Equi-energy sampler with applications in statistical inference and statistical mechanics

Discussion of "Equi-energy sampler" by Kou, Zhou and Wong

We congratulate Samuel Kou, Qing Zhou and Wing Wong [math.ST/0507080] (referred to 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. Overall, we found the two algorithms to be of comparable efficiency for the simulation problem considered. In the second part, we develop some additional convergence results for the EE sampler.

A note on convergence of the equi-energy sampler

In a recent paper `The equi-energy sampler with applications statistical inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou, Zhou & Wong have presented a new stochastic simulation method called the equi-energy (EE) sampler. This technique is designed to simulate from a probability measure $π$, perhaps only known up to a normalizing constant. The authors demonstrate that the sampler performs well in quite challenging problems but their convergence results (Theorem 2) appear incomplete. This was pointed out, in the discussion of the paper, by Atchadé & Liu (2006) who pro…

Discussion of "EQUI-energy sampler" by Kou, Zhou and Wong

Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of a protein chain given the sequence of its amino acid building blocks. The complexity of the problem strongly depends on the protein representation and its energy function. The more detailed the model, the more complex its corresponding energy function and the more challenge it sets for sampling algorithms. Kou, Zhou and Wong [math.ST/0507080] have introduced…

分段确定性马尔可夫过程用于PDE系数的贝叶斯推断

Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients

本文提出了一种基于分段确定性马尔可夫过程的框架，利用代理模型提升贝叶斯推断效率，特别适用于PDE系数的非线性反问题。