没有合适的资源?快使用搜索试试~ 我知道了~
首页Markov Chain Monte Carlo in Practice
MCMC方法就是*构造合适的马尔科夫链进行抽样而使用蒙特卡洛方法进行积分计算,既然马尔科夫链可以收敛到平稳分布。我们可以建立一个以π为平稳分布的马尔科夫链,对这个链运行足够长时间之后,可以达到平稳状态。此时马尔科夫链的值就相当于在分布π(x)中抽取样本。利用马尔科夫链进行随机模拟的方法就是MCMC。 第一个MC: Monte Carlo(蒙特卡洛)。这个简单来说是让我们使用随机数(随机抽样)来解决计算问题。在MCMC中意味着:后验分布作为一个随机样本生成器,我们利用它来生成样本(simulation),然后通过这些样本对一些感兴趣的计算问题(特征数,预测)进行估计。 第二个MC:Markov Chain(马尔科夫链)。第二个MC是这个方法的关键,因为我们在第一个MC中看到,我们需要利用后验分布生成随机样本,但后验分布太复杂,当这些样本独立时,利用大数定律样本均值会收敛到期望值。如果得到的样本是不独立的,那么就要借助于马尔科夫链进行抽样,利用Markov Chain的平稳分布这个概念实现对复杂后验分布的抽样。
资源详情
资源评论
资源推荐


Markov Chain
Monte
Carlo
in
Practice

Markov
Chain
Monte
Carlo
in
Practice
Edited
by
W.R.
Gilks
Medical Research Council Biostatistics Unit
Cambridge
UK
S.
Richardson
French National Institute
for
Health
and
Medical Research
Vilejuif
France
and
D.J. Spiegelhalter
Medical Research Council Biostatistics Unit
Cambridge
UK
I
unl
SPRlNGER-SCIENCE+BUSINESS MEDIA, B.V.

First edition 1996
© Springer Science+Business Media Dordrecht 1996
Originall y published by Chapman & Hall in 1996
Softcover reprint of the hardcover
1
st edition 1996
ISBN 978-0-412-05551-5 ISBN 978-1-4899-4485-6 (eBook)
DOI 10.1007/978-1-4899-4485-6
Apart from any fair dealing for the purposes of research or private study, or
criticism or review, as permitted under the UK Copyright Designs and Patents
Act, 1988, this publication may not be reproduced, stored, or transmitted, in
any form or by any means, without the prior permission in writing of the
publishers, or in the case of reprographic reproduction only in accordance with
the terms of the licences issued by the Copyright Licensing Agency in the UK,
or in accordance with the terms of licences issued by the appropriate
Reproduction Rights Organization outside the UK. Enquiries concerning
reproduction outside the terms stated here should be sent to the publishers at the
London address printed on this page.
The publisher makes no representation, express or implied, with regard to the
accuracy of the information contained in this book and cannot accept any legal
responsibilit y or liability for any errors or omissions that may be made.
A Catalogue record for this book is available from the British Library

Contents
Contributors
xv
1
Introducing
Markov
chain
Monte
Carlo
1
W.
R. Gilks, S. Richardson and
D.
J.
Spiegelhalter
1.1 Introduction 1
1.2
The
problem
2
1.2.1
Bayesian inference
2
1.2.2
Calculating expectations
3
1.3
Markov chain Monte Carlo 4
1.3.1
Monte Carlo integration
4
1.3.2
Markov chains
5
1.3.3
The
Metropolis-Hastings algorithm
5
1.4
Implementation
8
1.4.1 Canonical forms of proposal distribution
8
1.4.2
Blocking
12
1.4.3 Updating order
12
1.4.4
Number of chains 13
1.4.5 Starting values
13
1.4.6
Determining burn-in
14
1.4.7
Determining stopping time
15
1.4.8
Output
analysis
15
1.5
Discussion
16
2
Hepatitis
B: a
case
study
in
MCMC
methods
21
D.
J.
Spiegelhalter, N.
G.
Best,
W.
R. Gilks and
H.
Inskip
2.1
Introduction
21
2.2
Hepatitis B immunization
22
2.2.1
Background
22
2.2.2
Preliminary analysis
22
2.3
Modelling
25
2.3.1
Structural modelling
25
2.3.2
Probability modelling
27
2.3.3
Prior distributions
27
剩余486页未读,继续阅读













安全验证
文档复制为VIP权益,开通VIP直接复制

评论0