Prediction distribution for linear regression model with multivariate Student-t errors under the Bayesian approach

Abstract

[Abstract]: Prediction distribution is a basis for predictive inferences applied in many real world situations. It is a distribution of the unobserved future response(s) conditional on a set of realized responses from an informative experiment. Various statistical approaches can be used to obtain prediction distributions for different models. This study derives the prediction distribution(s) for multiple linear regression model using the Bayesian method when the error components of both the performed and future models have a multivariate Student-t distribution. The study observes that the prediction distribution(s) of future response(s) has a multivariate Student-t distribution whose degrees of freedom depends on the size of the realized sample and the dimension of the regression parameters’ vector but does not depend on the degrees of freedom of the errors distribution.