论文信息 - Discussion of “Equi-energy sampler” by Kou, Zhou and Wong

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.

Jun S. Liu | Yves F. Atchad'e

[1] Berg,et al. Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[2] D. Landau,et al. Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[3] Dean Isaacson,et al. Markov Chains: Theory and Applications , 1976 .

[4] J. Rosenthal,et al. On adaptive Markov chain Monte Carlo algorithms , 2005 .

[5] G. Parisi,et al. Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[6] Kazuoki Azuma. WEIGHTED SUMS OF CERTAIN DEPENDENT RANDOM VARIABLES , 1967 .