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

Zahra Barkhordar; Mohsen Maleki; Zahra Khodadadi; Darren Wraith; Farajollah Negahdari

doi:10.1080/02664763.2020.1854203

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

J Appl Stat. 2020 Dec 3;49(5):1305-1322. doi: 10.1080/02664763.2020.1854203. eCollection 2022.

Authors

Zahra Barkhordar¹, Mohsen Maleki², Zahra Khodadadi¹, Darren Wraith³, Farajollah Negahdari⁴

Affiliations

¹ Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran.
² Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran.
³ Institute of Health and Biomedical Innovation (IHBI), Queensland University of Technology (QUT), Queensland, Australia.
⁴ Neyriz Branch, Islamic Azad University, Neyriz, Iran.

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.