Transdimensional Markov Chains A Decade of Progress and Future Perspectives

• Published in: Journal of the American Statistical Association Vol. 100; no. 471; pp. 1077 - 1089
• Main Author: Sisson, Scott A
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2005; American Statistical Association; Taylor & Francis Ltd
• Subjects: Automatic sampling; Automation; Bayesian analysis; Bayesian networks; Computer software; Convergence; Convergence assessment; Efficient chains; Exact sciences and technology; Markov analysis; Markov chains; Markov processes; Mathematical vectors; Mathematics; Metropolitan areas; Modeling; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric models; Probabilities; Probability and statistics; Probability theory and stochastic processes; Reference priors; Reversible jump; Sampling techniques; Sciences and techniques of general use; Software; Statistics; Theory and Methods; Markov chain; Statistical method; Convergence assessment; Efficient chains; Automatic sampling; Reversible jump; Reference priors; Software; Sample survey; Convergence; Parameter space
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214505000000664

The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current state of the art and evaluate some of the most recent advances in this field. We also discuss future research perspectives in the context of the drive to develop sampling mechanisms with high degrees of both efficiency and automation.