Examples comparing importance sampling and the Metropolis algorithm

Importance sampling, particularly sequential and adaptive importance sampling, have emerged as competitive simulation techniques to Markov-chain Monte-Carlo techniques. We compare importance sampling and the Metropolis algorithm as two ways of changing the output of a Markov chain to get a different stationary distribution.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  D. Knuth.  Estimating the efficiency of backtrack programs. , 1974 .

[3]  P. Peskun.  Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains , 1981 .

[4]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[5]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[6]  L. Saloff-Coste,et al.  Lectures on finite Markov chains , 1997 .

[7]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[8]  P. Diaconis,et al.  Comparison Techniques for Random Walk on Finite Groups , 1993 .

[9]  Jun S. Liu,et al.  Metropolized independent sampling with comparisons to rejection sampling and importance sampling , 1996, Stat. Comput..

[10]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[11]  P. Prescott,et al.  Monte Carlo Methods , 1964, Computational Statistical Physics.

[12]  D E Knuth,et al.  Mathematics and Computer Science: Coping with Finiteness , 1976, Science.

[13]  D. Siegmund.  Importance Sampling in the Monte Carlo Study of Sequential Tests , 1976 .

[14]  Persi Diaconis,et al.  What do we know about the Metropolis algorithm? , 1995, STOC '95.

[15]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[16]  M. Piccioni,et al.  Importance sampling for families of distributions , 1999 .

[17]  A. Sokal.  Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms , 1997 .

[18]  P. Diaconis,et al.  Geometric Bounds for Eigenvalues of Markov Chains , 1991 .

[19]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[20]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[21]  P. A. Androsenko,et al.  Modification of the monte carlo method for calculating the local characteristics of a radiation flux , 1978 .

[22]  Yuguo Chen,et al.  Sequential Monte Carlo Methods for Statistical Analysis of Tables , 2005 .

[23]  Jeff Moad,et al.  International Business Machines Corp. , 1993 .

[24]  P. Peskun,et al.  Optimum Monte-Carlo sampling using Markov chains , 1973 .