Related papers: Limitations of Markov chain Monte Carlo algorithms…

Phylogenetic inference is an intractable statistical problem on a complex space. Markov chain Monte Carlo methods are the primary tool for Bayesian phylogenetic inference but it is challenging to construct efficient schemes to explore the…

Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an enterprise that yields valuable evolutionary understanding of many biological systems. Bayesian phylogenetic algorithms, which approximate a…

In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data,…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters.…

Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

A method was developed for Bayesian inference of species phylogeny using the multi-species coalescent model. To improve the mixing properties of the Markov chain Monte Carlo (MCMC) algorithm that traverses the space of species trees, we…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful evaluation of the…

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…

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…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. It faces the challenging problem of. moving throughout the high-dimensional space of trees. However, hyperbolic space offers a low…

This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…