Vehicle tracking in environments containing occlusion and clutter is an active research area. The problem of tracking vehicles through such environments presents a variety of challenges. These challenges include vehicle track initialization, tracking an unknown number of targets and the variations in real-world lighting, scene conditions and camera vantage. Scene clutter and target occlusion present additional challenges. A stochastic framework is proposed which allows for vehicles tracks to be identified from a sequence of images. The work focuses on the identification of vehicle tracks present in transportation scenes, namely, vehicle movements at intersections. The framework combines background subtraction and motion history based approaches to deal with the segmentation problem. The tracking problem is solved using a Monte Carlo Markov Chain Data Association (MCMCDA) method. The method includes a novel concept of including the notion of discrete, independent regions in the MCMC scoring function. Results are presented which show that the framework is capable of tracking vehicles in scenes containing multiple vehicles that occlude one another, and that are occluded by foreground scene objects.

No description available.

The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

This thesis presents several aspects of simulation-based point estimation in the context of Bayesian decision theory. The first part of the thesis (Chapters 4 - 5) concerns the estimation-then-minimisation (ETM) method as an efficient computational approach to compute simulation-based Bayes estimates. We are interested in applying the ETM method to compute Bayes estimates under some non-standard loss functions. However, for some loss functions, the ETM method cannot be implemented straightforwardly. We examine the ETM method via Taylor approximations and cubic spline interpolations for Bayes estimates in one dimension. In two dimensions, we implement the ETM method via bicubic interpolation. The second part of the thesis (Chapter 6) concentrates on the analysis of a mixture posterior distribution with a known number of components using the Markov chain Monte Carlo (MCMC) output. We aim for Bayesian point estimation related to a label invariant loss function which allows us to estimate the parameters in the mixture posterior distribution without dealing with label switching. We also investigate uncertainty of the point estimates which is presented by the uncertainty bound and the crude uncertainty bound of the expected loss evaluated at the point estimates based on MCMC samples. The crude uncertainty bound is relatively cheap, but it seems to be unreliable. On the other hand, the uncertainty bound which is approximated a 95% confidence interval seems to be reliable, but are very computationally expensive. The third part of the thesis (Chapter 7), we propose a possible alternative way to present the uncertainty for Bayesian point estimates. We adopt the idea of leaving out observations from the jackknife method to compute jackknife-Bayes estimates. We then use the jackknife-Bayes estimates to visualise the uncertainty of Bayes estimates. Further investigation is required to improve the method and some suggestions are made to maximise the efficiency of this approach.

"We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic. In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once. We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution."

The purpose of this thesis is to explore methodology concerning Markov Chain Monte Carlo (MCMC), a powerful technique in the Bayesian framework, on binary variables. The primary application of interest in this thesis is applying this methodology to phase haplotypes, a type of categorical variable. Haplotypes are the combination of variants present in an individual’s genome. Phasing refers to estimating the true haplotype. By considering only biallelic and heterozygous variants, the haplotype can be expressed as a vector of binary variables. Accounting for differences in haplotypes is essential for the study of associations between genotype and disease. MCMC is an extremely popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. Techniques for sampling categorical variables in MCMC have been developed in a variety of disparate settings. Samplers include Gibbs, Metropolis-Hastings, and exact Hamiltonian based samplers. A review of these techniques is presented and their relevance to the genetic model discussed. An important consideration in using simulated MCMC draws for inference is that they have converged to the distribution of interest. Since the distribution is typically of a non-standard form, convergence cannot generally be proven and, instead, is assessed with convergence diagnostics. The convergence diagnostics developed so far focus on continuous variables and may be inappropriate for binary variables or categorical variables in general. Two convergence diagnostics are proposed that are tailor-made for categorical variables by modeling the data using categorical time series models. Performance of the convergence diagnostics is evaluated under various simulations. The methodology developed in the thesis is applied to estimate haplotypes. There are two main challenges involved in accounting for haplotype differences. One is estimating the true combination of genetic variants on a single chromosome, known as haplotype phasing. The other is the phenomenon of allele-specific expression (ASE) in which haplotypes can be expressed non-equally. No existing method addresses these two intrinsically linked challenges together. Rather, current strategies rely on known haplotypes or family trio data, i.e. having data on subject of interest and their parents. A novel method is presented, named IDP-ASE, which is capable of phasing haplotypes and quantifying ASE using only RNA-seq data. This model leverages the strengths of both Second Generation Sequencing (SGS) data and Third Generation Sequencing (TGS) data. The long read length of TGS data facilitates phasing, while the accuracy and depth of SGS data facilitates estimation of ASE. Moreover, IDP-ASE is capable of estimating ASE at both the gene and isoform level.

