A Bayesian approach on the two-piece scale mixtures of normal homoscedastic nonlinear regression models

Abstract

In this application note paper, we propose and examine the performance of a Bayesian approach for a homoscedastic nonlinear regression (NLR) model assuming errors with two-piece scale mixtures of normal (TP-SMN) distributions. The TP-SMN is a large family of distributions, covering both symmetrical/ asymmetrical distributions as well as light/heavy tailed distributions, and provides an alternative to another well-known family of distributions, called scale mixtures of skew-normal distributions. The proposed family and Bayesian approach provides considerable flexibility and advantages for NLR modelling in different practical settings. We examine the performance of the approach using simulated and real data.

KEYWORDS:

• Gibbs sampling
• MCMC method
• nonlinear regression model
• scale mixtures of normal family
• two-piece distributions

Acknowledgements

We would like to express our very great appreciation to associate editor and reviewer(s) for their valuable and constructive suggestions during the planning and development of this research work.

Disclosure statement

No potential conflict of interest was reported by the author(s).