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  • 201.
    Hössjer, Ola
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Nyberg, Tommy
    Petrovic, Stefan
    Sjöberg, Frank
    Öberg, Tommy
    Bayesian Distributed Detection by Sensor Networks with Missing Data2012Rapport (Annet vitenskapelig)
    Abstract [en]

    We consider detection and identication of a moving target, using a network of sensors. The target emits a signal; a stationary stochastic process corrupted by additive noise, independently across sensors. Before intersensor communication, all sensors reduce external data as energy over disjoint frequency bands and time blocks. One sensor, the internal fusion center (IFC), gathers feature vectors from the other sensors, possibly after message passing. Using Bayesian decision theory, it decides for presence or absence of the target and computes a maximum posterior estimate of target (trajectory and spectral) parameters. The main novelties of the paper are: 1) To apply statistical theory of missing data to an inter-sensor communication protocol which censors weak signals before transmission and an imperfect channel in which some transmitted signals are lost. A Naive Bayes approximate detector is dened, which requires recursive computation of reception probabilities. 2) To derive asymptotic approximations of the distribution of the spectral feature vectors and a Laplace type approximation of the detector. The performance of the proposed Bayesian detector is shown in a simulation study to be only slightly inferior to that of an ideal Bayesian detector (with no missing data), as well as superior to a naive detector.

  • 202.
    Hössjer, Ola
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Ryman, Nils
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för genetik, mikrobiologi och toxikologi.
    Quasi equilibrium, variance effective population size and fixation index for models with spatial structure2012Rapport (Annet vitenskapelig)
  • 203.
    Hössjer, Ola
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tyvand, Peder A.
    A monoecious and diploid Moran model of random mating2016Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 394, s. 182-196Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An exact Markov chain is developed for a Moran model of random mating for monoecious diploid individuals with a given probability of self-fertilization. The model captures the dynamics of genetic variation at a biallelic locus. We compare the model with the corresponding diploid Wright-Fisher (WF) model. We also develop a novel diffusion approximation of both models, where the genotype frequency distribution dynamics is described by two partial differential equations, on different time scales. The first equation captures the more slowly varying allele frequencies, and it is the same for the Moran and WF models. The other equation captures departures of the fraction of heterozygous genotypes from a large population equilibrium curve that equals Hardy-Weinberg proportions in the absence of selfing. It is the distribution of a continuous time Ornstein-Uhlenbeck process for the Moran model and a discrete time autoregressive process for the WF model. One application of our results is to capture dynamics of the degree of non-random mating of both models, in terms of the fixation index f(IS). Although f(IS) has a stable fixed point that only depends on the degree of selfing, the normally distributed oscillations around this fixed point are stochastically larger for the Moran than for the WF model.

  • 204.
    Ingre, Michael
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Stressforskningsinstitutet.
    Why small low-powered studies are worse than large high-powered studies and how to protect against "trivial" findings in research: comment on Friston (2012)2013Inngår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 81, s. 496-498Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is sometimes argued that small studies provide better evidence for reported effects because they are less likely to report findings with small and trivial effect sizes (Friston, 2012). But larger studies are actually better at protecting against inferences from trivial effect sizes, if researchers just make use of effect sizes and confidence intervals. Poor statistical power also comes at a cost of inflated proportion of false positive findings, less power to "confirm" true effects and bias in reported (inflated) effect sizes. Small studies (n=16) lack the precision to reliably distinguish small and medium to large effect sizes (r<.50) from random noise (α=.05) that larger studies (n=100) does with high level of confidence (r=.50, p=.00000012). The present paper presents the arguments needed for researchers to refute the claim that small low-powered studies have a higher degree of scientific evidence than large high-powered studies.

  • 205. Ingre, Michael
    et al.
    Nilsonne, Gustav
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Stressforskningsinstitutet. Karolinska Institutet, Sweden; Stanford University, USA.
    Estimating statistical power, posterior probability and publication bias of psychological research using the observed replication rate2018Inngår i: Royal Society Open Science, E-ISSN 2054-5703, Vol. 5, nr 9, artikkel-id 181190Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we show how Bayes' theorem can be used to better understand the implications of the 36% reproducibility rate of published psychological findings reported by the Open Science Collaboration. We demonstrate a method to assess publication bias and show that the observed reproducibility rate was not consistent with an unbiased literature. We estimate a plausible range for the prior probability of this body of research, suggesting expected statistical power in the original studies of 48-75%, producing (positive) findings that were expected to be true 41-62% of the time. Publication bias was large, assuming a literature with 90% positive findings, indicating that negative evidence was expected to have been observed 55-98 times before one negative result was published. These findings imply that even when studied associations are truly NULL, we expect the literature to be dominated by statistically significant findings.

