Title: Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

Journal Article · · Journal of the American Statistical Association
 [1];  [2];  [3];  [4]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Aeronautics and Astronautics; DOE/OSTI
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Aeronautics and Astronautics
  3. Harvard Univ., Cambridge, MA (United States). Dept. of Statistics
  4. Univ. of Ottawa, Ottawa (Canada). Dept. of Mathematics and Statistics
+ Show Author Affiliations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data. Supplementary materials for this article are available online.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0007099
OSTI ID:
1535376
Journal Information:
Journal of the American Statistical Association, Journal Name: Journal of the American Statistical Association Journal Issue: 516 Vol. 111; ISSN 0162-1459
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (9)

A transport-based multifidelity preconditioner for Markov chain Monte Carlo journal November 2019
Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models journal February 2019
Surrogate‐Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error journal January 2020
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs journal March 2019
Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error text January 2018
A transport-based multifidelity preconditioner for Markov chain Monte Carlo preprint January 2018
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs text January 2019
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs text January 2018
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs text January 2019

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97 MATHEMATICS AND COMPUTING
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