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...

Markov Chain Monte Carlo (MCMC) is a family of algorithms which is used to draw samples from arbitrary probability distributions in order to estimate otherwise intractable integrals. When the distribution is complex, simple MCMC becomes inefficient and advanced variations are employed. This paper proposes a novel FPGA architecture to accelerate Parallel Tempering, a computationally expensive, p...

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...

Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large number of likelihood terms that need to be calculated at each iteration. In order to perform Bayesian inference for a large set of time series, we consider an al...

We here propose an exponential family of permutation models that is suitable for inferring the direction and strength of association among dyadic relational structures. A linear-time algorithm is shown for MCMC simulation of model draws, as is the use of simulated draws for maximum likelihood estimation (MCMC-MLE) and/or estimation of Monte Carlo standard errors. We also provide an easily perfo...

In many modern applications, difficulty in evaluating the posterior density makes performing even a single MCMC step slow. This difficulty can be caused by intractable likelihood functions, but also appears for routine problems with large data sets. Many researchers have responded by running approximate versions of MCMC algorithms. In this note, we develop quantitative bounds for showing the er...

We propose a general MCMC method for Bayesian inference in logic-based probabilistic modeling. It covers a broad class of generative models including Bayesian networks and PCFGs. The idea is to generalize an MCMC method for PCFGs to the one for a Turing-complete probabilistic modeling language PRISM in the context of statistical abduction where parse trees are replaced with explanations. We des...