no code implementations • 14 Mar 2024 • Filippo Ascolani, Gareth O. Roberts, Giacomo Zanella
This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional regimes where both number of datapoints and parameters increase.
no code implementations • 24 May 2022 • Jun Yang, Krzysztof Łatuszyński, Gareth O. Roberts
High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in empirically observed ``stickiness'' and poor theoretical mixing properties -- lack of geometric ergodicity.
2 code implementations • 14 Oct 2021 • Ryan S. Y. Chan, Murray Pollock, Adam M. Johansen, Gareth O. Roberts
Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior.
no code implementations • 4 Jan 2021 • Christian P. Robert, Gareth O. Roberts
Rao-Blackwellization is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao--Blackwell theorem (Rao, 1945 and Blackwell, 1947), including a reduction of the variance of the resulting Monte Carlo approximations.
Computation Statistics Theory Statistics Theory
no code implementations • 26 Mar 2018 • Omiros Papaspiliopoulos, Gareth O. Roberts, Giacomo Zanella
We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance.
no code implementations • 23 Nov 2016 • Paul Fearnhead, Joris Bierkens, Murray Pollock, Gareth O. Roberts
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes.
1 code implementation • 28 Aug 2007 • Omiros Papaspiliopoulos, Gareth O. Roberts, Martin Sköld
In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring posterior distributions from these models.
Methodology
