Classification by Decomposition: A Partitioning of the Space of 2X2 Symmetric Games2017Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    Game theory is the study of strategic interaction between rational agents. The need for understanding interaction arises in many different fields, such as: economics, psychology, philosophy, computer science and biology. The purpose of game theory is to analyse the outcomes and strategies of these interactions, in mathematical models called games. Some of these games have stood out from the rest, e.g. Prisoner's Dilemma, Chicken and Stag Hunt. These games, commonly referred to as the standard games, have attracted interest from many fields of research. In order to understand why these games are interesting and how they differ from each other and other games, many have attempted to sort games into interestingly different classes. In this thesis some already existing classifications are reviewed based on their mathematical structure and how well justified they are. Emphasis is put on mathematical simplicity because it makes the classification more generalisable to larger game spaces. From this review we conclude that none of the classifications captures both of these aspects. We therefore propose a classification of symmetric 2x2 games based on decomposition. We show that our proposed method captures everything that the previous classifications caputure. Our method arguably explains the interesting differences between the games, and we justify this claim by computer experiments. Moreover it has a simple mathematical structure. We also provide some results concerning the size of different game spaces.

  • 19.
    Corander, Jukka
    et al.
    Department of Mathematics, Åbo Akademi University, Åbo, Finland.
    Ekdahl, Magnus
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Koski, Timo
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A bayesian random fragment insertion model for de novo detection of DNA regulatory binding regions2007Manuscript (preprint) (Other academic)
    Abstract [en]

    Identification of regulatory binding motifs within DNA sequences is a commonly occurring problem in computationnl bioinformatics. A wide variety of statistical approaches have been proposed in the literature to either scan for previously known motif types or to attempt de novo identification of a fixed number (typically one) of putative motifs. Most approaches assume the existence of reliable biodatabasc information to build probabilistic a priori description of the motif classes. No method has been previously proposed for finding the number of putative de novo motif types and their positions within a set of DNA sequences. As the number of sequenced genomes from a wide variety of organisms is constantly increasing, there is a clear need for such methods. Here we introduce a Bayesian unsupervised approach for this purpose by using recent advances in the theory of predictive classification and Markov chain Monte Carlo computation. Our modelling framework enables formal statistical inference in a large-scale sequence screening and we illustrate it by a set of examples.

  • 20.
    Corander, Jukka
    et al.
    Department of Mathematics, Åbo Akademi University, Åbo, Finland.
    Ekdahl, Magnus
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Koski, Timo
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Parallell interacting MCMC for learning of topologies of graphical models2008In: Data mining and knowledge discovery, ISSN 1384-5810, E-ISSN 1573-756X, Vol. 17, no 3, p. 431-456Article in journal (Refereed)
    Abstract [en]

    Automated statistical learning of graphical models from data has attained a considerable degree of interest in the machine learning and related literature. Many authors have discussed and/or demonstrated the need for consistent stochastic search methods that would not be as prone to yield locally optimal model structures as simple greedy methods. However, at the same time most of the stochastic search methods are based on a standard Metropolis–Hastings theory that necessitates the use of relatively simple random proposals and prevents the utilization of intelligent and efficient search operators. Here we derive an algorithm for learning topologies of graphical models from samples of a finite set of discrete variables by utilizing and further enhancing a recently introduced theory for non-reversible parallel interacting Markov chain Monte Carlo-style computation. In particular, we illustrate how the non-reversible approach allows for novel type of creativity in the design of search operators. Also, the parallel aspect of our method illustrates well the advantages of the adaptive nature of search operators to avoid trapping states in the vicinity of locally optimal network topologies.

