Statistics and Its Interface

Volume 12 (2019)

Number 3

Quantitative evaluation of impacts of likelihood functions on Bayesian parametric estimation of epidemic models

Pages: 415 – 422

DOI: https://dx.doi.org/10.4310/19-SII559

Authors

Zhu Meixia (School of Computer Science and Technology, Tianjin Polytechnic University, Tianjin, China)

Pei Yongzhen (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, China)

Ye Ming (School of Computer Science and Technology, Tianjin Polytechnic University, Tianjin, China; and Department of Scientific Computing, Florida State University, Tallahassee, Fl., U.S.A.)

Li Changguo (Department of Basic Science, Army Military Transportation University, Tianjin, China)

Abstract

In epidemic modeling, the selection of likelihood function plays a crucial role on estimating model parameters and making efficient prevention strategies. Compared with the Poisson likelihood function ($L_P$) and normal likelihood function ($L_N$) based on the assumption of population homogeneity, the likelihood function, $L_L$, derived from Liapunov’s central limit theory deals with the population heterogeneity issue that each person has a different probability of being infected. This study focuses on quantifying the performance of the three likelihood functions with particular attention paid to explore the influence of population heterogeneity on the results of parameter estimation for three epidemic models. Our results show that $L_L$ outperforms $L_P$ and $L_N$ based on six sets of data, three models, and three evaluation criteria. Furthermore, $L_L$ improves predictive capability of the three models in comparing with the prediction results of Liu et al. (2015). However, asserting the superiority of $L_L$ for all circumstances should be cautious because the performance of the three likelihood functions are affected jointly by evaluation criteria, data sets, and the models under evaluation.

Keywords

parameter estimation, likelihood functions, quantitative evaluation, Ebola

Full Text (PDF format)

The authors’ work was supported by the Natural Science Foundation of Tianjin (2017KJ092) and by the National Natural Science Foundation of China (11471243, 11501411).

Received 3 April 2018

Published 4 June 2019