We introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. These problems are usually addressed using Sequential Monte Carlo (SMC) methods. The alternative Sequentially Interacting Markov Chain Monte Carlo (SIMCMC) scheme proposed here works by generating interacting non-Markovian sequences which...

Appropriate models in biostatistics are often quite complicated. Such models are typically most easily fit using Bayesian methods, which can often be implemented using simulation techniques. Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overview and references of this rapidly emerging technology along with a relatively simple example. MCM...

Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions.Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and...

Marginal Data Augmentation and Parameter-Expanded Data Augmentation are related methods for improving the the convergence properties of the two-step Gibbs sampler know as the Data Augmentation sampler. These methods expand the parameter space with a so-callled working parameter that is unidentifiable given the observed data but is identifiable given the so-called augmented data. Although these ...