Layered adaptive importance sampling

Abstract

Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a layered (i.e., hierarchical) procedure to generate samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. Furthermore, we provide a general unified importance sampling (IS) framework, where multiple proposal densities are employed and several IS schemes are introduced by applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov Chain Monte Carlo (MCMC) chains. The resulting algorithms efficiently combine the benefits of both IS and MCMC methods.

Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling

“…Also, the use of transformation can be similarly extended to improve other IS estimators, e.g. other multiple IS schemes (Veach and Guibas, 1995;Owen and Zhou, 2000;Elvira et al, 2015;Martino et al, 2017), parallel, serial or simulated tempering (George and Doss, 2018;Marinari and Parisi, 1992). Likewise, the proposed method of choosing importance densities for GIS can also be used for other IS estimators.…”

Consistency of adaptive importance sampling and recycling schemes

“…We study here the theoretical proporties of a Modified version of AMIS (MAMIS), which introduces a simpler recycling strategy than AMIS. The MAMIS strategy, that was proposed in a previous version of this work, has been considered in various works such as Martino et al (2016); Schuster (2015a,b); Bugallo, Martino and Corander (2015); Cameron and Pettitt (2014); Feroz et al (2013). rely on the same adaptive scheme as MAMIS to build their Adaptive Population Importance Sampling, called APIS.…”

Efficient Adaptive Multiple Importance Sampling

“…In order to overcome this problem, substantial effort has been devoted to the design of adaptive IS (AIS) schemes, where the proposal density is updated by learning from all the previously generated samples [3], [4]. Population Monte Carlo (PMC) schemes [5]- [9] and the adaptive population importance samplers (APIS) [10], [11] are two general approaches that combine the proposal adaptation idea with the cooperative use of a cloud of proposal pdfs. In the PMC schemes a population of proposals is updated, e.g., changing their location parameters, by the use of resampling steps [2,Chapter 14], [5], [9].…”

“…In other methodologies, such as mixture PMC (M-PMC), all the parameters of a mixture proposal distribution are adapted [6]. Moreover, different types of adaptation have been proposed, for instance, by the use of MCMC outputs [11]- [14]. Some of these techniques consider the application of the so-called deterministic mixture weighting procedure, which provides more efficient IS estimators when several different proposal pdfs are jointly employed [15]- [17].…”