  • 21.
    Dawyndt, Peter
    et al.
    Laboratorium voor Microbiologie University of Gent.
    Swings, Jean
    Laboratorium voor microbiologie University of Gent.
    Austin, Brian
    School of Biological Sciences Heriot-Watt University.
    Thompson, Fabiano
    laboratorium voor microbiologie University of Gent.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Gyllenberg, Mats
    Department of mathematics and statistics University of Helsinki.
    A complementary approach to systematics2005In: Microbiology Today, ISSN 1464-0570, no February, p. 38-38Article in journal (Other academic)
  • 22.
    Dawyndt, Peter
    et al.
    Laboratorium voor Microbiologie University of Gent.
    Thompson, Fabiano
    Laboratorium voor Microbiologie University of Gent.
    Austin, Brian
    School of Life Sciences Heriot-Watt University.
    Swings, Jean
    laboratorium voor Microbiologie University of Gent.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Gyllenberg, Mats
    Department of Mathematics University of Turku.
    Application of sliding-window discretization and minimization of stochastic complexity for the analysis of fAFLP genotyping fingerprint patterns of Vibrionaceae2005In: International Journal of Systematic and Evolutionary Microbiology, ISSN 1466-5026, E-ISSN 1466-5034, Vol. 55, no 1, p. 57-66Article in journal (Refereed)
    Abstract [en]

    Minimization of stochastic complexity (SC) was used as a method for classification of genotypic fingerprints. The method was applied to fluorescent amplified fragment length polymorphism (fAFLP) fingerprint patterns of 507 Vibrionaceae representatives. As the current BinClass implementation of the optimization algorithm for classification only works on binary vectors, the original fingerprints were discretized in a preliminary step using the sliding-window band-matching method, in order to maximally preserve the information content of the original band patterns. The novel classification generated using the BinClass software package was subjected to an in-depth comparison with a hierarchical classification of the same dataset, in order to acknowledge the applicability of the new classification method as a more objective algorithm for the classification of genotyping fingerprint patterns. Recent DNA-DNA hybridization and 16S rRNA gene sequence experiments proved that the classification based on SC-minimization forms separate clusters that contain the fAFLP patterns for all representatives of the species Enterovibrio norvegicus, Vibrio fortis, Vibrio diazotrophicus or Vibrio campbellii, while previous hierarchical cluster analysis had suggested more heterogeneity within the fAFLP patterns by splitting the representatives of the above-mentioned species into multiple distant clusters. As a result, the new classification methodology has highlighted some previously unseen relationships within the biodiversity of the family Vibrionaceae.

  • 23.
    Ejaz Ahmed, S.
    et al.
    Brock University, Canada.
    Fallahpour, Saber
    University of Windsor, Canada.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
    von Rosen, Tatjana
    Stockholm University, Sweden.
    Estimation of Several Intraclass Correlation Coefficients2015In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 44, no 9, p. 2315-2328Article in journal (Refereed)
    Abstract [en]

    An intraclass correlation coefficient observed in several populations is estimated. The basis is a variance-stabilizing transformation. It is shown that the intraclass correlation coefficient from any elliptical distribution should be transformed in the same way. Four estimators are compared. An estimator where the components in a vector consisting of the transformed intraclass correlation coefficients are estimated separately, an estimator based on a weighted average of these components, a pretest estimator where the equality of the components is tested and then the outcome of the test is used in the estimation procedure, and a James-Stein estimator which shrinks toward the mean.

  • 24.
    Ekdahl, Magnus
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Approximations of Bayes Classifiers for Statistical Learning of Clusters2006Licentiate thesis, monograph (Other academic)
    Abstract [en]

    It is rarely possible to use an optimal classifier. Often the classifier used for a specific problem is an approximation of the optimal classifier. Methods are presented for evaluating the performance of an approximation in the model class of Bayesian Networks. Specifically for the approximation of class conditional independence a bound for the performance is sharpened.

    The class conditional independence approximation is connected to the minimum description length principle (MDL), which is connected to Jeffreys’ prior through commonly used assumptions. One algorithm for unsupervised classification is presented and compared against other unsupervised classifiers on three data sets.

  • 25.
    Ekdahl, Magnus
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    On approximations and computations in probabilistic classification and in learning of graphical models2007Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Model based probabilistic classification is heavily used in data mining and machine learning. For computational learning these models may need approximation steps however. One popular approximation in classification is to model the class conditional densities by factorization, which in the independence case is usually called the ’Naïve Bayes’ classifier. In general probabilistic independence cannot model all distributions exactly, and not much has been published on how much a discrete distribution can differ from the independence assumption. In this dissertation the approximation quality of factorizations is analyzed in two articles.