  • 206. Jacobs, Rianne
    et al.
    Lesaffre, Emmanuel
    Teunis, Peter F. M.
    Höhle, Michael
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    van de Kassteele, Jan
    Identifying the source of food-borne disease outbreaks: An application of Bayesian variable selection2019Inngår i: Statistical Methods in Medical Research, ISSN 0962-2802, E-ISSN 1477-0334, Vol. 28, nr 4, s. 1126-1140Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Early identification of contaminated food products is crucial in reducing health burdens of food-borne disease outbreaks. Analytic case-control studies are primarily used in this identification stage by comparing exposures in cases and controls using logistic regression. Standard epidemiological analysis practice is not formally defined and the combination of currently applied methods is subject to issues such as response misclassification, missing values, multiple testing problems and small sample estimation problems resulting in biased and possibly misleading results. In this paper, we develop a formal Bayesian variable selection method to account for misclassified responses and missing covariates, which are common complications in food-borne outbreak investigations. We illustrate the implementation and performance of our method on a Salmonella Thompson outbreak in the Netherlands in 2012. Our method is shown to perform better than the standard logistic regression approach with respect to earlier identification of contaminated food products. It also allows relatively easy implementation of otherwise complex methodological issues.

  • 207.
    Jafari-Mamaghani, Mehrdad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A Treatise on Measuring Wiener-Granger Causality2014Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Wiener-Granger causality is a well-established concept of causality based on stochasticity and the flow of time, with applications in a broad array of quantitative sciences. The majority of methods used to measure Wiener-Granger causality are based on linear premises and hence insensitive to non-linear signals. Other frameworks based on non-parametric techniques are often computationally expensive and susceptible to overfitting or lack of sensitivity.

    In this thesis, Paper I investigates the application of linear Wiener-Granger causality to migrating cancer cell data obtained using a Systems Microscopy experimental platform. Paper II represents a review of non-parametric measures based on information theory and discusses a number of related bottlenecks and potential routes of circumvention. Paper III studies the properties of a frequently used non-parametric information theoretical measure for a class of non-Gaussian distributions. Paper IV introduces a new efficient scheme for non-parametric analysis of Wiener-Granger causality based on kernel canonical correlations, and studies the connection between this new scheme and the information theoretical approach. Lastly, Paper V draws upon the results in the preceding paper to discuss non-parametric analysis of Wiener-Granger causality in partially observed systems.

    Altogether, the work presented in this thesis constitutes a comprehensive review on measures of Wiener-Granger causality in general, and in particular, features new insights on efficient non-parametric analysis of Wiener-Granger causality in high-dimensional settings.

  • 208.
    Jafari-Mamaghani, Mehrdad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Non-parametric analysis of Granger causality using local measures of divergence2013Inngår i: Applied Mathematical Sciences, ISSN 1312-885X, E-ISSN 1314-7552, Vol. 7, nr 83, s. 4107-4236Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The employment of Granger causality analysis on temporal data is now a standard routine in many scientific disciplines. Since its in- ception, Granger causality has been modeled using a wide variety of analytical frameworks of which, linear models and derivations thereof have been the dominant choice. Nevertheless, a body of research on Granger causality and its applications has focused on non-linear and non-parametric models. One common choice for such models is based on employment of multivariate density estimators and measures of divergence. However, these models are subject to a number of estimations and tuning components that have a great impact on the final outcome. Here we focus on one such general model and improve a number of its tuning bodies. Crucially, we i) investigate the bandwidth selection issue in kernel density estimation, and ii) discuss and propose a solu- tion to the sensitivity of estimated information theoretic measures of divergence to non-linear correspondence. The resulting framework of analysis is evaluated using varied series of simulations.

  • 209.
    Jafari-Mamaghani, Mehrdad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Non-parametric Wiener-Granger Causality in Partially Observed Systems2014Inngår i: IEEE 2014 Conference on Norbert Wiener in the 21st Century: Driving Technology's Future, 2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wiener’s definition of causality, now known as Wiener-Granger causality, has become a frequently used quantification of temporally resolved causality in numerous fields of science. In many empirical studies, the system of interest cannot be observed in its entirety and the observations may include non-informative data. To this end, partial Wiener-Granger causality has been developed to circumvent this issue. In this paper, we extend partial Wiener-Granger causality to the non-parametric case and discuss two approaches to obtain estimates of this non-parametric, entropy-based measure.

  • 210.
    Jafari-Mamaghani, Mehrdad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Robust Non-linear Wiener-Granger Causality For Large High-dimensional DataManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is able to detect non-linear and non-monotonous signals, is designed to be immune to noise, and offers tunability in terms of computational complexity in its estimations. Furthermore, we show that, under specified conditions, the intro- duced measure can be regarded as an estimate of conditional mutual information (tranfer entropy). The functionality of this measure is assessed using comparative simulations where it outperforms other existing methods. The paper is concluded with an application to climatological data.

  • 211.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Transfer entropy expressions for a class of non-Gaussian distributionsManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I − IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 212.
    Jansson, Ingegerd
    et al.
    Statistiska centralbyrån, Statistics Sweden.
    Bernström, Fredrik
    Statistiska centralbyrån, Statistics Sweden.
    Carlson, Michael
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen. Statistiska centralbyrån, Statistics Sweden.
    The Process of Practicing Statistical Disclosure Control in Tabular Data at Statistics Sweden2010Inngår i: Q2010 European Conference on Quality in Official Statistics, Helsinki, Finland, 3-6 May 2010, 2010Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    It follows from Swedish legislation that Statistics Sweden, when publishing statistical data, must first assess the risk of disclosing confidential information, and then assess the risk that disclosure will result in any harm or damage. In case of considerable risk of the latter, data should be properly protected. We are attempting to handle this by a simple process describing how disclosure control should be applied within Statistics Sweden. Following the general process orientation of statistics production within Statistics Sweden, the process of statistical disclosure control (SDC) in tables must fit within the general production process, and the recommended methods and tools used should as much as possible be shared by all statistical products. We will describe the process for SDC in tables, the contents of a handbook where the process and appropriate methods are described, and the ongoing work with IT-solutions. Presently, work is concentrated on making it possible to run τ-Argus from SAS. Plans for implementation and training will also be briefly described.

