In the paper, we mainly study ergodicity of adaptive MCMC algorithms. Assume that under some regular conditions about target distributions, all the MCMC samplers in {Pγ : γ ∈ Y} simultaneously satisfy a group of drift conditions, and have the uniform small set C in the sense of the m-step transition such that each MCMC sampler converges to target at a polynomial rate. We say that the family {Pγ...

In this paper, the Markov chain Monte Carlo (MCMC) method has been used to estimate the parameters of Exponentiated Gumbel(EG) model based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the Exponentiated Gumbel model using MCMC simulation method in OpenBUGS, an established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) method....

The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets and runs independent sampling algorithms on each subset. The subset posterior draw...

In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. While MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps underappreciated, problems associated with the MCMC analysis of mixtures. ...

The Unobserved ARCH model is a good description of the phenomenon of changing volatility that is commonly appeared in the financial time series. We study this model adopting Bayesian inference via Markov Chain Monte Carlo (MCMC). In order to provide an easy to implement MCMC algorithm we adopt some suitable non-linear transformations of the parameter space such that the resulting MCMC algorithm...

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves ε error (in 2-Wasserstein distance) in O( √ d/ε) steps. This is a significant improvement over the best known rate for overdamped Langevin MCMC, which is O(d/ε) steps under the same smoothness/concav...

Missing data are often a problem in statistical modeling. The Bayesian paradigm offers a natural modelbased solution for this problem by treating missing values as random variables and estimating their posterior distributions. This paper reviews the Bayesian approach and describes how the MCMC procedure implements it. Beginning with SAS/STAT® 12.1, PROC MCMC automatically samples all missing va...

Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood given parameter value. However, pMCMC can be computationally intensive when large number particles in PF r...

The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely encountered as a statistical model. A family of distributions that vastly gen...

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in highdimensiona...