Discussion of "EQUI-energy sampler" by Kou, Zhou and Wong
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Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
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Discussion of "EQUI-energy sampler" by Kou, Zhou and Wong
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]
math.STstat.TH
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.
math.STstat.TH
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…
math.STstat.TH
Rejoinder to "Equi-energy sampler with applications in statistical inference and statistical mechanics"
Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics'' by Kou, Zhou and Wong [math.ST/0507080]
math.STstat.TH
Adaptive Equi-Energy Sampler : Convergence and Illustration
Markov chain Monte Carlo (MCMC) methods allow to sample a distribution known up to a multiplicative constant. Classical MCMC samplers are known to have very poor mixing properties when sampling multimodal distributions. The Equi-Energy sampler is an interacting MCMC sampler proposed by Kou, Zhou and Wong in 2006 to sample difficult multimodal distributions. This algorithm runs several chains at different temperatures in parallel, and allow lower-tempered chains to jump to a state from a higher-tempered chain having an energy 'close' to that of the current state. A major drawback of this algori…
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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…
math.STstat.COstat.TH