  • 213.
    Jansson, Ingegärd
    Stockholms universitet.
    On Statistical Modeling of Social Networks1997Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    A social network is formed by a collection of individuals and the contacts or relations between them. The focus is here on relations defined by sociometric choices, implying that the individuals in the network have been required to choose among the other individuals in the group according to some criteria.

    Some statistical models of the sociometric choice structure in a social network are presented. A recurrent assumption in the models is the assumption that there exists latent or underlying structures in a network, structures that can not be directly observed. The models also have in common the assumption of independence or conditional independence between entities of the network, assumptions not uncommon in statistical network models. These assumptions are often crucial for the possibility to find simple ways of estimating models. Here an attempt is made to find probabilistic models where independence is an ingredient but which also allow for structure.

    The models are illustrated and evaluated by application to data where the sociometric choices are based on friendship or cooperation. The large number of networks available makes it possible to find and evaluate empirical distributions of the test statistics.

    The simplest model presented assumes dyad independence. Possible simplifications by choice or edge independence are also discussed. It appears that dyad independence can not be ruled out, but that choice independence is inappropriate.

    In order to model the transitive structure of a network, a model is introduced that is based on a random choice structure and an unknown underlying clique structure. Two different approaches for estimating the clique structure are discussed, the maximum likelihood approach and the Bayesian approach. The empirical results show no large deviation between model and observations.

    A model of popularity structure is introduced where popularity is viewed as a latent attribute of the individuals in the network. The group of individuals is assumed to have a latent popularity structure, composed of individuals from three popularity groups. It is shown how the popularity structure can be estimated and how latent popularity can be considered in combination with manifest individual attributes.

    A model is also presented for the situation when two sociometric relations are measured on one set of individuals. The model assumes that there exists a latent network structure which can not be observed directly. When the relations are measured on the network, deviations from the underlying structure might occur with some probability. Approximate estimates of model parameters are given. Empirical findings suggest that the birelational latent model is sufficiently accurate for the data, but that there appear to be convergence problems, possibly due to the relatively large number of parameters in the model.

  • 214.
    Japec, Lilli
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Quality Issues in Interview Surveys: Some Contributions2005Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In Paper I, I give a brief overview of the “state of the art” in methodological research related to interview surveys and I discuss some implications for survey practices. I study the literature on participation strategies, interviewer effects that can occur during the interview, methods for quality assurance and interviewer training. Methods that are used to study quality aspects of interview surveys are also described. The discussion highlights areas where more research is needed.

    Paper II deals with the interview process and the concept of interviewer burden. Interviewer errors have been described in the survey methodology literature. This literature, however, has not to a great extent addressed the question of why interviewer errors occur or why interviewers behave the way they do. In this paper these issues are addressed. I model the interview process, address interviewers’ cognitive processes, define the concept of interviewer burden and discuss its effects. Data from two interviewer surveys are used to illustrate aspects of interviewer burden.

    In Paper III I explore some components of interviewer burden further. I use data from the Swedish part of the European Social Survey (ESS) to study the effects of interviewer burden and strategies on data quality. Multilevel regression analysis is used to model effects due to respondents and to interviewers. From the data analysis I found that interviewer burden, as I define it, affects data quality. For example, interviewers with a heavy burden tend to have lower response rates, higher refusal and noncontact rates, and shorter interview time.

    In Paper IV we study the effects of the fieldwork on nonresponse bias in the Swedish Labour Force Survey. In the evaluation study we use external data that is available for both respondents and nonrespondents to estimate the nonresponse bias. We apply the generalised regression estimator (GREG) using strong auxiliary information in the estimation procedure. We also carry out the same analysis assuming a simple random sample was drawn and that no auxiliary information is available. Furthermore we study noncontacts and refusals to address the question whether there is a bias caused by either group of nonrespondents. Finally we estimate the cost for the current fieldwork strategy compared with less elaborate strategies.

  • 215. Javed, Farrukh
    et al.
    Mazur, Stepan
    Ngailo, Edward
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Dar es salaam University College of Education, Tanzania.
    Higher order moments of the estimated tangency portfolio weights2017Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we consider the estimated weights of tangency portfolio. The returns are assumed to be independently and multivariate normally distributed. We derive analytical expressions for the higher order non-central and central moments of these weights. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed-forms. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns of eight financial indexes listed in NASDAQ stock exchange.

  • 216.
    Karlberg, Forough
    Stockholms universitet.
    Survey estimation for highly skewed data1999Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    Estimation of the population total of a highly skewed survey variable from a small sample is problematic if straightforward methods are used since (i) when there are no extreme values in the sample, too small estimates will be obtained (ii) if extreme values are sampled, the estimates will become grotesquely large. Traditional methods for outlier treatment will usually compensate for outliers in the sample, thereby avoiding (ii), whereas the small negative bias of (i) will persist. Here, a lognormal superpopulation model is proposed. A particular strength of the lognormal model estimator is that even in the absence of extremely large values in the sample, the assumed lognormal structure of the survey variable is used for estimating the population total.

