Objective Bayes analysis of zero-inflated Poisson distribution with application to healthcare data

Abstract

In this article, non-informative priors are investigated for a zero-inflated Poisson distribution with two parameters: the probability of zeros and the mean of the Poisson part. Both the reference prior and the Jeffreys prior are derived and shown to be second-order matching priors when only the mean of the Poisson part is of interest. However, when the probability of zeros is of interest, the reference prior is still a second-order matching prior, whereas the Jeffreys prior is not so. Furthermore, when both parameters are of interest, the reference prior is a unique second-order matching prior. Frequentist coverage probabilities of the posterior confidence sets based on the Jeffreys and reference priors are compared with each other using Monte Carlo simulations and with confidence sets based on the maximum likelihood estimation.

Keywords:

• Zero-inflated Poisson
• objective Bayes
• Jeffreys prior
• non-informative prior
• count data

Additional information

Notes on contributors

Hai-yan Xu

Hai-Yan Xu is a research scientist at the Institute of High Performance Computing, Singapore. She received her M.S. (2002) in Applied Mathematics and Ph.D. (2005) in Computational Statistics from Shanghai Normal University. She joined Shanghai Normal University in 2005 and was promoted to Associate Professor in 2009. She received a Third Prize of Sci-Tech in 2006 from National Defense Science and Technology Industry Committee, China. She is also a committee member of Division of Reliability, the Operations Research Society of China. She has published more than 20 papers in peer-reviewed conferences and journals such as IEEE Transactions on Reliability, Computational Statistics & Data Analysis, and Communications in Statistics - Theory and Methods. Her research interests include applied statistics and probability, impact of climate change on public health, discrete time series analysis, accelerated life and degradation testing, optimal design and data analysis, and large-scale data analysis.

Min Xie

Min Xie received his Ph.D. in Quality Technology from Linköping University, Sweden (1987). He was awarded the prestigious LKY research fellowship and joined National University of Singapore in 1991. Currently, he is with City University of Hong Kong as Chair Professor of Industrial Engineering. He has authored or co-authored numerous papers and eight books on quality and reliability engineering, including Statistical Models and Control Charts for High-Quality Processes published by Kluwer Academic, Advanced QFD Applications published by ASQ Press, Weibull Models published by John Wiley, and Computing Systems Reliability by published Kluwer Academic. He is a Department Editor of IIE Transactions, Area Editor of Computers & Industrial Engineering, and Associate Editor of IEEE Transactions on Reliability and is to on the editorial board of over 10 other international journals. He has advised over 30 Ph.D. students who are now working in academia, industry, or financial institutions in Asia, America, and Europe. He has served as chair or committee member for over 100 international conferences. He is an elected fellow of the IEEE.

Thong Ngee Goh

T. N. Goh holds a Ph.D. from the University of Wisconsin–Madison. He is a former Dean of Engineering and former Head of the Department of Industrial and Systems Engineering at the National University of Singapore. He is the Founding President of the Institute of Industrial Engineers Singapore (formerly the Singapore Chapter of the American Institute of Industrial Engineers) and a former President of the Singapore Institute of Statistics. He specializes in the application of statistical methodologies to quality and productivity problems in industry. He has authored or co-authored more than 300 journal and conference papers and five books. Among many other honors, he is the recipient of the William G. Hunter Award of the American Society for Quality (ASQ) Statistics Division in 2007 and the Grant Medal of ASQ in 2012.