Gibbs Sampling : Mathematics, Physics, Algorithm, Joint probability, Random variable, Integral, Metropolis-Hastings algorithm, Markov chain Monte Carlo

Frederic P. Miller

ISBN 10: 6132669841 / ISBN 13: 9786132669841

Published by Omniscriptum, 2010

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In mathematicsand physics, Gibbs sampling or Gibbs sampler is an algorithm to generatea sequence of samples from the joint probability distribution of two ormore random variables. The purpose of such a sequence is to approximatethe joint distribution, or to compute an integral. Gibbs sampling is aspecial case of the Metropolis-Hastings algorithm, and thus an exampleof a Markov chain Monte Carlo algorithm. The algorithm is named afterthe physicist J. W. Gibbs, in reference to an analogy between thesampling algorithm and statistical physics. The algorithm was describedby brothers Stuart and Donald Geman in 1984, some eight decades afterthe passing of Gibbs. Gibbs sampling is applicable when the jointdistribution is not known explicitly, but the conditional distributionof each variable is known. The Gibbs sampling algorithm generates aninstance from the distribution of each variable in turn, conditional onthe current values of the other variables. It can be shown that thesequence of samples constitutes a Markov chain, and the stationarydistribution of that Markov chain is just the sought-after jointdistribution.

Seller Inventory # 9786132669841

Bibliographic Details

• Title: Gibbs Sampling : Mathematics, Physics, Algorithm, Joint probability, Random variable, Integral, Metropolis-Hastings algorithm, Markov chain Monte Carlo
• Publisher: Omniscriptum
• Publication Date: 2010
• Language: English
• ISBN 10: 6132669841
• ISBN 13: 9786132669841
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 9D millimeters 220 millimeters width by 150 millimeters height by 9 millimeters depth
• Weight: 238 grams

About this title

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and physics, Gibbs sampling or Gibbs sampler is an algorithm to generate a sequence of samples from the joint probability distribution of two or more random variables. The purpose of such a sequence is to approximate the joint distribution, or to compute an integral. Gibbs sampling is a special case of the Metropolis-Hastings algorithm, and thus an example of a Markov chain Monte Carlo algorithm. The algorithm is named after the physicist J. W. Gibbs, in reference to an analogy between the sampling algorithm and statistical physics. The algorithm was described by brothers Stuart and Donald Geman in 1984, some eight decades after the passing of Gibbs. Gibbs sampling is applicable when the joint distribution is not known explicitly, but the conditional distribution of each variable is known. The Gibbs sampling algorithm generates an instance from the distribution of each variable in turn, conditional on the current values of the other variables. It can be shown that the sequence of samples constitutes a Markov chain, and the stationary distribution of that Markov chain is just the sought-after joint distribution.