In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the posterior distribution. In this article, we investigate this problem on phylogenetic tree topologies with a metric that is especially well suited to the task: the subtree prune-and-regraft (SPR) ...

Abstract The use of heuristics to assess the convergence and compress output Markov chain Monte Carlo can be sub-optimal in terms empirical approximations that are produced. Typically a number initial states attributed ‘burn in’ removed, while remainder is ‘thinned’ if compression also required. In this paper, we consider problem retrospectively selecting subset states, fixed cardinality, from ...

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent methods have been used enhance autoencoders, need robust uncertainty quantification remains a challenge. This has addressed with variational autoencoders so far. Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling faced several ...

This paper is a review of computational strategies for Bayesian shrinkage and variable selection in the linear model. Our focus is less on traditional MCMC methods, which are covered in depth by earlier review papers. Instead, we focus more on recent innovations in stochastic search and adaptive MCMC, along with some comparatively new research on shrinkage priors. One of our conclusions is that...

In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. Whilst MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps under appreciated, problems associated with the MCMC analysis of mixtures...

Markov Chain Monte Carlo (MCMC) samplers have been a very powerful methodology for estimating signal parameters. With the introduction of the reversible jump MCMC sampler, which is a Metropolis-Hastings method adapted to general state spaces, the potential of the MCMC methods has risen to a new level. Consequently, the MCMC methods currently play a major role in many research activities. In thi...

We propose a simple and novel framework for MCMC inference in continuoustime discrete-state systems with pure jump trajectories. We construct an exact MCMC sampler for such systems by alternately sampling a random discretization of time given a trajectory of the system, and then a new trajectory given the discretization. The first step can be performed efficiently using properties of the Poisso...

We describe the importance and widespread use of Markov chain Monte Carlo (MCMC) algorithms, with an emphasis on the roles in which theoretical analysis can help with their practical implementation. In particular, we discuss how to achieve rigorous quantitative bounds on convergence to stationarity using the coupling method together with drift and minorisation conditions. We also discuss recent...

We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly.