A nonparametric Bayesian analysis for meningococcal disease counts based on integer-valued threshold time series models

Abstract

To better describe the characteristics of time series of counts showing over-dispersion, asymmetry and structural change features, this paper considers a class of random coefficient integer-valued threshold autoregressive processes that properly capture flexible asymmetric and nonlinear responses without assuming the distributions for the errors. By the Taylor expansion, a normally distributed working likelihood is obtained and the Bayesian empirical likelihood inference is conducted for the model parameters. Through the normalized approximation of the nonparametric likelihood, the originally complicated Bayesian calculation has been greatly simplified. Finally, the proposed method is verified via some simulations and an empirical analysis of the meningococcal disease data set in Germany.

Keywords:

• Infectious disease modeling
• time series of counts
• threshold autoregressive process
• Bayesian empirical likelihood
• Bayesian model selection

Additional information

Funding

This work is supported by National Natural Science Foundation of China (No. 11901053), Scientific Research Project of Jilin Provincial Department of Education (No. JJKH20220671KJ), Qiushi Foundation Cultivation Project of Changchun University (No. 2020JBC08L07).