Discussion of the paper by Kou, Zhou and Wong
نویسندگان
چکیده
We congratulate Samuel Kou, Qing Zhou and Wing Wong (referred subsequently as KZW) for this beautifully written paper, which opens a new direction in Monte Carlo computation. This discussion has two parts. First, we describe a very closely related method, multicanonical sampling (MCS), and report a simulation example that compares the Equi-Energy (EE) sampler with MCS. Over all, we found the two algorithms to be of comparable e ciency for the simulation problem considered. In the second part, we develop some additional convergence results for the EE sampler.
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Discussion of “ Equi - Energy Sampler ” by Kou , Zhou and Wong
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1. Questions. To simplify the language, we use π(x) to denote a distribution we want to sample from, and q(x) to denote a distribution at a higher temperature (with energy truncation). The distributions π(x) and q(x) can be understood as two consecutive levels in the EE-sampler. Suppose we have obtained a sample from q(x) by running a Markov chain (with a burn-in period), and let us call the sa...
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We provide a complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler (Kou, Zhou, and Wong, 2006) in the case that the state space is countable. We show that in a countable state space, each sampling chain in the EE sampler is strongly ergodic a.s. with the desired steady-state distribution. Furthermore, all chains satisfy the individual e...
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