Analysis of MCMC algorithms for Bayesian linear regression with Laplace errors

JOURNAL OF MULTIVARIATE ANALYSIS

卷:117

Article

Choi, Hee Min¹  Hobert, James P.¹ 

[1] Univ Florida, Dept Stat, Gainesville, FL 32611 USA

关键词: Asymmetric Laplace distribution;    Data augmentation algorithm;    Eigenvalues;    Geometric convergence rate;    Markov chain;    Markov operator;    Monte Carlo;    Sandwich algorithm;    Trace-class operator;   

DOI  :  10.1016/j.jmva.2013.02.004

来源: Elsevier

【 摘 要 】

Let pi denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring pi. In particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sandwich variant are both trace-class. Consequently, both Markov chains are geometrically ergodic. It is also established that for each i is an element of (1, 2, 3, ...}, the ith largest eigenvalue of the sandwich operator is less than or equal to the corresponding eigenvalue of the DA operator. It follows that the sandwich algorithm converges at least as fast as the DA algorithm. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free