8 papers
Weak Poincaré inequalities for Deterministic-scan Metropolis-within-Gibbs samplers
Mengxi Gao, Gareth O. Roberts, Andi Q. Wang
Using the framework of weak Poincaré inequalities, we analyze the convergence properties of deterministic-scan Metropolis-within-Gibbs samplers, an important class of Markov chain…
On micromodes in Bayesian posterior distributions and their implications for MCMC
Sanket Agrawal, Sebastiano Grazzi, Gareth O. Roberts
We investigate the existence and severity of local modes in posterior distributions from Bayesian analyses. These are known to occur in posterior tails resulting from heavy-tailed…
Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models
Filippo Ascolani, Gareth O. Roberts, Giacomo Zanella
We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their…
Central Limit Theorem for ergodic averages of Markov chains \& the comparison of sampling algorithms for heavy-tailed distributions
Miha BreÅ¡ar, Aleksandar MijatoviÄ, Gareth Roberts
Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478…
Exact Bayesian inference for Markov switching diffusions
Timothée Stumpf-Fétizon, Krzysztof ÅatuszyÅski, Jan Palczewski +1
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusio…
Transient regime of piecewise deterministic Monte Carlo algorithms
Sanket Agrawal, Joris Bierkens, Kengo Kamatani +1
Piecewise Deterministic Markov Processes (PDMPs) such as the Bouncy Particle Sampler and the Zig-Zag Sampler, have gained attention as continuous-time counterparts of classical Mar…