    A specific class of factorizations is the factorizations represented by graphical models. Several challenges arise from the use of statistical methods for learning graphical models from data. Examples of problems include the increase in the number of graphical model structures as a function of the number of nodes, and the equivalence of statistical models determined by different graphical models. In one article an algorithm for learning graphical models is presented. In the final article an algorithm for clustering parts of DNA strings is developed, and a graphical representation for the remaining DNA part is learned.

    List of papers
    1. Bounds for the Loss in Probability of Correct Classification Under Model Based Approximation
    Open this publication in new window or tab >>Bounds for the Loss in Probability of Correct Classification Under Model Based Approximation
    2006 (English)In: Journal of Machine Learning Research, ISSN 1532-4435, Vol. 7, p. 2449-2480Article in journal (Refereed) Published
    Abstract [en]

    In many pattern recognition/classification problem the true class conditional model and class probabilities are approximated for reasons of reducing complexity and/or of statistical estimation. The approximated classifier is expected to have worse performance, here measured by the probability of correct classification. We present an analysis valid in general, and easily computable formulas for estimating the degradation in probability of correct classification when compared to the optimal classifier. An example of an approximation is the Na¨ıve Bayes classifier. We show that the performance of the Naïve Bayes depends on the degree of functional dependence between the features and labels. We provide a sufficient condition for zero loss of performance, too.

    Keywords
    Bayesian networks, na¨ıve Bayes, plug-in classifier, Kolmogorov distance of variation, variational learning
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-13104 (URN)
    Available from: 2008-03-31 Created: 2008-03-31
    2. Concentrated or non-concentrated discrete distributions are almost independent
    Open this publication in new window or tab >>Concentrated or non-concentrated discrete distributions are almost independent
    2007 (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    The task of approximating a simultaneous distribution with a product of distributions in a single variable is important in the theory and applications of classification and learning, probabilistic reasoning, and random algmithms. The evaluation of the goodness of this approximation by statistical independence amounts to bounding uniformly upwards the difference between a joint distribution and the product of the distributions (marginals). In this paper we develop a bound that uses information about the most probable state to find a sharp estimate, which is often as sharp as possible. We also examine the extreme cases of concentration and non-conccntmtion, respectively, of the approximated distribution.

    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-13105 (URN)
    Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2014-09-29
    3. Parallell interacting MCMC for learning of topologies of graphical models
    Open this publication in new window or tab >>Parallell interacting MCMC for learning of topologies of graphical models
    2008 (English)In: Data mining and knowledge discovery, ISSN 1384-5810, E-ISSN 1573-756X, Vol. 17, no 3, p. 431-456Article in journal (Refereed) Published
    Abstract [en]

    Automated statistical learning of graphical models from data has attained a considerable degree of interest in the machine learning and related literature. Many authors have discussed and/or demonstrated the need for consistent stochastic search methods that would not be as prone to yield locally optimal model structures as simple greedy methods. However, at the same time most of the stochastic search methods are based on a standard Metropolis–Hastings theory that necessitates the use of relatively simple random proposals and prevents the utilization of intelligent and efficient search operators. Here we derive an algorithm for learning topologies of graphical models from samples of a finite set of discrete variables by utilizing and further enhancing a recently introduced theory for non-reversible parallel interacting Markov chain Monte Carlo-style computation. In particular, we illustrate how the non-reversible approach allows for novel type of creativity in the design of search operators. Also, the parallel aspect of our method illustrates well the advantages of the adaptive nature of search operators to avoid trapping states in the vicinity of locally optimal network topologies.

    Keywords
    MCMC, Equivalence search, Learning graphical models
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-13106 (URN)10.1007/s10618-008-0099-9 (DOI)
    Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2017-12-13
    4. A bayesian random fragment insertion model for de novo detection of DNA regulatory binding regions
    Open this publication in new window or tab >>A bayesian random fragment insertion model for de novo detection of DNA regulatory binding regions
    2007 (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Identification of regulatory binding motifs within DNA sequences is a commonly occurring problem in computationnl bioinformatics. A wide variety of statistical approaches have been proposed in the literature to either scan for previously known motif types or to attempt de novo identification of a fixed number (typically one) of putative motifs. Most approaches assume the existence of reliable biodatabasc information to build probabilistic a priori description of the motif classes. No method has been previously proposed for finding the number of putative de novo motif types and their positions within a set of DNA sequences. As the number of sequenced genomes from a wide variety of organisms is constantly increasing, there is a clear need for such methods. Here we introduce a Bayesian unsupervised approach for this purpose by using recent advances in the theory of predictive classification and Markov chain Monte Carlo computation. Our modelling framework enables formal statistical inference in a large-scale sequence screening and we illustrate it by a set of examples.