    Two estimators based on a lognormal superpopulation distribution are proposed: (i) one estimator applicable if the shape parameter of the assumed lognormal superpopulation distribution is known (ii) one estimator applicable if the shape parameter is unknown. For both estimators, any number of auxiliary variables can be utilized. Estimator (i) is of little practical importance, but has the advantage that it is model unbiased, and that a model unbiased estimator of its estimation error variance also easily can be derived. Estimator (ii), although only approximately model unbiased, is more practically applicable, because of the more realistic assumption of unknown shape parameter.

    Both estimators (i) and (ii) are applicable only for variables that are strictly positive. A third estimator, based on a combined lognormal-logistic superpopulation model is therefore proposed; this estimator can be applied to situations in which the survey variable, while highly skewed, may assume the value zero for a number of units.

    The three model-based estimators are compared to a number of alternative estimators (design-based estimators as well as estimators specifically constructed for outlier treatment) in a simulation study, using random populations as well as real survey populations. The simulation results give at hand that the model-based estimators constitute a sensible alternative to the alternative estimators, in particular when the sample size is small and when the distribution of the survey variable is close to the assumed superpopulation distribution.

  • 217.
    Karlberg, Martin
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Triad count estimation and transitivity testing in graphs and digraphs1997Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Triads and transitivity are two concepts within the field of social network analysis that are closely related to each other. We study some estimation and testing problems related to those concepts, using the tools of graph theory; the results obtained could be applied to graphs representing other kinds of data than social relations. Throughout this thesis, we focus on the role of local networks. A local network for an individual in a friendship network may be regarded as the network between the friends of this person. Two local network attributes that we pay special attention to are the size and the density. The local size of a vertex is defined so that it counts the number of transitive relationships in which that vertex is involved; this definition is not undisputable in the digraph situation, since not all edges in the local network are counted using that definition. We define the local density of a vertex in such a way, that its expected value is equal to the expected overall density of the network under some commonly used simple random graph and random digraph models. When dealing with triad count estimation, we consider the situation when we have observed information about a probability sample of vertices in a graph or digraph; we let the amount of information observed for each vertex range from the vertex degree to the entire local network of that vertex. Horvitz-Thompson estimators (and variance estimators for those estimators) for the triad counts are given. A main result is that when local networks without information on the identities of the vertices in that network are observed, the triad counts may be expressed as sums of vertex attributes; this greatly facilitates the estimation based on vertex sampling designs more complex than simple random sampling. Transitivity testing is considered for graphs and digraphs that are observed in their entirety. We study two different kinds of transitivity tests; tests based on the counts of transitive and intransitive triads and triples, and tests based on the mean local density over all vertices. The null hypothesis used is that the graphs and digraphs observed have been generated according to some conditional uniform random graph model that does not imply a high degree of transitivity. The powers of the tests against random graph distributions that generate highly transitive graphs are examined in simulation studies. In other simulation studies, the tests are applied to a large set of school class sociograms. When (undirected) graphs are considered, the test based on the proportion of transitive triads out of the non-vacuously transitive ones is found to be best at detecting transitivity; for digraphs, the test based on the difference between the mean local density and the overall network density is the best transitivity detector.

  • 218.
    Kollo, Tõnu
    et al.
    University of Tartu, Institute of mathematical statistics.
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    The Department of Energy and Technology, SLU, Sweden.
    Estimation in high-dimensional analysis and multivariate linear models2008Rapport (Annet vitenskapelig)
    Abstract [en]

    When the number of variables compared with the number of observationsis large this paper presents a new approach of estimating the parametersdescribing the mean structure in the Growth Curve model. An explicitestimator is obtained which is unbiased, consistent and asymptoticallynormally distributed. Its variance is also derived.

  • 219. Kollo, Tõnu
    et al.
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    Estimation in high-dimensional analysis and multivariate linear models2011Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, nr 7, s. 1241-1253Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article presents a new approach of estimating the parameters describing the mean structure in the Growth Curve model when the number of variables compared with the number of observations is large.

  • 220.
    Koskinen, Johan
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Essays on Bayesian Inference for Social Networks2004Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time.

    A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation.

    The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step.

    In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications.

    Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.

