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Bayesian Nonparametric Density Autoregression with Lag Selection

Authors :
Heiner, Matthew
Kottas, Athanasios
Source :
Bayesian Analysis. 17
Publication Year :
2022
Publisher :
Institute of Mathematical Statistics, 2022.

Abstract

We develop a Bayesian nonparametric autoregressive model applied to flexibly estimate general transition densities exhibiting nonlinear lag dependence. Our approach is related to Bayesian density regression using Dirichlet process mixtures, with the Markovian likelihood defined through the conditional distribution obtained from the mixture. This results in a Bayesian nonparametric extension of a mixtures-of-experts model formulation. We address computational challenges to posterior sampling that arise from the Markovian structure in the likelihood. The base model is illustrated with synthetic data from a classical model for population dynamics, as well as a series of waiting times between eruptions of Old Faithful Geyser. We study inferences available through the base model before extending the methodology to include automatic relevance detection among a pre-specified set of lags. Inference for global and local lag selection is explored with additional simulation studies, and the methods are illustrated through analysis of an annual time series of pink salmon abundance in a stream in Alaska. We further explore and compare transition density estimation performance for alternative configurations of the proposed model.

Details

ISSN :
19360975
Volume :
17
Database :
OpenAIRE
Journal :
Bayesian Analysis
Accession number :
edsair.doi.dedup.....9fc75b154f5513fac240da4803fe15ad
Full Text :
https://doi.org/10.1214/21-ba1296