    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-13107 (URN)
    Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2012-11-21
  • 26.
    Ekdahl, Magnus
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Stokastisk komplexitet i klustringsanalys2004In: Workshop i tillämpad matematik,2004, 2004Conference paper (Other academic)
  • 27.
    Ekdahl, Magnus
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Koski, Timo
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Bounds for the Loss in Probability of Correct Classification Under Model Based Approximation2006In: Journal of Machine Learning Research, ISSN 1532-4435, Vol. 7, p. 2449-2480Article in journal (Refereed)
    Abstract [en]

    In many pattern recognition/classification problem the true class conditional model and class probabilities are approximated for reasons of reducing complexity and/or of statistical estimation. The approximated classifier is expected to have worse performance, here measured by the probability of correct classification. We present an analysis valid in general, and easily computable formulas for estimating the degradation in probability of correct classification when compared to the optimal classifier. An example of an approximation is the Na¨ıve Bayes classifier. We show that the performance of the Naïve Bayes depends on the degree of functional dependence between the features and labels. We provide a sufficient condition for zero loss of performance, too.

  • 28.
    Ekdahl, Magnus
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Koski, Timo
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    On Concentration of Discrete Distributions with Applications to Supervised Learning of Classifiers2007In: Machine Learning and Data Mining in Pattern Recognition: 5th International Conference, MLDM 2007, Leipzig, Germany, July 18-20, 2007. Proceedings / [ed] Petra Perner, Springer Berlin/Heidelberg, 2007, p. 2-16Chapter in book (Refereed)
    Abstract [en]

    Computational procedures using independence assumptions in various forms are popular in machine learning, although checks on empirical data have given inconclusive results about their impact. Some theoretical understanding of when they work is available, but a definite answer seems to be lacking. This paper derives distributions that maximizes the statewise difference to the respective product of marginals. These distributions are, in a sense the worst distribution for predicting an outcome of the data generating mechanism by independence. We also restrict the scope of new theoretical results by showing explicitly that, depending on context, independent ('Naïve') classifiers can be as bad as tossing coins. Regardless of this, independence may beat the generating model in learning supervised classification and we explicitly provide one such scenario.

  • 29.
    Ekdahl, Magnus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    On the Performance of Approximations of Bayesian Networks in Model-2006In: The Annual Workshop of the Swedish Artificial Intelligence Society,2006, Umeå: SAIS , 2006, p. 73-Conference paper (Refereed)
    Abstract [en]

    When the true class conditional model and class probabilities are approximated in a pattern recognition/classification problem the performance of the optimal classifier is expected to deteriorate. But calculating this reduction is far from trivial in the general case. We present one generalization, and easily computable formulas for estimating the degradation in performance with respect to the optimal classifier. An example of an approximation is the Naive Bayes classifier. We generalize and sharpen results for evaluating this classifier.

  • 30.
    Ekdahl, Magnus
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Koski, Timo
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Concentrated or non-concentrated discrete distributions are almost independent2007Manuscript (preprint) (Other academic)
    Abstract [en]

    The task of approximating a simultaneous distribution with a product of distributions in a single variable is important in the theory and applications of classification and learning, probabilistic reasoning, and random algmithms. The evaluation of the goodness of this approximation by statistical independence amounts to bounding uniformly upwards the difference between a joint distribution and the product of the distributions (marginals). In this paper we develop a bound that uses information about the most probable state to find a sharp estimate, which is often as sharp as possible. We also examine the extreme cases of concentration and non-conccntmtion, respectively, of the approximated distribution.

