Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in ...

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...

While adaptive methods for MCMC are under active development, their utility has been under-recognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adjusted Langevin algorithms. The benefits of this algorithm are immediate, and we demonstrate its p...

In this scribe, we are going to review the Parallel Monte Carlo Markov Chain (MCMC) method. First, we will recap of MCMC methods, particularly the Metropolis-Hasting and Gibbs Sampling algorithms. Then we will show the drawbacks of these classical MCMC methods as well as the Naive Parallel Gibbs Sampling approach. Finally, we will come up with the Sequential Monte Carlo and Parallel Inference f...

This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage req...

The problem of sampling from a given distribution on high-dimensional continuous spaces arises in the computational sciences and Bayesian statistics, and a frequentlyused solution is Markov chain Monte Carlo (MCMC); see [13] for many examples. Because MCMC methods produce good samples only after a lengthy mixing period, a long-standing mathematical question is to analyze the mixing times of the...

MOTIVATION Bayesian estimation of phylogeny is based on the posterior probability distribution of trees. Currently, the only numerical method that can effectively approximate posterior probabilities of trees is Markov chain Monte Carlo (MCMC). Standard implementations of MCMC can be prone to entrapment in local optima. Metropolis coupled MCMC [(MC)(3)], a variant of MCMC, allows multiple peaks ...

Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are...

This study investigated the impact of three prior distributions: matched, standard vague, and hierarchical in Bayesian estimation parameter recovery in two and one parameter models. Two Bayesian estimation methods were utilized: Markov chain Monte Carlo (MCMC) and the relatively new, Variational Bayesian (VB). Conditional (CML) and Marginal Maximum Likelihood (MML) estimates were used as baseli...

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as wel...