Understanding the content of a video sequence is not a particularly difficult problem for humans. We can easily identify objects, such as people, and track their position and pose within the 3D world. A computer system that could understand the world through videos would be extremely beneficial in applications such as surveillance, robotics, biology. Despite significant advances in areas like tracking and, more recently, 3D static scene understanding, such a vision system does not yet exist. In this work, I present progress on this problem, restricted to videos of objects that move in smoothly and which are relatively easily detected, such as people. Our goal is to identify all the moving objects in the scene and track their physical state (e.g., their 3D position or pose) in the world throughout the video. We develop a Bayesian generative model of a temporal scene, where we separately model data association, the 3D scene and imaging system, and the likelihood function. Under this model, the video data is the result of capturing the scene with the imaging system, and noisily detecting video features. This formulation is very general, and can be used to model a wide variety of scenarios, including videos of people walking, and time-lapse images of pollen tubes growing in vitro. Importantly, we model the scene in world coordinates and units, as opposed to pixels, allowing us to reason about the world in a natural way, e.g., explaining occlusion and perspective distortion. We use Gaussian processes to model motion, and propose that it is a general and effective way to characterize smooth, but otherwise arbitrary, trajectories. We perform inference using MCMC sampling, where we fit our model of the temporal scene to data extracted from the videos. We address the problem of variable dimensionality by estimating data association and integrating out all scene variables. Our experiments show our approach is competitive, producing results which are comparable to state-of-the-art methods.

Individual-level models are a class of complex statistical models, often fitted within a Bayesian Markov chain Monte Carlo framework, that have been effectively used to model the spread of infectious diseases. The ability of these models to incorporate individual-level covariate information allows them to be highly flexible, and to account for such characteristics as population heterogeneity. However, these models can be subject to inherent uncertainties often found in infectious disease data. As well, their complex nature can lead to a significant computational expense when fitting these models to epidemic data, particularly for large populations. An individual-level model that incorporates a latent grouping structure into the modeling procedure, based on some heterogeneous population characteristics, is investigated. The dependence of this latent conditional individual-level model on a discrete latent grouping variable alleviates the need for explicit, although possibly unreliable, covariate information. A simulation study is used to assess the posterior predictive ability of this model, in comparison to individual-level models that utilize the full covariate information, or that assume population homogeneity. These models are also applied to data from the 2001 UK foot-and-mouth disease epidemic. When attempting to compare complex models fitted within the Bayesian framework, the identification of appropriate model selection tools would be beneficial. The use of deviance information criterion (DIC) as model comparison tool, particularly for the latent conditional individual-level models, is investigated. A simulation study is used to compare five variants of the DIC, and the ability of each DIC variant to select the true model is determined. Finally, an investigation into methods to reduce the computational burden associated with individual-level models is carried out, based on an individual-level model that also incorporates population heterogeneity through a discrete grouping variable. A simulation study is used to determine the effect of reducing the overall population size by aggregating the data into spatial clusters. Reparameterized individual-level models, accounting for the aggregation effect, are fitted to the aggregated data. The effect of data aggregation on the ability of two reparameterized individual-level models to identify a covariate effect, as well as on the computational expense of the model fitting procedure, is explored.

Individual-level models (ILMs) are models that can use the spatial-temporal nature of disease data to capture the disease dynamics. Parameter estimation is usually done via Markov chain Monte Carlo (MCMC) methods, but correlation between model parameters negatively affects MCMC mixing. Introducing a normalization constant to alleviate the correlation results in MCMC convergence over fewer iterations, however this negatively effects computation time. It is important that model fitting is done as efficiently as possible. An upper-truncated distance kernel is introduced to quicken the computation of the likelihood, but this causes a loss in goodness-of-fit. The normalization constant and upper-truncated distance kernel are evaluated as components in various ILMs via a simulation study. The normalization constant is seen not to be worthwhile, as the effect of increased computation time is not outweighed by the reduced correlation. The upper-truncated distance kernel reduces computation time but worsens model fit as the truncation distance decreases. / Studies have been funded by OMAFRA & NSERC, with computing equipment provided by CSI.

