In mixed models, posterior densities are too difficult to work with directly. With the Markov chain Monte Carlo (MCMC) methods, to do statistical inference requires the convergence of the MCMC chain to its stationary distribution. To assess convergence of Markov chain has not a specific way. Assessing convergence of Markov chain has been developed many techniques. Although increasingly populari...

The conventional Markov chain Monte Carlo (MCMC) method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis (AM) algorithm and delayed rejection (DR) algor...

In the following article we investigate a particle filter for approximating Feynman-Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require ...

This paper demonstrates how a human-Markov Chain Monte Carlo (MCMC) method can be used to investigate models of facial expression categorization. Data were collected from four participants. At each step participants were asked to select a representation from a pair, that most resembled a particular emotional state; this was repeated iteratively. As such, they formed a component in the MCMC proc...

Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the with a local approximation based on small number of carefully chosen evaluations can significantly reduce computational expense Markov chain Monte Carlo (MCMC) sampling. Moreover, continual refinement guarantee asymptotically exact We devise new strategy...

In recent years, stochastic gradient Markov Chain Monte Carlo (SG-MCMC) methods have been raised to process large-scale dataset by iterative learning from small minibatches. However, the high variance caused by naive subsampling usually slows down the convergence to the desired posterior distribution. In this paper, we propose an effective subsampling strategy to reduce the variance based on a ...

Sampling from the posterior distribution using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations to fully explore the correct posterior. This is often the case when the posterior of interest is multi-modal, as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a...

The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore a high-dimensional space for accurate inference. This struggle is compounded in physical applications when the nonlinear forward model is computationally expensive. One approach to acce...