  • 221.
    Kum, Cletus Kwa
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Bayesian Analysis of Two Malaria Treatments and Probability Modelling of Malaria Parasite Genotypes2009Licentiatavhandling, monografi (Annet vitenskapelig)
  • 222.
    Kum, Cletus Kwa
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Bayesian Analysis of Two Malaria Treatments and Probability Modelling of Malaria Parasite Gentypes2009Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 223. Kum, Cletus Kwa
    et al.
    Thorburn, Daniel
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Ghilagaber, Gebrenegus
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Björkman, Anders
    Gil, José Pedro
    Effects of Some Biological Covariates on the Probability of First Recurrence of Malaria following Treatment with Artemisinin Combination Therapy2018Inngår i: International Journal of Statistics in Medical Research, ISSN 1929-6029, Vol. 7, nr 1, s. 1-9Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Many investigations have shown that artemisinin-based combination therapies are effective in the treatment of uncomplicated malaria and that they do not increase parasite resistance to treatment as much as treatment with single substance. We study the relation between some biological covariates and the time to first recurrence of malaria for children treated for malaria in a clinical trial. One group received artesunate plus sulfadoxine-pyrimethamine and the other only sulfadoxine-pyrimethamine. We consider the event malaria-free for the first 42 (and 84) days. We use logistic regression models for the analyses. The main results show that the probability of no recurrence is higher if the parasite density in the blood is high. The results are inconclusive for other explanatory biological variables. The infecting parasites having genes that indicate resistance, gave different results at the two different treatment centres. There was no appreciable difference in the effects of treatment over the two follow-up periods and these treatments do not have any effect on the probability of a recurrence.

  • 224.
    Kum, Cletus Kwa
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Thorburn, Daniel
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Ghilagaber, Gebrenegus
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Gil, Perdo
    Björkman, Anders
    On the Effects of Malaria Treatment on Parasite Drug Resistance: Probability Modelling of Genotyped Malaria Infections2013Inngår i: The International Journal of Biostatistics, ISSN 1557-4679, E-ISSN 1557-4679, Vol. 9, nr 1, s. 135-148Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We compare the frequency of resistant genes of malaria parasites before treatment and at first malaria incidence after treatment. The data come from a clinical trial at two health facilities in Tanzania and concerns single nucleotide polymorphisms (SNPs) at three positions believed to be related to resistance to malaria treatment. A problem is that mixed infections are common, which both obscures the underlying frequency of alleles at each locus as well as the associations between loci in samples where alleles are mixed. We use combinatorics and quite involved probability methods to handle multiple infections and multiple haplotypes. The infection with the different haplotypes seemed to be independent of each other. We showed that at two of the three studied SNPs, the proportion of resistant genes had increased after treatment with sulfadoxine-pyrimethamine alone but when treated in combination with artesunate, no effect was noticed. First recurrences of malaria associated more with sulfadoxine-pyrimethamine alone as treatment than when in combination with artesunate. We also found that the recruited children had two different ongoing malaria infections where the parasites had different gene types.

  • 225.
    Kum, Cletus Kwa
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Thorburn, Daniel
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Ghilagaber, Gebrenegus
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Pedro, Gil
    Björkman, Anders
    A Nonparametric Bayesian Approach to Estimating Malaria Prophylactic Effect After Two Treatments2013Inngår i: International Journal of Statistics in Medical Research, ISSN 1929-6029, Vol. 2, nr 2, s. 76-87Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Two treatment regimens for malaria are compared in their abilities to cure and combat reinfection. Bayesian analysis techniques are used to compare two typical treatment therapies for uncomplicated malaria in children under five years, not only in their power to resist recrudescence, but also how long they can postpone recrudescence or reinfection in case of failure. We present a new way of analysing this type of data using Markov Chain Monte Carlo techniques. This is done using data from clinical trials at two different centres. The results which give the full posterior distributions show that artemisinin-based combination therapy is more efficacious than sulfadoxine-pyrimethamine. It both reduced the risk of recrudescence and delayed the time until recrudescence.

  • 226.
    Lagerås, Andreas Nordvall
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematisk statistik.
    A population model for $\Lambda$-coalescents with neutral mutations2007Inngår i: Electronic Communications in Probability, ISSN 1083-589X, Vol. 12, s. 9-20Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $\Lambda$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by Möhle (2007).

  • 227. Lakens, Daniel
    et al.
    Nilsonne, Gustav
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Stressforskningsinstitutet. Karolinska Institutet, Sweden; Stanford University, USA.
    Swaan, Rolf A.
    Justify your alpha2018Inngår i: Nature Human Behaviour, ISSN 2397-3374, Vol. 2, nr 3, s. 168-171Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In response to recommendations to redefine statistical significance to P ≤ 0.005, we propose that researchers should transparently report and justify all choices they make when designing a study, including the alpha level.

  • 228. Lantos, Paul M.
    et al.
    Hoffman, Kate
    Höhle, Michael
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Anderson, Benjamin
    Gray, Gregory C.
    Are People Living Near Modern Swine Production Facilities at Increased Risk of Influenza Virus Infection?2016Inngår i: Clinical Infectious Diseases, ISSN 1058-4838, E-ISSN 1537-6591, Vol. 63, nr 12, s. 1558-1563Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Background

    Swine can harbor influenza viruses that are pathogenic to humans. Previous studies support an increased risk of human influenza cases among individuals with swine contact. North Carolina has the second-largest swine industry in the United States.

    Methods

    We investigated the spatiotemporal association between influenza-like illnesses (ILIs) and licensed swine operations from 2008 to 2012 in North Carolina. We determined the week in which ILI cases peaked and statistically estimated their week of onset. This was performed for all 100 North Carolina counties for 4 consecutive influenza seasons. We used linear models to correlate the number of permitted swine operations per county with the weeks of onset and peak ILI activity.

