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We consider various versions of adaptive Gibbs and Metropoliswithin-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run,â€¦ (More)

- Krzysztof Latuszynski, Wojciech Niemiro
- J. Complexity
- 2011

interest and ÃŽt,n = (1/n) âˆ‘t+nâˆ’1 i=t f(Xi) its MCMC estimate. Precisely, we derive lower bounds for the length of the trajectory n and burn-in time t which ensure that P (|ÃŽt,n âˆ’ I| â‰¤ Îµ) â‰¥ 1âˆ’ Î±. Theâ€¦ (More)

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state spaceâ€¦ (More)

- Peter J. Green, Krzysztof Latuszynski, Marcelo Pereyra, Christian P. Robert
- Statistics and Computing
- 2015

Recent decades have seen enormous improvements in computational inference for statistical models; there have been competitive continual enhancements in a wide range of computational tools. Inâ€¦ (More)

An essential part of many problems encountered in Bayesian inference is the computation of analytically intractable integral I = Ï€f = âˆ« X f(x)Ï€(x)dx, where f(x) is the target function of interest, Xâ€¦ (More)

- Krzysztof Latuszynski, Ioannis Kosmidis, Omiros Papaspiliopoulos, Gareth O. Roberts
- Random Struct. Algorithms
- 2011

Assume that one aims to simulate an event of unknown probability s âˆˆ (0, 1) which is uniquely determined, however only its approximations can be obtained using a finite computational effort. Suchâ€¦ (More)

We consider various versions of adaptive Gibbs and Metropoliswithin-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run,â€¦ (More)

- Krzysztof Latuszynski, Jeffrey S. Rosenthal
- J. Applied Probability
- 2014

This short note investigates convergence of adaptive MCMC algorithms, i.e. algorithms which modify the Markov chain update probabilities on the fly. We focus on the Containment condition introducedâ€¦ (More)

We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples toâ€¦ (More)

Abstract: For a Markov transition kernel P and a probability distribution Î¼ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel PÎ¼ = âˆ‘ k Î¼(k)P k. In thisâ€¦ (More)