Bayesian Nonlinear Regression Models based on Slash Skew-t Distribution

Abstract

This paper considers the Bayesian analysis for estimating the parameters of nonlinear regression model when the error term has a slash skew-t distribution. This model is an asymmetric nonlinear regression model which is suitable for fitting the data sets with heavy tail and skewness. The properties of this model are derived and a hierarchical representation of this model based on the stochastic representation of slash skew-t distribution is given. This representation allows us to use Markov Chain Monte Carlo method to estimate the parameters of model. To compare this model with other asymmetric nonlinear regression models, we use conditional predictive ordinate statistic and deviance information, expected Akaike information and expected Bayesian information criterions, and show the performance of the proposed model by a simulation study. Also an application of the new model to fitting a real data set is discussed.