    Results

    We found that during the 2009–2010 and 2010–2011 influenza seasons, both seasons in which the pandemic 2009 H1N1 influenza A virus circulated, ILI peaked earlier in counties with a higher number of licensed swine operations. We did not observe this in 2008–2009 or 2011–2012, nor did we observe a relationship between ILI onset week and number of swine operations.

    Conclusions

    Our findings suggest that concentrated swine feeding operations amplified transmission of influenza during years in which H1N1 was circulating. This has implications for vaccine strategies targeting swine workers, as well as virologic surveillance in areas with large concentrations of swine.

  • 229.
    Li, Feng
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Bayesian Modeling of Conditional Densities2013Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis develops models and associated Bayesian inference methods for flexible univariate and multivariate conditional density estimation. The models are flexible in the sense that they can capture widely differing shapes of the data. The estimation methods are specifically designed to achieve flexibility while still avoiding overfitting. The models are flexible both for a given covariate value, but also across covariate space. A key contribution of this thesis is that it provides general approaches of density estimation with highly efficient Markov chain Monte Carlo methods. The methods are illustrated on several challenging non-linear and non-normal datasets.

    In the first paper, a general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student-t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. The second paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables. In the third paper we propose a multivariate Gaussian surface regression model that combines both additive splines and interactive splines, and a highly efficient MCMC algorithm that updates all the multi-dimensional knot locations jointly. We use shrinkage priors to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. In the last paper we present a general Bayesian approach for directly modeling dependencies between variables as function of explanatory variables in a flexible copula context. In particular, the Joe-Clayton copula is extended to have covariate-dependent tail dependence and correlations. Posterior inference is carried out using a novel and efficient simulation method. The appendix of the thesis documents the computational implementation details.

  • 230.
    Li, Feng
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Modeling Covariate-Contingent Correlation  and Tail-Dependence with CopulasManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Copula functions give an approach of constructing multivariate densities with  flexible combinations of distinct marginal distributions and also measures  degrees of dependence in the tail and correlations of the marginal  distributions via a novel strategy. Nevertheless common approaches of  estimating tail dependence and correlations are through nuisance parameters  which yields the final results neither tractable nor interpretable for  practitioners. In this paper we address the problem by presenting a general  Bayesian approach for directly modeling covariate-linked tail dependence and  correlations. Posterior inference is carried out using a novel and efficient  simulation method.

  • 231.
    Li, Feng
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Villani, Mattias
    Efficient Bayesian Multivariate Surface Regression2013Inngår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 40, nr 4, s. 706-723Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they are likely to be less successful in that setting because of the curse of dimensionality, especially when there are more than a couple of covariates. We propose a regression model for a multivariate Gaussian response that combines both additive splines and interactive splines, and a highly efficient MCMC algorithm that updates all the multivariate knot locations jointly. We use shrinkage priors to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. This makes it possible for the model to adapt to varying degrees of nonlinearity in different parts of the data in a parsimonious way. Simulated data and an application to firm leverage data show that the approach is computationally efficient, and that allowing for freely estimated knot locations can offer a substantial improvement in out-of-sample predictive performance.

  • 232.
    Li, Feng
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Kohn, Robert
    Flexible Modeling of Conditional Distributions using Smooth Mixtures of Asymmetric Student T Densities2010Inngår i: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, nr 12, s. 3638-3654Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A general model is proposed for flexibly estimating the density of a continuous response variableconditional on a possibly high-dimensional set of covariates. The model is a finite mixture ofasymmetric student-t densities with covariate-dependent mixture weights. The four parameters ofthe components, the mean, degrees of freedom, scale and skewness, are all modeled as functionsof the covariates. Inference is Bayesian and the computation is carried out using Markov chainMonte Carlo simulation. To enable model parsimony, a variable selection prior is used in each setof covariates and among the covariates in the mixing weights. The model is used to analyze thedistribution of daily stock market returns, and shown to more accurately forecast the distributionof returns than other widely used models for financial data.

  • 233.
    Li, Feng
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Kohn, Robert
    Modeling Conditional Densities using Finite Smooth Mixtures2011Inngår i: Mixtures: Estimation and Applications / [ed] Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington, Chichester: John Wiley & Sons, 2011, , s. 20s. 123-144Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights,are very useful flexible models for conditional densities. Previous work shows that using toosimple mixture components for modeling heteroscedastic and/or heavy tailed data can givea poor fit, even with a large number of components. This paper explores how well a smoothmixture of symmetric components can capture skewed data. Simulations and applications onreal data show that including covariate-dependent skewness in the components can lead tosubstantially improved performance on skewed data, often using a much smaller number ofcomponents. Furthermore, variable selection is effective in removing unnecessary covariates inthe skewness, which means that there is little loss in allowing for skewness in the componentswhen the data are actually symmetric. We also introduce smooth mixtures of gamma andlog-normal components to model positively-valued response variables.

  • 234.
    Liang, Yuli
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A study of multilevel models with block circular  symmetric covariance structures2011Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis concerns the study of multilevel models with specific patterned covariance structures and addresses the issues of maximum likelihoodestimation. In particular, circular symmetric hierarchical datastructures are considered.

