Efficient Adaptive MCMC Through Precision Estimation
Artikel i vetenskaplig tidskrift, 2018

The performance of Markov chain Monte Carlo (MCMC) algorithms like the Metropolis Hastings Random Walk (MHRW) is highly dependent on the choice of scaling matrix for the proposal distributions. A popular choice of scaling matrix in adaptive MCMC methods is to use the empirical covariance matrix (ECM) of previous samples. However, this choice is problematic if the dimension of the target distribution is large, since the ECM then converges slowly and is computationally expensive to use. We propose two algorithms to improve convergence and decrease computational cost of adaptive MCMC methods in cases when the precision (inverse covariance) matrix of the target density can be well-approximated by a sparse matrix. The first is an algorithm for online estimation of the Cholesky factor of a sparse precision matrix. The second estimates the sparsity structure of the precision matrix. Combining the two algorithms allows us to construct precision-based adaptive MCMC algorithms that can be used as black-box methods for densities with unknown dependency structures. We construct precision-based versions of the adaptive MHRW and the adaptive Metropolis adjusted Langevin algorithm and demonstrate the performance of the methods in two examples. Supplementary materials for this article are available online.

Online estimation

MHRW

Cholesky estimation

AMCMC

MALA

MCMC

Partial correlation

Författare

Jonas Wallin

Lunds universitet

David Bolin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Journal of Computational and Graphical Statistics

1061-8600 (ISSN) 1537-2715 (eISSN)

Vol. 27 4 887-897

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Signalbehandling

DOI

10.1080/10618600.2018.1459303

Mer information

Senast uppdaterat

2019-01-08