  • 31.
    Erhardsson, Torkel
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Conditions for convergence of random coefficient AR(1) processes and perpetuities in higher dimensions2014In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 20, no 2, p. 990-1005Article in journal (Refereed)
    Abstract [en]

    A d-dimensional RCA(1) process is a generalization of the d-dimensional AR(1) process, such that the coefficients {M-t; t =1, 2, ...} are i.i.d. random matrices. In the case d =1, under a nondegeneracy condition, Goldie and Mailer gave necessary and sufficient conditions for the convergence in distribution of an RCA(1) process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition parallel to Pi(n)(t=1) M-t parallel to -greater than(a.s.) 0 as n -greater than infinity, most of the results of Goldie and Mailer can be extended to the case d greater than 1. If this condition does not hold, some of their results cannot be extended.

  • 32.
    Erhardsson, Torkel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Non-parametric Bayesian inference for integrals with respect to an unknown finite measure2008In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 35, no 2, p. 369-384Article in journal (Refereed)
    Abstract [en]

    We consider the problem of estimating a collection of integrals with respect to an unknown finite measure μ from noisy observations of some of the integrals. A new method to carry out Bayesian inference for the integrals is proposed. We use a Dirichlet or Gamma process as a prior for μ, and construct an approximation to the posterior distribution of the integrals using the sampling importance resampling algorithm and samples from a new multidimensional version of a Markov chain by Feigin and Tweedie. We prove that the Markov chain is positive Harris recurrent, and that the approximating distribution converges weakly to the posterior as the sample size increases, under a mild integrability condition. Applications to polymer chemistry and mathematical finance are given. © 2008 Board of the Foundation of the Scandinavian Journal of Statistics.

  • 33.
    Erhardsson, Torkel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Poisson and compound Poisson approximation2005In: An introduction to Stein's method / [ed] A.D. Barbour, Louis H.Y. Chen, Singapore: Singapore University Press , 2005, p. 61-113Chapter in book (Other academic)
    Abstract [en]

    A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems. This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.

  • 34.
    Erhardsson, Torkel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Stein's method, Markov renewal point processes, and strong memoryless times2005In: Stein's method and applications / [ed] A.D. Barbour, Louis H.Y. Chen, Singapore: Singapore University Press , 2005, p. 119-130Chapter in book (Other academic)
    Abstract [en]

    Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 1983, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.

  • 35.
    Erhardsson, Torkel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Strong memoryless times and rare events in Markov renewal point processes2004In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 32, no 3B, p. 2446-2462Article in journal (Refereed)
    Abstract [en]

    Let $W$ be the number of points in $(0,t]$ of a stationary finite-state Markov ren ewal point process. We derive a bound for the total variation distance between the distribution of $W$ and a compound Poisson distribution. For any nonnegative rand om variable $\zeta$ we construct a ``strong memoryless time'' $\hat\zeta$ such tha t $\zeta-t$ is exponentially distributed conditional on $\{\hat\zeta\leq t,\zeta>t \}$, for each $t$. This is used to embed the Markov renewal point process into ano ther such process whose state space contains a frequently observed state which rep resents loss of memory in the original process. We then write $W$ as the accumulat ed reward of an embedded renewal reward process, and use a compound Poisson approx imation error bound for this quantity by Erhardsson. For a renewal process, the bo und depends in a simple way on the first two moments of the interrenewal time dist ribution, and on two constants obtained from the Radon-Nikodym derivative of the i nterrenewal time distribution with respect to an exponential distribution. For a Poisson process, the bound is 0.

  • 36.
    Eriksson, Annika
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Ockert-Eriksson, G
    Karolinska Inst, Dept Dent Biomat Sci, Huddinge, Sweden Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Lockowandt, P
    Karolinska Inst, Dept Dent Biomat Sci, Huddinge, Sweden Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Eriksson, O
    Clinical factors and clinical variation influencing the reproducibility of interocclusal recording methods2002In: British Dental Journal, ISSN 0007-0610, E-ISSN 1476-5373, Vol. 192, no 7, p. 395-400Article in journal (Refereed)
    Abstract [en]

