Computational Methods for Multiplicative Intensity Models Using Weighted Gamma Processes

Proportional Hazards, Marked Point Processes, and Panel Count Data

Hemant Ishwaran, Lancelot F. James

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the weighted gamma process, we show that with some care, one can adapt efficient algorithms used for the Dirichlet process to this setting. We discuss blocked Gibbs sampling procedures and Pólya urn Gibbs samplers. We illustrate our methods with applications to proportional hazard models, Poisson spatial regression models, recurrent events, and panel count data.

Original languageEnglish
Pages (from-to)175-190
Number of pages16
JournalJournal of the American Statistical Association
Volume99
Issue number465
StatePublished - Mar 1 2004
Externally publishedYes

Fingerprint

Gamma Process
Marked Point Process
Proportional Hazards
Dirichlet Process
Count Data
Panel Data
Posterior distribution
Computational Methods
Multiplicative
Bayesian Hierarchical Model
Recurrent Events
Bayesian Nonparametrics
Proportional Hazards Model
Gibbs Sampler
Gibbs Sampling
Spatial Model
Regression Model
Siméon Denis Poisson
Efficient Algorithms
kernel

Keywords

  • Blocked Gibbs sampler
  • Dirichlet process
  • Hazard function
  • Intensity
  • Kernel
  • Nonhomogeneous Poisson process
  • Pólya urn Gibbs sampler
  • Recurrent events
  • Spatially correlated counts

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

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