Bayesian Analysis of ARMA Processes: Complete Sampling Based Inference Under Full Likelihoods

Abstract

For a general stationary and. invertible ARMA (p,q) process, we show how to carry out a fully Bayesian analysis. Our approach is through the use of sampling based methods involving three novel aspects. First the constraints on the parameter space arising from the stationary and invertibility conditions are handled by a convenient reparametrization to all of Euclidean (p+q)-space. Second, required sampling is facilitated by the introduction of latent variables which, though increasing the dimensionality of the problem, greatly simplifies the evaluation of the likelihood. Third, the particular sampling based approach used is a Markov chain Monte Carlo method which is a hybrid of the Gibbs sampler and the Metropolis algorithm. We also briefly show how straightforwardly the sampling based approach accommodates missing observations, outlier detection, prediction and model determination. Finally we illustrate the approach with two examples.

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Document Details

Document Type
Technical Report
Publication Date
Jun 24, 1993
Accession Number
ADA269168

Entities

People

  • A. E. Gelfand
  • John Marriott
  • N. Ravishanker

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Bayesian Inference
  • Bayesian Networks
  • Data Science
  • Information Science
  • Markov Chains
  • Military Research
  • Monte Carlo Method
  • New York
  • Normal Distribution
  • Plastic Explosives
  • Sampling
  • Standards
  • Statistical Algorithms
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Space