Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data

Abstract

The purpose of this paper is to develop a data augmentation technique for statistical inference concerning stochastic cusp catastrophe model subject to missing data and partially observed observations. We propose a Bayesian inference solution that naturally treats missing observations as parameters and we validate this novel approach by conducting a series of Monte Carlo simulation studies assuming the cusp catastrophe model as the underlying model. We demonstrate that this Bayesian data augmentation technique can recover and estimate the underlying parameters from the stochastic cusp catastrophe model.

Keywords

• cusp catastrophe model
• stochastic differential equation
• transition density
• Bayesian inference
• data augmentation
• Hamiltonian Monte Carlo