scholarly journals Markov Chain Monte Carlo Algorithms: Theory and Practice

2009 ◽  
pp. 157-169 ◽  
Author(s):  
Jeffrey S. Rosenthal
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Theory And Practice ◽  
Monte Carlo Algorithms

scholarly journals Convergence of adaptive and interacting Markov chain Monte Carlo algorithms

2011 ◽  
Vol 39 (6) ◽  
pp. 3262-3289 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
P. Priouret
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Algorithms

scholarly journals In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p

Biometrika ◽  
2020 ◽  
Author(s):  
J E Griffin ◽  
K G Łatuszyński ◽  
M F J Steel
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Variable Selection ◽  
Adaptive Design ◽  
Mixing Time ◽  
Bayesian Variable Selection ◽  
Monte Carlo Algorithms ◽  
Large Numbers ◽  
Large P Small N

Summary The availability of datasets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these datasets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. We propose new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large-$p$, small-$n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable nonlocal proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speed-ups of up to four orders of magnitude are observed.

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