In recent years, parallel processing has become widely available to researchers. It can be applied in an obvious way in the context of Monte Carlo simulation, but techniques for “parallelizing” Markov chain Monte Carlo (MCMC) algorithms are not so obvious, apart from the natural approach of generating multiple chains in parallel. While generation of parallel chains is generally the easiest appr...

Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct a Markov chain. However, the resulting chains are harder to tune to a target distribution than conventional MCMC, and the types of updates available are limi...

We present a novel Markov chain Monte Carlo (MCMC) algorithm that generates samples from transdimensional distributions encoding complex constraints. We use factor graphs, a type of graphical model, to encode constraints as factors. Our proposed MCMC method, called locally annealed reversible jump MCMC, exploits knowledge of how dimension changes affect the structure of the factor graph. We emp...

In this paper, we have illustrated the suitability of Gumbel Model for software reliability data. The model parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. The quasi NewtonRaphson algorithm is applied to obtain the maximum likelihood estimates and associated probability intervals. The Bayesian estimates of the parameters of Gumbel model are ...

The increasing availability of multi-core and multi-processor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has found a wide variety of applications in ...

Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method h...

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the W...

W wielu modelach statystyki bayesowskiej kluczowym problemem jest obliczanie całek względem rozkładów a posteriori, które są skomplikowane i możliwe jest jedynie wyznaczenie ich gęstości z dokładnością do stałej normującej. W tej sytuacji najczęściej stosowanym i bardzo skutecznym narzędziem są markowowskie metody Monte Carlo (Markov Chain Monte Carlo, MCMC). Jest to rodzina algorytmów, które p...

This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compare...