On Bayesian Modeling of Fat Tails and Skewness

We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails. The latter two features are often observed characteristics of empirical datasets, and we formally incorporate them in the inferential process. A general procedure for introduci...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the American Statistical Association 1998-03, Vol.93 (441), p.359-371
Main Authors: Fernández, Carmen, Steel, Mark F. J.
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian method
Bayesian networks
Buckles
Datasets
Exact sciences and technology
Gibbs sampling
Improper prior
Inference
Linear inference, regression
Linear models
Linear regression
Linear regression model
Mathematics
Modeling
Posterior moments
Probability and statistics
Regression analysis
Sampling distributions
Sampling theory, sample surveys
Sciences and techniques of general use
Skewed distribution
Stable distribution
Statistical analysis
Statistical models
Statistics
Steels
Student t sampling
Theory and Methods
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails. The latter two features are often observed characteristics of empirical datasets, and we formally incorporate them in the inferential process. A general procedure for introducing skewness into symmetric distributions is first proposed. Even though this allows for a great deal of flexibility in distributional shape, tail behavior is not affected. Applying this skewness procedure to a Student t distribution, we generate a "skewed Student" distribution, which displays both flexible tails and possible skewness, each entirely controlled by a separate scalar parameter. The linear regression model with a skewed Student error term is the main focus of the article. We first characterize existence of the posterior distribution and its moments, using standard improper priors and allowing for inference on skewness and tail parameters. For posterior inference with this model, we suggest a numerical procedure using Gibbs sampling. The latter proves very easy to implement and renders the analysis of quite challenging problems a practical possibility. Some examples illustrate the use of this model in empirical data analysis.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1998.10474117