TY - GEN
T1 - MCMC-driven adaptive multiple importance sampling
AU - Martino, Luca
AU - Elvira, Víctor
AU - Luengo, David
AU - Corander, Jukka
PY - 2015/2/26
Y1 - 2015/2/26
N2 - Monte Carlo (MC) methods are widely used for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling (IS) and its adaptive extensions (such as adaptive multiple IS and population MC). In this work, we introduce an iterated batch importance sampler using a population of proposal densities, which are adapted according to a Markov Chain Monte Carlo (MCMC) technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the generated samples weighted according to the so-called deterministic mixture scheme. Compared with a traditional multiple IS scheme with the same number of samples, the performance is substantially improved at the expense of a slight increase in the computational cost due to the additional MCMC steps. Moreover, the dependence on the choice of the cloud of proposals is sensibly reduced, since the proposal density in the MCMC method can be adapted in order to optimize the performance. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error.
AB - Monte Carlo (MC) methods are widely used for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling (IS) and its adaptive extensions (such as adaptive multiple IS and population MC). In this work, we introduce an iterated batch importance sampler using a population of proposal densities, which are adapted according to a Markov Chain Monte Carlo (MCMC) technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the generated samples weighted according to the so-called deterministic mixture scheme. Compared with a traditional multiple IS scheme with the same number of samples, the performance is substantially improved at the expense of a slight increase in the computational cost due to the additional MCMC steps. Moreover, the dependence on the choice of the cloud of proposals is sensibly reduced, since the proposal density in the MCMC method can be adapted in order to optimize the performance. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error.
UR - http://www.scopus.com/inward/record.url?scp=84924063717&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-12454-4_8
DO - 10.1007/978-3-319-12454-4_8
M3 - Conference contribution
AN - SCOPUS:84924063717
VL - 118
T3 - Springer Proceedings in Mathematics & Statistics
SP - 97
EP - 109
BT - Interdisciplinary Bayesian Statistics, EBEB 2014
A2 - Polpo, Adriano
A2 - Louzada, Francisco
A2 - Lauretto, Marcelo
A2 - Stern, Julio Michael
A2 - Rifo, Laura Letícia Ramos
PB - Springer
T2 - 12th Brazilian Meeting on Bayesian Statistics, EBEB 2014
Y2 - 10 March 2014 through 14 March 2014
ER -