 
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)
