| 1. |
- Berglund, Daniel
(författare)
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Models for Additive and Sufficient Cause Interaction
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this thesis is to develop and explore models in, and related to, the sufficient cause framework, and additive interaction. Additive interaction is closely connected with public health interventions and can be used to make inferences about the sufficient causes in order to find the mechanisms behind an outcome, for instance a disease.In paper A we extend the additive interaction, and interventions, to include continuous exposures. We show that there does not exist a model that does not lead to inconsistent conclusions about the interaction.The sufficient cause framework can also be expressed using Boolean functions, which is expanded upon in paper B. In this paper we define a new model based on the multifactor potential outcome model (MFPO) and independence of causal influence models (ICI).In paper C we discuss the modeling and estimation of additive interaction in relation to if the exposures are harmful or protective conditioned on some other exposure. If there is uncertainty about the effects direction there can be errors in the testing of the interaction effect.
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| 2. |
- Ohlson, Martin, 1977-
(författare)
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Studies in Estimation of Patterned Covariance Matrices
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Many testing, estimation and confidence interval procedures discussed in the multivariate statistical literature are based on the assumption that the observation vectors are independent and normally distributed. The main reason for this is that often sets of multivariate observations are, at least approximately, normally distributed. Normally distributed data can be modeled entirely in terms of their means and variances/covariances. Estimating the mean and the covariance matrix is therefore a problem of great interest in statistics and it is of great significance to consider the correct statistical model. The estimator for the covariance matrix is important since inference on the mean parameters strongly depends on the estimated covariance matrix and the dispersion matrix for the estimator of the mean is a function of it.In this thesis the problem of estimating parameters for a matrix normal distribution with different patterned covariance matrices, i.e., different statistical models, is studied.A p-dimensional random vector is considered for a banded covariance structure reflecting m-dependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m.Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on numerical optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linearly structured covariance matrix.This thesis also deals with the problem of estimating the Kronecker product structure. The sample observation matrix is assumed to follow a matrix normal distribution with a separable covariance matrix, in other words it can be written as a Kronecker product of two positive definite matrices. The proposed estimators are used to derive a likelihood ratio test for spatial independence. Two cases are considered, when the temporal covariance is known and when it is unknown. When the temporal covariance is known, the maximum likelihood estimates are computed and the asymptotic null distribution is given. In the case when the temporal covariance is unknown the maximum likelihood estimates of the parameters are found by an iterative alternating algorithm and the null distribution for the likelihood ratio statistic is discussed.
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| 3. |
- Källberg, David, 1982-
(författare)
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Nonparametric Statistical Inference for Entropy-type Functionals
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we study statistical inference for entropy, divergence, and related functionals of one or two probability distributions. Asymptotic properties of particular nonparametric estimators of such functionals are investigated. We consider estimation from both independent and dependent observations. The thesis consists of an introductory survey of the subject and some related theory and four papers (A-D).In Paper A, we consider a general class of entropy-type functionals which includes, for example, integer order Rényi entropy and certain Bregman divergences. We propose U-statistic estimators of these functionals based on the coincident or epsilon-close vector observations in the corresponding independent and identically distributed samples. We prove some asymptotic properties of the estimators such as consistency and asymptotic normality. Applications of the obtained results related to entropy maximizing distributions, stochastic databases, and image matching are discussed.In Paper B, we provide some important generalizations of the results for continuous distributions in Paper A. The consistency of the estimators is obtained under weaker density assumptions. Moreover, we introduce a class of functionals of quadratic order, including both entropy and divergence, and prove normal limit results for the corresponding estimators which are valid even for densities of low smoothness. The asymptotic properties of a divergence-based two-sample test are also derived.In Paper C, we consider estimation of the quadratic Rényi entropy and some related functionals for the marginal distribution of a stationary m-dependent sequence. We investigate asymptotic properties of the U-statistic estimators for these functionals introduced in Papers A and B when they are based on a sample from such a sequence. We prove consistency, asymptotic normality, and Poisson convergence under mild assumptions for the stationary m-dependent sequence. Applications of the results to time-series databases and entropy-based testing for dependent samples are discussed.In Paper D, we further develop the approach for estimation of quadratic functionals with m-dependent observations introduced in Paper C. We consider quadratic functionals for one or two distributions. The consistency and rate of convergence of the corresponding U-statistic estimators are obtained under weak conditions on the stationary m-dependent sequences. Additionally, we propose estimators based on incomplete U-statistics and show their consistency properties under more general assumptions.
