When fitting a model to any data, there is some uncertainty about which model is best. Green (1995) quantifies this uncertainty through the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method. When using the RJMCMC method in a regime-switching situation, the chain determines the optimal number of regimes by jumping between various possibilities. This method gives each model its posterior p...

Finite Poisson mixtures are widely used to model overdispersed data sets for which the simple Poisson distribution is inadequate. Such data sets are very common in real applications. In this paper we investigate Bayesian estimation via MCMC for finite Poisson mixtures and we discuss some computational issues. The related problem of determining the number of components in a mixture is also treat...

This paper presents a novel approach for characterizing wideband (CDMA) multiple dimensional channels for the wireless environment in arbitrarily coloured additive Gaussian noise. This characterization is sufficient for the specification of optimal multichannel space-time receivers. The proposed solution is defined in the Bayesian framework and uses the Reversible Jump Markov Chain Monte Carlo ...

We provide a short overview of Importance Sampling – a popular sampling tool used for Monte Carlo computing. We discuss its mathematical foundation and properties that determine its accuracy in Monte Carlo approximations. We review the fundamental developments in designing efficient IS for practical use. This includes parametric approximation with optimization based adaptation, sequential sampl...

Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of such Markov chain quasi-Monte Carlo methods. We define a pull-back discrepancy of the driver sequence and state a close relation to the star-discrepancy of the...

We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods — Markov chain Monte Carlo and importance sampling — into a single algorithm. We show that for some illustrative and applied numerical examples the proposed Markov Chain importance sa...