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Adaptive Markov Chain Monte Carlo: Theory and Methods Yves Atchade 1
 

Summary: Chapter 1
Adaptive Markov Chain Monte Carlo: Theory and Methods
Yves Atchad´e 1
, Gersende Fort and Eric Moulines 2
, Pierre Priouret 3
1.1 Introduction
Markov chain Monte Carlo (MCMC) methods allow to generate samples from an
arbitrary distribution known up to a scaling factor; see Robert and Casella (1999).
The method consists in sampling a Markov chain {Xk, k 0} on a state space X
with transition probability P admitting as its unique invariant distribution, i.e
P = . Such samples can be used e.g. to approximate (f)
def
= X
f (x) (dx) for
some -integrable function f : X R, by
1
n
n
k=1
f(Xk) . (1.1)

  

Source: Atchadé, Yves F. - Department of Statistics, University of Michigan

 

Collections: Mathematics