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| 4. |
- Zickert, Gustav
(författare)
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Analytic and data-driven methods for 3D electron microscopy
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The central theme of this thesis is theoretical and algorithmic aspects of 3D electron microscopy (3D-EM). In particular, the thesis explores three parts of this theme. The first part concerns analysis of forward operators that, compared to those traditionally used, better account for the wave properties of the imaging electron. The second part concerns the adoption of data-driven methods in 3D-EM. The third part concerns the use of Gaussian dictionaries in image decomposition and image reconstruction.The thesis consists primarily of five papers, which are preceded by two introductory chapters. The first chapter provides a background for the thesis and the second one constitutes a summary of the papers.In paper A we propose a fast non-linear reconstruction method for joint phase-retrieval and image reconstruction in cryo electron tomography. We evaluate the method on simulated and real data. In paper B we train a deep convolutional neural network on a database of previously determined molecular structures. This network is used to model a prior distribution in single particle analysis (SPA) within a maximum-a-posteriori framework. We show in a simulation study that the proposed method is able to significantly improve on one of the current state-of-the-art methods.In paper C we propose a greedy method for decomposing a signal as a mixture of Gaussians. We also derive an upper bound for the distance from any local maximum of a Gaussian mixture to the set of mean vectors.In paper D we generalise the method in paper C and introduce an algorithm for reconstructing a mixture of Gaussians from its ray-transform projection images. We also derive exact and approximate expressions for the Riesz potential of isotropic and anisotropic Gaussians, respectively.In paper E we prove a uniqueness theorem for an Ewald sphere corrected model for SPA. The theorem shows that accounting for a non-zero curvature of the Ewald sphere renders the noise-free SPA problem uniquely solvable, including the hand of the structure.
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| 5. |
- Hallgren, Jonas
(författare)
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Continuous time Graphical Models and Decomposition Sampling
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Two topics in temporal graphical probabilistic models are studied. The topics are treated in separate papers, both with applications in finance. The first paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model and some toy examples with promising results. The second paper treats probabilistic graphical models in continuous time —a class of models with the ability to express causality. Tools for inference in these models are developed and employed in the design of a causality measure. The framework is used to analyze tick-by-tick data from the foreign exchange market.
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| 6. |
- Hallgren, Jonas
(författare)
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Inference in Temporal Graphical Models
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis develops mathematical tools used to model and forecast different economic phenomena. The primary starting point is the temporal graphical model. Four main topics, all with applications in finance, are studied.The first two papers develop inference methods for networks of continuous time Markov processes, so called Continuous Time Bayesian Networks. Methodology for learning the structure of the network and for doing inference and simulation is developed. Further, models are developed for high frequency foreign exchange data.The third paper models growth of gross domestic product (GDP) which is observed at a very low frequency. This application is special and has several difficulties which are dealt with in a novel way using a framework developed in the paper. The framework is motivated using a temporal graphical model. The method is evaluated on US GDP growth with good results.The fourth paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model for stock prices and some toy examples with promising results.The fifth paper develops an algorithm for learning the full distribution in a harness race, a ranked event. It is demonstrated that the proposed methodology outperforms logistic regression which is the main competitor. It also outperforms the market odds in terms of accuracy.
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| 7. |
- Saize, Stefane, 1984-
(författare)
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Contributions to reciprocal processes
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Reciprocal processes are stochastic processes such that the current state only depends on the nearest past and future, and they have found many applications in various fields such as Euclidean quantum physics. This thesis focuses on the study of some classes of reciprocal processes in both discrete-time and continuous-time frameworks. The main contributions of this thesis can be splitted into two parts. The first and major part of this thesis consists of the study of several discrete-time reciprocal processes: reciprocal chains, hidden Markov models (HMMs) and hidden reciprocal models (HRMs). More specifically, we (i) formally define reciprocal chains and explore their properties and similarities/differences to Markov chains; (ii) point out that one of the three most commonly used definitions of HMMs has fatal flaws and list some key properties of HMMs; (iii) present the connections between undirected graphical models and HMMs/reciprocal chains; (iv) learn and compare HMMs and HRMs parameters based on the expectation-maximization algorithm. The second part of the thesis focuses on the study of Brownian bridges with pre-scribed terminal densities which are special continuous-time reciprocal processes. We derive large deviations for the family of Brownian bridges with the help of Girsanov transformation.
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