Efficient Interpolation of Computationally Expensive Posterior Densities With Variable Parameter Costs.

ABSTRACT: Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density ? of the parameter vector ?. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density ? is expensive to evaluate. In many such problems, it is possible to identify a minimal subvector ? of ? responsible for the expensive computation in the evaluation of ?. We propose two approaches, DOSKA and INDA, that approximate ? by interpolation in ways that exploit this computational structure to mitigate the curse of dimensionality. DOSKA interpolates ? directly while INDA interpolates ? indirectly by interpolating functions, for example, a regression function, upon which ? depends. Our primary contribution is derivation of a Gaussian processes interpolant that provably improves over some of the existing approaches by reducing the effective dimension of the interpolation problem from dim(?) to dim(?). This allows a dramatic reduction of the number of expensive evaluations necessary to construct an accurate approximation of ? when dim(?) is high but dim(?) is low. We illustrate the proposed approaches in a case study for a spatio-temporal linear model for air pollution data in the greater Boston area. Supplemental materials include proofs, details, and software implementation of the proposed procedures.

SUBMITTER: Bliznyuk N 

PROVIDER: S-EPMC5978746 | biostudies-literature | 2011

REPOSITORIES: biostudies-literature