The objectives of this study were to 1) evaluate marker associations for genomic regions of interest and significant ontology terms, 2) evaluate and compare 4 models for their efficacy in predicting genetic merit, 3) evaluate and compare the impact of using breed-of-origin genotypes in a Bayesian prediction model, and 4) evaluate the effects of data partitioning using family structure on predictions. Nellore-Angus F2, F3 and half-sibling calves were used with records for overall temperament at weaning (OTW; a subjective scoring system; n = 769) and Warner-Bratzler shear force (WBSF; a measure of tenderness; n = 389). After filtering, 34,913 markers were available for use. Bayesian methods employed were BayesB (using ̂) and BayesC (using π = 0 and ̂) in GenSel software, where, after estimation, π ̂ = 0.995 or 0.997 for WBSF or OTW, respectively. No regions associated with either trait were found using π ̂, but when π = 0 associated regions were identified (37 and 147 regions for OTW and WBSF, respectively). Comparison of genomic estimated breeding values from these 3 Bayesian models to an animal model showed that BayesC procedures (using ̂) had the highest accuracy for both traits, but that BayesB had the lowest indication of bias in either case. Using a subset of the population (n = 440), genotypes based on the breed in which the alleles originated from (i.e., breed-of-origin genotypes) were assigned to markers mapped to autosomes (n = 34,449), and incorporated into prediction analyses using BayesB (π ̂ = 0.997) with or without nucleotide-based genotypes. In either case, there was an increase in accuracy when breed-of-origin genotypes were incorporated into prediction analyses. Data partitions based on family structure resulted in 13 distinct training and validations groups. Relationship of individuals in the training with validation individuals did have an impact in some cases, but not all. There was poor prediction of genomic estimated breeding values for individuals in the validation population using BayesB methods, but performed better in all cases than breeding values generated using an animal model. Future studies incorporating breed-of-origin genotypes are of interest to determine if accuracy is improved in these groups.

Transfer Learning is an emerging framework for learning from data that aims at intelligently transferring information between tasks. This is achieved by developing algorithms that can perform multiple tasks simultaneously, as well as translating previously acquired knowledge to novel learning problems. In this thesis, we investigate the application of Gaussian Processes to various forms of transfer learning with a focus on classification problems. This process initiates with a thorough introduction to the framework of Transfer learning, providing a clear taxonomy of the areas of research. Following that, we continue by reviewing the recent advances on Multi-task learning for regression with Gaussian processes, and compare the performance of some of these methods on a real data set. This review gives insights about the strengths and weaknesses of each method, which acts as a point of reference to apply these methods to other forms of transfer learning. The main contributions of this thesis are reported in the three following chapters. The third chapter investigates the application of Multi-task Gaussian processes to classification problems. We extend a previously proposed model to the classification scenario, providing three inference methods due to the non-Gaussian likelihood the classification paradigm imposes. The forth chapter extends the multi-task scenario to the semi-supervised case. Using labeled and unlabeled data, we construct a novel covariance function that is able to capture the geometry of the distribution of each task. This setup allows unlabeled data to be utilised to infer the level of correlation between the tasks. Moreover, we also discuss the potential use of this model to situations where no labeled data are available for certain tasks. The fifth chapter investigates a novel form of transfer learning called meta-generalising. The question at hand is if, after training on a sufficient number of tasks, it is possible to make predictions on a novel task. In this situation, the predictor is embedded in an environment of multiple tasks but has no information about the origins of the test task. This elevates the concept of generalising from the level of data to the level of tasks. We employ a model based on a hierarchy of Gaussian processes, in a mixtures of expert sense, to make predictions based on the relation between the distributions of the novel and the training tasks. Each chapter is accompanied with a thorough experimental part giving insights about the potentials and the limits of the proposed methods.

<p>Two-sample comparison is a fundamental problem in statistics. Given two samples of data, the interest lies in understanding whether the two samples were generated by the same distribution or not. Traditional two-sample comparison methods are not suitable for modern data where the underlying distributions are multivariate and highly multi-modal, and the differences across the distributions are often locally concentrated. The focus of this thesis is to develop novel statistical methodology for two-sample comparison which is effective in such scenarios. Tools from the nonparametric Bayesian literature are used to flexibly describe the distributions. Additionally, the two-sample comparison problem is decomposed into a collection of local tests on individual parameters describing the distributions. This strategy not only yields high statistical power, but also allows one to identify the nature of the distributional difference. In many real-world applications, detecting the nature of the difference is as important as the existence of the difference itself. Generalizations to multi-sample comparison and more complex statistical problems, such as multi-way analysis of variance, are also discussed.</p> / Dissertation

Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior distribution. The algorithm is both verified and validated, and then finally applied to the given data, with comparisons to the results of different methods.

Understanding demographic and disease processes in wildlife populations tends to be hampered by incomplete observations which can include significant errors. Models provide useful insights into the potential impacts of key processes and the value of such models greatly improves through integration with available data in a way that includes all sources of stochasticity and error. To date, the impact on disease of spatial and social structures observed in wildlife populations has not been widely addressed in modelling. I model the joint effects of differential fecundity and spatial heterogeneity on demography and disease dynamics, using a stochastic description of births, deaths, social-geographic migration, and disease transmission. A small set of rules governs the rates of births and movements in an environment where individuals compete for improved fecundity. This results in realistic population structures which, depending on the mode of disease transmission can have a profound effect on disease persistence and therefore has an impact on disease control strategies in wildlife populations. I also apply a simple model with births, deaths and disease events to the long-term observations of TB (Mycobacterium bovis) in badgers in Woodchester Park. The model is a continuous time, discrete state space Markov chain and is fitted to the data using an implementation of Bayesian parameter inference with an event-based likelihood. This provides a flexible framework to combine data with expert knowledge (in terms of model structure and prior distributions of parameters) and allows us to quantify the model parameters and their uncertainties. Ecological observations tend to be restricted in terms of scope and spatial temporal coverage and estimates are also affected by trapping efficiency and disease test sensitivity. My method accounts for such limitations as well as the stochastic nature of the processes. I extend the likelihood function by including an error term that depends on the difference between observed and inferred state space variables. I also demonstrate that the estimates improve by increasing observation frequency, combining the likelihood of more than one group and including variation of parameter values through the application of hierarchical priors.