    In the first paper (Paper I), we consider so-called dihedral block symmetrymodels and extend them to models which covariance structures reflects both circularity and exchangeability present in the data. The main contribution of Paper I are two derived patterns of the covariancematrices which characterizes models under consideration. The relationship between these two patterned covariance matrices was investigatedand it has been verified they are similar matrices. New expressions for the eigenvalues of block circular symmetric matrices are obtained which take into account the block structure. Paper II deals with estimation ofbalanced multilevel models with block circular symmetric covariance matrices. The spectral properties of such patterned covariance matrices are established. Maximum likelihood estimation is considered through the spectral decomposition of the patterned covariance matrix. The main results of Paper II concern the spectrum of the covariance matrix inthe model of interest and the existence of explicit maximum likelihood estimators for the covariance parameters.

  • 235.
    Liang, Yuli
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Contributions to Estimation and Testing Block Covariance Structures in Multivariate Normal Models2015Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis concerns inference problems in balanced random effects models with a so-called block circular Toeplitz covariance structure. This class of covariance structures describes the dependency of some specific multivariate two-level data when both compound symmetry and circular symmetry appear simultaneously.

    We derive two covariance structures under two different invariance restrictions. The obtained covariance structures reflect both circularity and exchangeability present in the data. In particular, estimation in the balanced random effects with block circular covariance matrices is considered. The spectral properties of such patterned covariance matrices are provided. Maximum likelihood estimation is performed through the spectral decomposition of the patterned covariance matrices. Existence of the explicit maximum likelihood estimators is discussed and sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and the corresponding maximum likelihood estimators are presented.

    This thesis also deals with hypothesis testing of block covariance structures, especially block circular Toeplitz covariance matrices. We consider both so-called external tests and internal tests. In the external tests, various hypotheses about testing block covariance structures, as well as mean structures, are considered, and the internal tests are concerned with testing specific covariance parameters given the block circular Toeplitz structure. Likelihood ratio tests are constructed, and the null distributions of the corresponding test statistics are derived.

  • 236.
    Liang, Yuli
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    På väg att lära sig statistik2014Inngår i: Qvintense, ISSN 2000-1819, Vol. 3, s. 6-7Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
  • 237.
    Liang, Yuli
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    Tatjana, von Rosen
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    On estimation in multilevel models with block circular symmetric covariance structure2012Inngår i: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 16, nr 1, s. 83-96Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

  • 238.
    Liang, Yuli
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    On estimation in hierarchical models with block circular covariance structures2015Inngår i: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 67, nr 4, s. 773-791Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance–covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented. The theory is illustrated through covariance matrices of small sizes and a real-life example.

  • 239.
    Liang, Yuli
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Testing in multivariate normal models with block circular covariance structures2015Rapport (Annet vitenskapelig)
    Abstract [en]

    In this article, the results concerning hypothesis testing in multivariate normal models with block circular covariance structures are obtained. Hypotheses about a general block structure of the covariance matrix and specific covariance parameters have been of main interest. In addition, the tests about patterned mean vectors have been considered.The corresponding likelihood ratio statistics are derived and their null distributions are studied.

  • 240.
    Liang, Yuli
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    Block Circular Symmetry in Multilevel Models2011Rapport (Annet vitenskapelig)
    Abstract [en]

    Models that describe symmetries present in the error structure of observations have been widely used in dierent applications, with early examples from psychometric and medical research. The aim of this article is to study a multilevel model with a covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

  • 241.
    Liang, Yuli
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Tatjana
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, Dietrich
    The Department of Energy and Technology, SLU.
    Estimation in multilevel models with block circular symmetric covariance structure2011Rapport (Annet vitenskapelig)
    Abstract [en]

    In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

  • 242.
    Lindberg, Mattias
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Guban, Peter
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Auxiliary variables a weight against nonresponse bias: A simulation study2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    Today’s surveys face a growing problem with increasing nonresponse.  The increase in nonresponse rate causes a need for better and more effective ways to reduce the nonresponse bias.  There are three major scientific orientation of today’s research dealing with nonresponse. One is examining the social factors, the second one studies different data collection methods and the third investigating the use of weights to adjust estimators for nonresponse.  We would like to contribute to the third orientation by evaluating estimators which use and adjust weights based on auxiliary variables to balance the survey nonresponse through simulations. For the simulation we use an artificial population consisting of 35455 participants from the Representativity Indicators for Survey Quality project. We model three nonresponse mechanisms (MCAR, MAR and MNAR) with three different coefficient of determination s between our study variable and the auxiliary variables and under three response rates resulting in 63 simulation scenarios. The scenarios are replicated 1000 times to acquire the results. We outline our findings and results for each estimator in all scenarios with the help of bias measures.

  • 243.
    Lindell, Andreas
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Theoretical and Practical Applications of Probability: Excursions in Brownian Motion, Risk Capital Stress Testing, and Hedging of Power Derivatives2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The thesis treats three different areas; (i) Ranked increments of stable processes and ranked excursions of Brownian motion, (ii) Sufficient capital levels for banks, and (iii) Trading strategies for reduction of the fluctuations of revenues for power plants.

    The first part is a theoretcial investigation involved with the calculation of distribution functions concerning special properties of stable processes.

    The second part is a description of a framework in which the sufficiency of capital levels for banks can be evaluated.

    The third part is a typical example of how financial mathematics can be used to derive practical methods applicable in risk management of energy derivatives and real options.

