Advances and Applications in Perfect Sampling
Ulrike Schneider · 2003
The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Schneider, Ulrike (Ph.D., Applied Mathematics) Advances and Applications in Perfect Sampling Thesis directed by Prof. Jem Corcoran Perfect sampling algorithms are Markov Chain Monte Carlo (MCMC) methods without statistical error. The latter are used when one needs to get samples from certain (non-standard) distributions. This can be accomplished by creating a Markov chain that has the desired distribution as its stationary distribution, and by running sample paths ”for a long time”, i.e. until the chain is believed to be in equilibrium. The question ”how long is long enough? ” is generally hard to answer and the assessment of convergence is a major concern when applying MCMC schemes. This issue completely vanishes with the use of perfect sampling algorithms which – if applicable – enable exact simulation from the stationary distribution of a Markov chain.