The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling
methods defined on the Riemann manifold to resolve the shortcomings of existing Monte …

We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise
their performance. Using simple toy examples we review their theoretical underpinnings …

Many problems in the physical sciences, machine learning, and statistical inference
necessitate sampling from a high-dimensional, multimodal probability distribution. Markov …

Since the first edition of Stochastic Modelling for Systems Biology, there have been many
interesting developments in the use of" likelihood-free" methods of Bayesian inference for …

We propose to combine two quite powerful ideas that have recently appeared in the Markov
chain Monte Carlo literature: adaptive Metropolis samplers and delayed rejection. The …

We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain
parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate …

We consider basic ergodicity properties of adaptive Markov chain Monte Carlo algorithms
under minimal assumptions, using coupling constructions. We prove convergence in …

The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen (Bernoulli 7 (2):
223–242, 2001) uses the estimated covariance of the target distribution in the proposal …

Many Bayesian inference problems require exploring the posterior distribution of high-
dimensional parameters that represent the discretization of an underlying function. This work …

Recent decades have seen enormous improvements in computational inference for
statistical models; there have been competitive continual enhancements in a wide range of …