This dissertation quantitatively evaluates selected labor market policies in a search-matching model with skill heterogeneity where high-skilled workers can take temporary jobs with skill requirements below their skill levels. The joint posterior distribution of structural parameters of the theoretical model is obtained conditional on the data on labor markets histories of the NLSY79 respondents. The information on AFQT scores of individuals and the skill requirements of occupations is utilized to identify the skill levels of workers and complexity levels of jobs in the job-worker matches realized in the data. The model and the data are used to simulate the posterior distributions of impacts of labor market policies on the endogenous variables of interest to a policy-maker, including unemployment rates, durations and wages of low- and high-skilled workers. In particular, the effects of the following policies are analyzed: increase in proportion of high-skilled workers, subsidies for employing or hiring high- and low-skilled workers and increase in unemployment income.

Language diversi cation is a stochastic process which presents similarities with phylogenetic evolution. Recently, there has been interest in modelling this process to help solve problems which traditional linguistic methods cannot resolve. The problem of estimating and quantifying the uncertainty in the age of the most recent common ancestor of the Indo-European languages is an example. We model lexical change by a point process on a phylogenetic tree. Our model is speci cally tailored to lexical data and in particular treats aspects of linguistic change which are hitherto unaccounted for and which could have a strong impact on age estimates: catastrophic rate heterogeneity and missing data. We impose a prior distribution on the tree topology, node ages and other model parameters, give recursions to compute the likelihood and estimate all parameters jointly using Markov Chain Monte Carlo. We validate our methods using an extensive cross-validation procedure, reconstructing known ages of internal nodes. We make a second validation using synthetic data and show that model misspeci cations due to borrowing of lexicon between languages and the presence of meaning categories in lexical data do not lead to systematic bias. We fit our model to two data sets of Indo-European languages and estimate the age of Proto-Indo-European. Our main analysis gives a 95% highest posterior probability density interval of 7110 9750 years Before the Present, in line with the so-called Anatolian hypothesis for the expansion of the Indo- European languages. We discuss why we are not concerned by the famous criticisms of statistical methods for historical linguistics leveled by Bergsland and Vogt [1962]. We also apply our methods to the reconstruction of the spread of Swabian dialects and to the detection of punctuational bursts of language change in the Indo-European family.

This dissertation presents an algorithm to solve optimization problems with "black-box" objective functions, i.e., functions that can only be evaluated by running a computer program. Such optimization problems often arise in engineering applications, for example, the design of sensor placement. Due to the complexity in engineering systems, the objective functions usually have multiple local optima and depend on a huge number of decision variables. These difficulties make many existing methods less effective. The proposed algorithm is called adaptive evolutionary Monte Carlo (AEMC), and it combines sampling-based and metamodel-based search methods. AEMC incorporates strengths from both methods and compensates limitations of each individual method. Specifically, the AEMC algorithm combines a tree-based predictive model with an evolutionary Monte Carlo sampling procedure for the purpose of heuristic optimization. AEMC is able to escape local optima due to the random sampling component, and it improves the quality of solutions quickly by using information learned from the tree-based model. AEMC is also an adaptive Markov chain Monte Carlo (MCMC) algorithm, and is in fact the rst adaptive MCMC algorithm that simulates multiple Markov chains in parallel. The ergodicity property of the AEMC algorithm is studied. It is proven that the distribution of samples obtained by AEMC converges asymptotically to the "target" distribution determined by the objective function. This means that AEMC has a larger probability of collecting samples from regions containing the global optimum than from other regions, which implies that AEMC will reach the global optimum given enough run time. The AEMC algorithm falls into the category of heuristic optimization algorithms, and is applicable to the problems that can be solved by other heuristic methods, such as genetic algorithm. Advantages of AEMC are demonstrated by applying it to a sensor placement problem in a manufacturing process, as well as to a suite of standard test functions. It is shown that AEMC is able to enhance optimization effectiveness and efficiency as compared to a few alternative strategies, including genetic algorithm, Markov chain Monte Carlo algorithms, and meta-model based methods. The effectiveness of AEMC for sampling purposes is also shown by applying it to a mixture Gaussian distribution.

The thesis provides a well-researched classical approach to fit and predict the losses (extreme) for Lloyds Bank’s Dutch mortgage portfolio, their defaulted Dutch mortgage portfolio, and their German personal and car loan portfolio. This is a crucial piece for quantification of the economic loss, required for effective credit risk management by the Bank. For starters, the distribution of losses needs to be defined in order to determine the amount of losses that a bank can possibly experience in an event that corresponds to a specific confidence level. To get to that point, the data needs to be approximated with either one or more distributions, this thesis covers the single distribution approach and the mixture model approach that uses two distributions to solve the approximation of the data. Our work concludes that the optimal distribution for the regular Dutch mortgage portfolio losses include a Beta-Beta mixture and a Lognormal-Gamma mixture. Where the Lognormal-Gamma mixture has utilized a threshold approach that splits the data into two separate data sets and then fits the data separately before combining them with a weight function. While, for the second Dutch mortgage portfolio at the specific snapshots, the Beta and the Generalized Pareto outperformed the rest. Furthermore, for the German personal and car loan portfolio, the Generalized Pareto also performed the best. This is a crucial step for calculating the necessary economic capital that Lloyds Banking Group plans to do in the near future.