Rate-optimal refinement strategies for local approximation MCMC
Name
11222_2022_10123_ReferencePDF.pdf
Size
23.33 MB
Format
Adobe PDF
Checksum (MD5)
fc5631e83d88a0a0944df3192496c3b6
Author(s)
Davis, Andrew D.
Marzouk, Youssef
Smith, Aaron
Pillai, Natesh
Date Issued
August 9, 2022
Publisher
Springer US
Citation
Statistics and Computing. 2022 Aug 09;32(4):60
Version
Author's final manuscript
Abstract
Abstract
Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the target density with a local approximation based on a small number of carefully chosen density evaluations can significantly reduce the computational expense of Markov chain Monte Carlo (MCMC) sampling. Moreover, continual refinement of the local approximation can guarantee asymptotically exact sampling. We devise a new strategy for balancing the decay rate of the bias due to the approximation with that of the MCMC variance. We prove that the error of the resulting local approximation MCMC (LA-MCMC) algorithm decays at roughly the expected
$$1/\sqrt{T}$$
1
/
T
rate, and we demonstrate this rate numerically. We also introduce an algorithmic parameter that guarantees convergence given very weak tail bounds, significantly strengthening previous convergence results. Finally, we apply LA-MCMC to a computationally intensive Bayesian inverse problem arising in groundwater hydrology.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11222-022-10123-0
