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There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
Random Walk Metropolis Hastings (RWMH) algorithm, is quite inefficient in high dimensions because of its abysmally slow acceptance rate. The slow acceptance rate results from the fact that RWMH separately updates each coordinate of the…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin…
We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to…
The random walk Metropolis (RWM) is one of the most common Markov chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with…
An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the…
The two dominant approaches for the analysis of species-habitat associations in animals have been shown to reach divergent conclusions. Models fitted from the viewpoint of an individual (step selection functions), once scaled up, do not…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those…
One of the most widely used samplers in practice is the component-wise Metropolis-Hastings (CMH) sampler that updates in turn the components of a vector valued Markov chain using accept-reject moves generated from a proposal distribution.…