This paper takes the reader on a journey through history of Bayesian computation, from 18th century to present day. Beginning with one-dimensional integral first confronted by Bayes in 1763, we highlight key contributions of: Laplace, Metropolis (and, importantly, his co-authors!), Hammersley and Handscomb, Hastings, all which set foundations for computational revolution late 20th -- led, prima...

Ergodicity of Adaptive MCMC and its Applications Chao Yang Doctor of Philosophy Graduate Department of Statistics University of Toronto 2008 Markov chain Monte Carlo algorithms (MCMC) and Adaptive Markov chain Monte Carlo algorithms (AMCMC) are most important methods of approximately sampling from complicated probability distributions and are widely used in statistics, computer science, chemist...

A Bayesian model selection for modelling a time series by an autoregressive–moving–average model (ARMA) is presented. The posterior distribution of unknown parameters and the selected orders are obtained by the Markov chain Monte Carlo (MCMC) method. An MCMC algorithm that represents the parameters of the model as a point process has been implemented. The method is illustrated on simulated seri...

Introduction Bayesian hierarchical models with random effects are one of the most widely used methods in modern disease mapping, as a superior alternative to standardized ratios. These models are traditionally fitted through Markov Chain Monte Carlo sampling (MCMC). Due to the nature of the hierarchical models and random effects, the convergence of MCMC is very slow and unpredictable. Recently,...

In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions (Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not ne...

Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations— which introduce a prior distribution over decision trees, and formulate learning as posterior inference given data—have been shown to produce competitive performance. Unlike classic decision tree learning algorithms like ID3, C4.5 and CART, which work in ...

Switching state-space models (SSSM) are a popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov chain Monte Carlo (MCMC) techniques. However, even sophisticated MCMC methods dedicated to SSSM can prove quite ine cient as they update potentially strongly corr...

In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algori...

We tackle the problem of object recognition using a Bayesian approach. A marked point process [1] is used as a prior model for the (unknown number of) objects. A sample is generated via Markov chain Monte Carlo (MCMC) techniques using a novel combination of Metropolis-coupled MCMC (MCMCMC) [2] and the Delayed Rejection Algorithm (DRA) [4]. The method is illustrated on some synthetic data contai...

Abstract. Bayesian modelling is fluently employed to assess natural ressources. It is associated with Monte Carlo Markov Chains (MCMC) to get an approximation of the distribution law of interest. Hence in such situations it is important to be able to propose N independent realizations of this distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains interact in ord...