    Altogether, five papers are presented.

  • 244.
    Lindensjö, Kristoffer
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A regular equilibrium solves the extended HJB systemManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A fundamental result of time-inconsistent stochastic control is a verification theorem saying that solving the extended HJB system is a sufficient condition for equilibrium. We show that solving the extended HJB system is a necessary condition for equilibrium, under regularity assumptions. The controlled process is a general Itô diffusion.

  • 245.
    Lindensjö, Kristoffer
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Constructive martingale representation in functional Itô calculus: a local martingale extension2018Inngår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer , 2018, s. 165-172Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    The constructive martingale representation theorem of functional Itô cal-culus is extended, from the space of square integrable martingales, to the space of local martingales. The setting is that of an augmented filtration generated by a Wiener process.

  • 246.
    Lindenstrand, David
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Stochastic epidemic models in heterogeneous communities2012Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The aim of Paper I is to explain where randomness should be taken into account when modelling epidemic spread, i.e. when a stochastic model is preferable to a deterministic counterpart. Two examples are used to show that the probability of a large outbreak and the initial growth rate of the epidemic are affected by randomness in infectious period and latent period. It follows that the basic reproduction number is sensitive to assumptions about the distributions of the infectious and latent periods when using data from the early stages of an outbreak, which we illustrate with data from the H1N1 influenza A pandemic. In paper II we analyse an open population stochastic epidemic S-I-S model.  That is, individuals in the population move between the states of infectiousness and susceptibility, and enter of leave the population through birth and death. An approximate expression for the outbreak probability is derived using a coupling argument. It is proved that the number of infectives and susceptibles close to quasi-stationarity behaves like an Ornstein-Uhlenbeck process, for an exponentially distributed time before going extinct. In Paper III we analyse an estimator, based on martingale methods, of the Malthusian parameter, which determines the speed of epidemic spread. Asymptotic properties of the estimator are obtained, and compared to the results from simulations. The advantage of the estimator is that it may use any proportion of the information contained in the epidemic curve, in contrast to the more common simpler estimators. In paper IV a social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights. The aim is to analyse how individual heterogeneity in susceptibility and infectivity affects the basic reproduction number, but also the size and probability of a major outbreak. The main qualitative conclusion is that the basic reproduction number gets larger as the community becomes more heterogeneous.

  • 247.
    Lindenstrand, David
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Britton, Tom
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Inhomogeneous epidemics on weighted networksArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such that individuals are heterogeneous in terms of how susceptible and infectious they are. The basic reproduction number R_0 is derived and studied for various examples, but also the size and probability of a major outbreak. The qualitative conclusion is that R_0 gets larger as the community becomes more heterogeneous but that different heterogeneities (degree distribution, weight, susceptibility and infectivity can sometimes have the cumulative effect of homogenizing the community, thus making R_0 smaller. The effect on the probability and final size of an outbreak is more complicated.

  • 248.
    Lindenstrand, David
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Svensson, Åke
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Estimation of the Malthusian parameter using martingale methodsArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Data gathered from a large epidemic outbreak can be used to estimate disease related parameters. We analyse an estimate, based on martingale methods, of the Malthusian parameter, which determines the growth rate of the epidemic. This is done using a simple epidemic SIR model, with deterministic infectious period. We derive asymptotic properties of the estimate and compare them to the results from simulations of the epidemic. The advantage of our estimate is that is uses all the information contained in the epidemic curve, in contrast to the more common simpler estimates which uses only data from the start of the outbreak. The theoretical and numerical results show this in that the variance of the estimate decreases the more data we use.

  • 249.
    Lindholm, Mathias
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Stochastic Epidemic Models: Different Aspects of Heterogeneity2008Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis is concerned with the study of stochastic epidemic models for infectious diseases in heterogeneous populations. All diseases treated are of SIR type, i.e. individuals are either Susceptible, Infectious or Recovered (and immune). The transitions between these states are according to S to I to R.

    The thesis consists of five papers. Papers I and II treat approximations for the distribution of the time to extinction. In Paper I, a sub-community version of the SIR model with demography is considered. The interest is in how the distribution of the time to extinction is affected by varying the degree of interaction between the sub-communities. Paper II is concerned with a two-type version of Bartlett's model. The distribution of the time to extinction is studied when the difference in susceptibility/infectivity between the types of individuals is varied.

    Papers III and IV treat random intersection graphs with tunable clustering. In Paper III a Reed-Frost epidemic is run on such a random intersection graph. The critical parameter R_0 and the probability of a large outbreak are derived and it is investigated how these quantities are affected by the clustering in the graph. In Paper IV the interest is in the component structure of such a graph, i.e. the size and the emergence of a giant component is studied.

    The last paper, Paper V, treats the situation when a simple epidemic is running in a varying environment. A varying environment is in this context any external factor that affects the contact rate in the population, but is itself unaffected by the population. The model treated is a term-time forced version of the stochastic general epidemic where the contact rate is modelled by an alternating renewal process. A threshold parameter R_* and the probability of a large outbreak are derived and studied.

  • 250.
    Lodén, Kerstin
    Stockholms universitet.
    A statistical investigation of tangential velocities in selected areas.1963Doktoravhandling, med artikler (Annet vitenskapelig)
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