PLACE:  1652 Gilman

SPEAKER:

Professor Michael Lavine, Institute of Statistical Science, Duke University,  Durham, NC

TITLE:

A Marginal Ergodic Theorem

ABSTRACT:

In recent years there have been several papers giving examples of Markov
Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper
(have infinite mass) and which therefore are not positive recurrent, yet
which have subchains from which valid inference can be derived.  These are
nonergodic (not having a limiting distribution) Markov chains that can be
written, possibly after transformation, as Z(n) = (X(n),Y(n)) for which the
subchain X(n) is ergodic (has a limiting distribution).

This talk
  - gives several examples of such chains,
  - reviews regeneration ideas in Markov chains, and
  - gives a marginal ergodic theorem which (a) gives conditions on Z(n)
    guaranteeing that the subchain X(n) is ergodic, (b) gives a formula
    for computing the limiting distribution in case it exists, and (c)
    gives a formula for bounding the liminf and limsup of the distribution
    of X(n) in case the limit does not exist.