    Objective The reproducibility of clinical records of the occlusion was assessed in three dimensions using mounted casts. Three distinct areas were examined: 1) mandibular positions (intercuspal position (IP) or retruded contact position (RCP)), 2) materials used in recording the occlusion, 3) clinical variation. Design Interocclusal records were made in a random order of three patients: one fixed prosthodontics case, one removable partial denture case and one complete denture case, with two different types of waxes, record rims, two different brands of vinyl polysiloxanes and one irreversible hydrocolloid. Setting Private practice and Karolinska Institute, Huddinge, Sweden, Subjects One general dental practitioner and three voluntary patients. Results Point estimation of variance components indicate that 70-93% of the variation of the positions of the mounted casts are caused by: 1) clinical variation for all three cases and in three directions, 2) the influence of recording materials 0-29%, and 3) mandibular positions (IP/RCP) 0-11%. The ranges of the positions of the mounted casts were lower for the dentate case (0.04-1.39 mm) than for the partially dentate case (0.17-2.65 mm), which in turn was lower than those for the edentulous case (1.42-5.59 mm). Conclusion Clinical variation seems to dominate the variation in positions of mounting casts when making interocclusal records, rather than mandibular position or the recording materials used. Therefore a dentist who makes one single interocclusal record cannot presume that it will reproduce the interocclusal relationship intended, which in the present study was most obvious for the edentulous case. The results showed that impression materials stabilised by a tray did not differ significantly from waxes and record rims concerning the reproducibility. Therefore the stabilised impression materials are an alternative, which also give additional advantages like reduction of appointments as well as superior accuracy.

  • 37.
    Evarest, Emanuel
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Charles, Wilson
    Department of Mathematics, University of Dar es Salaam, Tanzania.
    Regime Switching models on Temperature Dynamics2016Report (Other academic)
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

  • 38.
    Evarest, Emanuel
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Charles, Wilson M.
    Department od Mathematics, University of Dar el Salaam, Tanzania.
    Regime Switching models on Temperature Dynamics2017In: International Journal of Applied Mathematics and Statistics, ISSN 0973-1377, E-ISSN 0973-7545, Vol. 56, no 2Article in journal (Refereed)
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

  • 39.
    Evarest Sinkwembe, Emanuel
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Modelling Weather Dynamics for Weather Derivatives Pricing2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis focuses on developing an appropriate stochastic model for temperature dynamics as a means of pricing weather derivative contracts based on temperature. There are various methods for pricing weather derivatives ranging from simple one like historical burn analysis, which does not involve modeling the underlying weather variable to complex ones that require Monte Carlo simulations to achieve explicit weather derivatives contract prices, particularly the daily average temperature (DAT) dynamics models. Among various DAT models, appropriate regime switching models are considered relative better than single regime models due to its ability to capture most of the temperature dynamics features caused by urbanization, deforestation, clear skies and changes of measurement station. A new proposed model for DAT dynamics, is a two regime switching models with heteroskedastic mean-reverting process in the base regime and Brownian motion with nonzero drift in the shifted regime. Before using the model for pricing temperature derivative contracts, we compare the performance of the model with a benchmark model proposed by Elias et al. (2014), interms of the HDDs, CDDs and CAT indices. Using ve data sets from dierent measurement locations in Sweden, the results shows that, a two regime switching models with heteroskedastic mean-reverting process gives relatively better results than the model given by Elias et al. We develop mathematical expressions for pricing futures and option contracts on HDDs, CDDs and CAT indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

    List of papers
    1. Regime Switching models on Temperature Dynamics
    Open this publication in new window or tab >>Regime Switching models on Temperature Dynamics
    2017 (English)In: International Journal of Applied Mathematics and Statistics, ISSN 0973-1377, E-ISSN 0973-7545, Vol. 56, no 2Article in journal (Refereed) Published
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

    Keywords
    Weather derivatives, Regime switching, temperature dynamics, expectationmaximization, temperature indices
    National Category
    Probability Theory and Statistics Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-135541 (URN)
    Available from: 2017-03-22 Created: 2017-03-22 Last updated: 2017-11-29
  • 40.
    Evarest Sinkwembe, Emanuel
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Weather derivatives pricing using regim switching models2017Report (Other academic)
    Abstract [en]

    In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with mean different from zero. We develop the mathematical formulas for pricing futures contract on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. We also present the mathematical expressions for pricing the corresponding options on futures contracts for the same temperature indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We provide the description of Montecarlo simulation method for pricing weather derivatives under this model and use it to price a few weather derivatives call option contracts.

