Stochastic cusp catastrophe model and its Bayesian computations

Ding-Geng Chen; Haipeng Gao; Chuanshu Ji; Xinguang Chen

doi:10.1080/02664763.2021.1922993

Stochastic cusp catastrophe model and its Bayesian computations

J Appl Stat. 2021 May 7;48(13-15):2714-2733. doi: 10.1080/02664763.2021.1922993. eCollection 2021.

Authors

Ding-Geng Chen^{1

2

3}, Haipeng Gao^{4

5}, Chuanshu Ji⁴, Xinguang Chen⁶

Affiliations

¹ School of Social Work, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
² Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
³ Department of Statistics, University of Pretoria, Pretoria, South Africa.
⁴ Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
⁵ PayPal, San Jose, CA, USA.
⁶ Department of Epidemiology, University of Florida, Gainesville, FL, USA.

Abstract

This paper revitalizes the investigation of the classical cusp catastrophe model in catastrophe theory and tackles the unsolved statistical inference problem concerning stochastic cusp differential equation. This model is challenging because its associated transition density hence the likelihood function is analytically intractable. We propose a novel Bayesian approach combining Hamiltonian Monte Carlo with two likelihood approximation methods, namely, Euler approximation and Hermite expansion. We validate this novel approach through a series of simulation studies. We further demonstrate potential application of this novel approach using the real USD/EUR exchange rate.

Keywords: 60G25; Bayesian inference; Cusp catastrophe model; Hamiltonian Monte Carlo; Hermite expansion; stochastic differential equation; transition density.

Grants and funding

This work is partially supported by the National Research Foundation of South Africa [grant number 127727) and the South African National Research Foundation (NRF) and South African Medical Research Council (SAMRC) (South African DST-NRF-SAMRC SARChI Research Chair in Biostatistics [grant number 114613].