In this thesis, I try to proceed one step further towards an understanding of the biogeographic processes forming the distribution patterns of organisms that we see today. Babblers and warblers are diverse groups of passerines that are phylogenetically intermixed with other groups in the superfamily Sylvioidea. First, the gross phylogeny of the babblers and associated groups was estimated. Five major lineages of a well-supported monophyletic babbler radiation were recovered, and we proposed a new classification at family and subfamily level. Further, the genus Pnoepyga was excluded from Timaliidae, and we proposed the new family Pnoepygidae fam. nov. Second, the systematic position was investigated for the Albertine Rift taxon Hemitesia neumanni, which was found to be nested within the almost entirely Asian family Cettidae, and possible biogeographical scenarios were discussed. We concluded that the most plausible explanation involved late Miocene vicariance in combination with local extinctions. Third, the historical biogeography of a Leiothrichinae subclade, the Turdoides babblers and allies, was inferred. We concluded that the Middle East region probably played an important role in the early history of this clade, followed by local extinctions in this region. Fourth, a Bayesian method to reconstruct the historical biogeography under an event-based model was proposed, where the total biogeographic histories are sampled from its posterior probability distribution using Markov chains. In conclusion, I believe that, especially with more sophisticated methods available, we will see an increasing number of studies inferring biogeographic histories that lead to distribution patterns built up by a combination of dispersals and vicariance, but where these distributions have been extensively reshaped, or litterally demolished, by local extinctions. Therefore, my answer to the frequently asked question dispersal or vicariance? is both, but not the least: extinctions. / At the time of the doctoral defence the following papers were unpublished and had a status as follows; Papers 3 and 4: Manuscripts

One of the main classes of spatial epidemiological studies is disease mapping, where the main aim is to describe the overall disease distribution on a map, for example, to highlight areas of elevated or lowered mortality or morbidity risk, or to identify important social or environmental risk factors adjusting for the spatial distribution of the disease. This thesis focused and proposed solutions to two most commonly seen obstacles in disease mapping applications, the changing census boundaries due to long study period and data aggregation for patients' confidentiality. In disease mapping, when target diseases have low prevalence, the study usually covers a long time period to accumulate sufficient cases. However, during this period, numerous irregular changes in the census regions on which population is reported may occur, which complicates inferences. A new model was developed for the case when the exact location of the cases is available, consisting of a continuous random spatial surface and fixed effects for time and ages of individuals. The process is modelled on a fine grid, approximating the underlying continuous risk surface with Gaussian Markov Random Field and Bayesian inference is performed using integrated nested Laplace approximations. The model was applied to clinical data on the location of residence at the time of diagnosis of new Lupus cases in Toronto, Canada, for the 40 years to 2007, with the aim of finding areas of abnormally high risk. Predicted risk surfaces and posterior exceedance probabilities are produced for Lupus and, for comparison, Psoriatic Arthritis data from the same clinic. Simulation studies are also carried out to better understand the performance of the proposed model as well as to compare with existing methods. When the exact locations of the cases are not known, inference is complicated by the uncertainty of case locations due to data aggregation on census regions for confidentiality. Conventional modelling relies on the census boundaries that are unrelated to the biological process being modelled, and may result in stronger spatial dependence in less populated regions which dominate the map. A new model was developed consisting of a continuous random spatial surface with aggregated responses and fixed covariate effects on census region levels. The continuous spatial surface was approximated by Markov random field, greatly reduces the computational complexity. The process was modelled on a lattice of fine grid cells and Bayesian inference was performed using Markov Chain Monte Carlo with data augmentation. Simulation studies were carried out to assess performance of the proposed model and to compare with the conventional Besag-York-Molli\'e model as well as model assuming exact locations are known. Receiver operating characteristic curves and Mean Integrated Squared Errors were used as measures of performance. For the application, surveillance data on the locations of residence at the time of diagnosis of syphilis cases in North Carolina, for the 9 years to 2007 are modelled with the aim of finding areas of abnormally high risk. Predicted risk surfaces and posterior exceedance probabilities are also produced, identifying Lumberton as a ``syphilis hotspot".