  • 41.
    Evarest Sinkwembe, Emanuel
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics .
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Weather Derivatives Pricing Using Regime Switching Model2018In: Monte Carlo Methods and Applications, ISSN 0929-9629, Vol. 24, no 1, p. 13-27Article in journal (Refereed)
    Abstract [en]

    In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with nonzero drift. We develop mathematical formulas for pricing futures and option contracts on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

  • 42.
    Gao, Fuchang
    et al.
    University of Idaho.
    Liu, Zhenxia
    Blåeldsvägen 12B, Sturefors, Sweden.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Conditional persistence of Gaussian random walks2014In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 19, no 70, p. 1-9Article in journal (Refereed)
    Abstract [en]

    Let $\{X_n\}_{n\geq1}$ be a sequence of i.i.d. standard Gaussian random variables, let $S_n=\sum_{i=1}^nX_i$ be the Gaussian random walk, and let $T_n=\sum_{i=1}^nS_i$ be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence:\begin{align*}\mathbb{P}\left\{\max_{1\leq k \leq n}T_{k} \leq 0\,\,\Big|\,\,T_n=0,S_n=0\right\}&\lesssim n^{-1/2},\\\mathbb{P}\left\{\max_{1\leq k \leq 2n}T_{k} \leq 0\,\,\Big|\,\,T_{2n}=0,S_{2n}=0\right\}&\gtrsim\frac{n^{-1/2}}{\log n},\end{align*}for $n\rightarrow\infty,$ which partially proves a conjecture by Caravenna and Deuschel (2008).

  • 43.
    Gao, FuChang
    et al.
    Univ Idaho, Dept Math, Moscow, ID 83844 USA.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Upper tail probabilities of integrated Brownian motions2015In: Science China Mathematics, ISSN 1674-7283, Vol. 58, no 5, p. 1091-1100Article in journal (Refereed)
    Abstract [en]

    We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the L (p) norm. For the uniform norm, Talagrands approach is used, while for the L (p) norm, Zolotares approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities (large ball probabilities) for general Gaussian random variables in Banach spaces. As applications, explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.

  • 44.
    Gauraha, Niharika
    et al.
    Indian Statistical Institute, Bangalore, India.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    Conditional Independence Models which are Totally Ordered2018Report (Other academic)
    Abstract [en]

    The totally ordered conditional independence (TOCI) model N(K) is defined to be the set of all normal distributions on RI such that for each adjacent pair (Ki, Ki+1)  K, the components of a multivariate normal vector x  RI, indexed by the set difference { Ki+1 \ Ki } are mutually conditionally independent given the variables indexed by Ki. Here K = {K1  …  Kq } is a totally ordered set of subsets of a finite index set I. It is shown that TOCI models constitute a proper subset of lattice conditional independence (LCI) models. It follows that like LCI models, for the TOCI models the likelihood function and parameter space can be factored into the products of conditional likelihood functions and disjoint parameter spaces, respectively, where each conditional likelihood function corresponds to an ordinary multivariate normal regression model. 

  • 45.
    Gyllenberg, M.
    et al.
    Department of Mathematics, University of Turku, 20014 Turku, Finland.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy2002In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 177-178, p. 161-184Conference paper (Other academic)
    Abstract [en]

    We present a theory of classification and predictive identification of bacteria. Bacterial strains are characterized by a binary vector and the taxonomy is specified by attaching a label to each vector. The theory is developed from only two basic assumptions, viz. that the sequence of pairs of feature vectors and the attached labels is judged (infinitely) exchangeable and predictively sufficient. We derive expressions for the training error and the probability of identification error and show that latter is an affine function of the former. We prove the law of large numbers for identification matrices, which contain the fundamental information of bacterial data. We prove the Bayesian risk consistency of the predictive identification rule given by the theory and show that the training error is a consistent estimate of the generalization error. © 2002 Published by Elsevier Science Inc.

  • 46. Gyllenberg, M
    et al.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Probabilistic models for bacterial taxonomy2001In: International Statistical Review, ISSN 0306-7734, E-ISSN 1751-5823, Vol. 69, no 2, p. 249-276Article, review/survey (Refereed)
    Abstract [en]

    We give a survey of different partitioning methods that have been applied to bacterial taxonomy. We introduce a theoretical framework, which makes it possible to treat the various models in a unified way. The key concepts of our approach are prediction and storing of microbiological information in a Bayesian forecasting setting. We show that there is a close connection between classification and probabilistic identification and that, in fact, our approach ties these two concepts together in a coherent way.

