Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0829.62080
Tierney, Luke
Markov chains for exploring posterior distributions (With discussion). (English)
[J] Ann. Stat. 22, No.4, 1701-1762 (1994). ISSN 0090-5364; ISSN 2168-8966/e

Summary: Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several variance reduction techniques and also gives guidance on the choice of sample size and allocation.

MSC 2000:: *62M05 Markov processes: estimation
60J27 Markov chains with continuous parameter
65C05 Monte Carlo methods
60J05 Markov processes with discrete parameter

Keywords: Monte Carlo; Metropolis-Hastings algorithm; Gibbs sampler; Metropolis algorithm; hybrid algorithms; general state space Markov chains; convergence rates; laws of large numbers; central limit theorems; simulation methodology; variance reduction; choice of sample size

Cited in: Zbl 1082.62505 Zbl 0903.60059

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]