Geometric Ergodicity and Hybrid Markov
نویسنده
چکیده
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will \inherit" the geometric ergodicity of its constituent parts. Tweedie for very helpful discussions. We thank the referee and the editor for many excellent suggestions.
منابع مشابه
Electronic Communications in Probability Geometric Ergodicity and Hybrid Markov Chains
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will \inherit" the geometric ergo...
متن کاملGeometric Ergodicity and Hybrid Markov Chains
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will “inherit” the geometric ergo...
متن کاملOn $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov processes
In the present paper we investigate the $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov processes with general state spaces. We provide a necessary and sufficient condition for such processes to satisfy the $L_1$-weak ergodicity. Moreover, we apply the obtained results to establish $L_1$-weak ergodicity of quadratic stochastic processes.
متن کاملTwo convergence properties of hybrid samplers
Theoretical work on Markov chain Monte Carlo (MCMC) algorithms has so far mainly concentrated on the properties of simple algorithms such as the Gibbs sampler, or the full-dimensional Hastings-Metropolis algorithm. In practice, these simple algorithms are used as building blocks for more sophisticated methods, which we shall refer to as hybrid samplers. It is often hoped that good convergence p...
متن کاملA note on geometric ergodicity and floating-point roundoff error
We consider the extent to which Markov chain convergence properties are affected by the presence of computer floating-point roundoff error. Both geometric ergodicity and polynomial ergodicity are considered. This paper extends previous work of Roberts, Rosenthal, and Schwartz (1998); connections between that work and the present paper are discussed.
متن کامل