Bounding convergence rates for Markov chains: An example of the use of computer algebra

Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697–702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129–142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).