Bayesian inference for smooth transition autoregressive (STAR) model: A prior sensitivity analysis

ABSTRACT

The main aim of this paper is to perform sensitivity analysis to the specification of prior distributions in a Bayesian analysis setting of STAR models. To achieve this aim, the joint posterior distribution of model order, coefficient, and implicit parameters in the logistic STAR model is first being presented. The conditional posterior distributions are then shown, followed by the design of a posterior simulator using a combination of Metropolis-Hastings, Gibbs Sampler, RJMCMC, and Multiple Try Metropolis algorithms, respectively. Following this, simulation studies and a case study on the prior sensitivity for the implicit parameters are being detailed at the end.

KEYWORDS:

• Gibbs Sampler algorithm
• Metropolis-Hastings algorithm
• Multiple Try Metropolis algorithm
• Prior sensitivity analysis
• Reversible Jump MCMC algorithm
• Smooth Transition Autoregressive (STAR) model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62M10
• 65C20
• 65C40
• 68U20

Acknowledgment

The authors thank two anonymous referees for their valuable suggestions and comments. This paper arises from work in the PhD study of G. Livingston, Jr, who is funded by The Australian Postgraduate Award PhD scholarship. The research of D. Nur was supported by the Establishment Grant funded by the Faculty of Science and Engineering and the School of Computer Science and Engineering and Mathematics at Flinders University, Australia.