  • 47.
    Gyllenberg, M
    et al.
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    Koski, Timo
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Dawyndt, P
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    Lund, T
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    Thompson, F
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    Austin, B
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    Swings, J
    Univ Turku, Dept Math, FIN-20014 Turku, Finland Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden State Univ Ghent, Microbiol Lab, B-9000 Ghent, Belgium Heriot Watt Univ, Dept Biol Sci, Edinburgh EH14 4AS, Midlothian, Scotland.
    New methods for the analysis of binarized BIOLOG GN data of vibrio species: Minimization of stochastic complexity and cumulative classification2002In: Systematic and Applied Microbiology, ISSN 0723-2020, E-ISSN 1618-0984, Vol. 25, no 3, p. 403-415Article in journal (Refereed)
    Abstract [en]

    We apply minimization of stochastic complexity and the closely related method of cumulative classification to analyse the extensively studied BIOLOG GN data of Vibrio spp. Minimization of stochastic complexity provides an objective tool of bacterial taxonomy as it produces classifications that are optimal from the point of view of information theory. We compare the outcome of our results with previously published classifications of the same data set. Our results both confirm earlier detected relationships between species and discover new ones.

  • 48.
    Habyarimana, Cassien
    et al.
    Integrated Polytechnic Regional Centre, Rwanda.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Nzabanita, Joseph
    University of Rwanda, Rwanda.
    Estimation of Parameters in the Growth Curve Model with a Linearly Structured Covariance Matrix: A Simulation Study2017In: International Journal of Scientific Engineering and Technology, ISSN 2277-1581, Vol. 6, no 1, p. 45-49Article in journal (Refereed)
    Abstract [en]

    In this paper, the implementation of algorithm proposed in (Nzabanita, J., et al. 2012) for some known linear structures on the covariance matrix Σ is performed and simulations for different sample sizes are repeated many times. For these simulations, the percentages of non positive definite estimates are produced, and the linear structures are identified and classified. 

  • 49.
    Hao, Chengcheng
    et al.
    Dept. Statist., Stockholm Univ., Stockholm, Sweden; Dept. Automation, Shanghai Jiao Tong Univ., Shanghai, China.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Dept. Energy and Technol., Swedish Univ. Agricultural Sci., Uppsala, Sweden.
    von Rosen, Tatjana
    Dept. Statist.Stockholm Univ., Stockholm, Sweden.
    Explicit influence analysis in two-treatment balanced crossover models2015In: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 24, no 1, p. 16-36Article in journal (Refereed)
    Abstract [en]

    This paper considers how to detect influential observations in crossover models with random individual effects. Two influence measures, the delta-beta influence and variance-ratio influence, are utilized as tools to evaluate the influence of the model on the estimates of mean and variance parameters with respect to case-weighted perturbations, which are introduced to the model for studying the ‘influence’ of cases. The paper provides explicit expressions of the delta-beta and variance-ratio influences for the general two-treatment balanced crossover models when the proposed decompositions for the perturbed models hold. The influence measures for each parameter turn out to be closed-form functions of orthogonal projections of specific residuals in the unperturbed model.

  • 50.
    Hao, Chengcheng
    et al.
    Stockholm University, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
    von Rosen, Tatjana
    Stockholm University, Sweden.
    Influence diagnostics for count data under AB-BA crossover trials2017In: Statistical Methods in Medical Research, ISSN 0962-2802, E-ISSN 1477-0334, Vol. 26, no 6, p. 2938-2950Article in journal (Refereed)
    Abstract [en]

    This paper aims to develop diagnostic measures to assess the influence of data perturbations on estimates in AB-BA crossover studies with a Poisson distributed response. Generalised mixed linear models with normally distributed random effects are utilised. We show that in this special case, the model can be decomposed into two independent sub-models which allow to derive closed-form expressions to evaluate the changes in the maximum likelihood estimates under several perturbation schemes. The performance of the new influence measures is illustrated by simulation studies and the analysis of a real dataset.

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