Simulation of Lévy Random Fields

An efficient recently developed method, the Inverse Levy Measure (ILM) algorithm, is presented for drawing random samples from gamma, skewed stable and other nonnegative independent-increment random fields, which we call Levy random fields. The method is useful for computing posterior distributions in nonparametric hierarchical Bayesian statistical analysis. Algorithms are illustrated through prototype implementations in S-PLUS.

[1]  P. Levy Théorie de l'addition des variables aléatoires , 1955 .

[2]  T. Ferguson,et al.  A Representation of Independent Increment Processes without Gaussian Components , 1972 .

[3]  T. Ferguson A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[4]  T. Ferguson Prior Distributions on Spaces of Probability Measures , 1974 .

[5]  C. Antoniak Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[6]  L. Rogers,et al.  Diffusions, Markov processes, and martingales , 1979 .

[7]  T. Ferguson,et al.  Bayesian Nonparametric Estimation Based on Censored Data , 1979 .

[8]  L. Bondesson On simulation from infinitely divisible distributions , 1982, Advances in Applied Probability.

[9]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[10]  N. Hjort Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data , 1990 .

[11]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[12]  L. Tierney Markov Chains for Exploring Posterior Distributions , 1994 .

[13]  Purushottam W. Laud,et al.  Approximate Random Variate Generation from Infinitely Divisible Distributions with Applications to Bayesian Inference , 1995 .

[14]  D. Dey,et al.  Semiparametric Bayesian analysis of survival data , 1997 .

[15]  R. Wolpert,et al.  Multiresolution Assessment of Forest Inhomogeneity , 1997 .

[16]  R. Wolpert,et al.  Poisson/gamma random field models for spatial statistics , 1998 .

[17]  Steven N. MacEachern,et al.  Computational Methods for Mixture of Dirichlet Process Models , 1998 .

[18]  Robert L. Wolpert,et al.  Modeling Travel Demand in Portland, Oregon , 1998 .

[19]  Zuqiang Qiou,et al.  Bayesian Inference for Time Series with Stable Innovations , 1998 .

[20]  D. Dey,et al.  Multivariate Survival Analysis with Positive Stable Frailties , 1999, Biometrics.

[21]  Eric R. Ziegel,et al.  Practical Nonparametric and Semiparametric Bayesian Statistics , 1998, Technometrics.