Convergence analysis of block Gibbs samplers for Bayesian linear mixed models with $p>N$
| Autor: | James P. Hobert, Tavis Abrahamsen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Rank (linear algebra) Markov chain Mathematics - Statistics Theory 010103 numerical & computational mathematics matrix inequality Statistics Theory (math.ST) 01 natural sciences Conjugate prior Generalized linear mixed model 010104 statistics & probability Matrix (mathematics) symbols.namesake convergence rate Prior probability FOS: Mathematics Applied mathematics 0101 mathematics geometric drift condition Monte Carlo Mathematics Markov chain Monte Carlo symbols conditionally conjugate prior Gibbs sampling |
| Zdroj: | Bernoulli 23, no. 1 (2017), 459-478 |
| Popis: | Exploration of the intractable posterior distributions associated with Bayesian versions of the general linear mixed model is often performed using Markov chain Monte Carlo. In particular, if a conditionally conjugate prior is used, then there is a simple two-block Gibbs sampler available. Rom\'{a}n and Hobert [Linear Algebra Appl. 473 (2015) 54-77] showed that, when the priors are proper and the $X$ matrix has full column rank, the Markov chains underlying these Gibbs samplers are nearly always geometrically ergodic. In this paper, Rom\'{a}n and Hobert's (2015) result is extended by allowing improper priors on the variance components, and, more importantly, by removing all assumptions on the $X$ matrix. So, not only is $X$ allowed to be (column) rank deficient, which provides additional flexibility in parameterizing the fixed effects, it is also allowed to have more columns than rows, which is necessary in the increasingly important situation where $p>N$. The full rank assumption on $X$ is at the heart of Rom\'{a}n and Hobert's (2015) proof. Consequently, the extension to unrestricted $X$ requires a substantially different analysis. Comment: Published at http://dx.doi.org/10.3150/15-BEJ749 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | OpenAIRE |
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