Related papers: A Sequential Scheme for Large Scale Bayesian Multi…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…

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…

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…

Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…

Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…

Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…

We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability,…

A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation…

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…

In many situations it is important to be able to propose $N$ independent realizations of a given distribution law. We propose a strategy for making $N$ parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of…

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…