Bayesian Change-Point Detection in Zero-Inflated Regression Models: Analyzing COVID-19 Mortality Patterns

Articles in Press

Document Type : Original Article

Author
Masoud Majidizadeh
Department of Statistics, Faculty of Mathemtical Sciences, Shahid Beheshti University, Tehran, Iran
10.22034/jirss.2026.2067102.1127
Abstract
Maintaining consistent experimental conditions over long periods is inherently challenging, and even when the underlying model structure remains stable, the assumption of constant model parameters may not hold. In this paper, we investigate the estimation of a single change-point within a flexible class of zero-inflated models, including well-known cases such as the Zero-Inflated Poisson (ZIP) model. Our goal is to characterize the change-point through shifts in model parameters by employing a fully Bayesian framework.

To achieve this, we develop a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm for parameter estimation and model selection, specifically tailored to detect the presence and location of a potential change-point in zero-inflated regression models, with particular emphasis on the ZIP formulation. This Bayesian approach allows practitioners to incorporate expert knowledge directly into the analysis of zero-inflated count data.

We assess the performance and properties of the proposed method through a series of simulation studies. In addition, we apply our approach to COVID-19 mortality data from two countries to identify change-points in death trends while accounting for relevant explanatory variables.
Keywords
Bayesian inference
Data augmentation
RJMCMC
Zero-inflated power series models
Change-point detection
Subjects
Agarwal DK, Gelfand AE, Citron-Pousty S. Zero-inflated models with application to spatial count data. Environmental and Ecological Statistics. 2002;9:341–355.
Angers JF, Biswas A. A Bayesian analysis of zero-inflated generalized Poisson model. Computational Statistics & Data Analysis. 2003;42(1-2):37–46.
Bhattacharyya A, Mitra R, Rai S, Pal S. Bayesian shrinkage priors in zero-inflated and negative binomial regression models with real world data applications of COVID-19 vaccine, and RNA-Seq. medRxiv. 2022;p. 2022–07.
Böhning D. Zero-inflated Poisson models and CA MAN: A tutorial collection of evidence. Biometrical Journal: Journal of Mathematical Methods in Biosciences. 1998;40(7):833–843.
Van den Broek J. A score test for zero inflation in a Poisson distribution. Biometrics.1995;51(2):738–743.
Brooks ME, Kristensen K, van Benthem KJ, Magnusson A, Berg CW, Nielsen A, et al. Modeling zero-inflated count data with glmmTMB. BioRxiv. 2017;p. 132753.
Brooks SP, Giudici P, Roberts GO. Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions. Journal of the Royal Statistical Society Series B: Statistical Methodology. 2003;65(1):3–39.
Cheung YB. Zero-inflated models for regression analysis of count data: a study of growth and development. Statistics in Medicine. 2002;21(10):1461–1469.
Fearnhead P. Exact and efficient Bayesian inference for multiple changepoint problems. Statistics and Computing. 2006;16(2):203–213.
Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. Chapman and Hall/CRC; 1995.
Ghosh SK, Mukhopadhyay P, Lu JCJ. Bayesian analysis of zero-inflated regression models. Journal of Statistical Planning and Inference. 2006;136(4):1360–1375.
Gilks WR, Wild P. Adaptive rejection sampling for Gibbs sampling. Journal of the Royal Statistical Society: Series C (Applied Statistics). 1992;41(2):337–348.
Green PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika. 1995;82(4):711–732.
Grimm KJ, Stegmann G. Modeling change trajectories with count and zero-inflated outcomes: Challenges and recommendations. Addictive Behaviors. 2019;94:4–15.
Hall DB. Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics. 2000;56(4):1030–1039.
Heilbron D, Gibson D. Shared needle use and health beliefs concerning AIDS: Regression modeling of zero-heavy count data. Poster session. In: Proceedings of the sixth international conference on AIDS, San Francisco, CA; 1990.
Jansakul N, Hinde J. Score tests for zero-inflated Poisson models. Computational Statistics & Data Analysis. 2002;40(1):75–96.
Junnumtuam S, Niwitpong SA, Niwitpong S. Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 PandemicData. CMES-ComputerModeling in Engineering& Sciences. 2023;135(2):1229–1254.
Khedhiri S. Statistical modeling of COVID-19 deaths with excess zero counts. Epidemiologic Methods. 2021;10(s1):20210007.
Klein N, Kneib T, Lang S. Bayesian generalized additive models for location, scale, and shape for zero-inflated and overdispersed count data. Journal of the American Statistical Association. 2015;110(509):405–419.
Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics. 1992;34(1):1–14.
Lee S, Lee Y, Chen CW. Parameter change test for zero-inflated generalized Poisson autoregressive models. Statistics. 2016;50(3):540–557.
Loeys T, Moerkerke B, De Smet O, Buysse A. The analysis of zero-inflated count data: Beyond zero-inflated Poisson regression. British Journal of Mathematical and Statistical Psychology. 2012;65(1):163–180.
Majidizadeh M. Bayesian analysis of the COVID-19 pandemic using a Poisson process with change-points. Monte Carlo Methods and Applications. 2024;30(4):449–465.
Majidizadeh M, Taheriyoun AR. Bayesian multiple change-points detection in autocorrelated binary process with application to COVID-19 infection pattern. Journal of Statistical Computation and Simulation. 2024;94(17):3723–3749.
Neelon B. Bayesian zero-inflated negative binomial regression based on pólya-gamma mixtures. Bayesian Analysis. 2019;14(3):829.
Özmen I, Demirhan H. A Bayesian approach for zero-inflated count regression models by using the reversible jump Markov chain Monte Carlo method and an application. Communications in Statistics—Theory and Methods. 2010;39(12):2109–2127.
Perumean-Chaney SE, Morgan C, McDowall D, Aban I. Zero-inflated and overdispersed: what’s one to do? Journal of Statistical Computation and Simulation. 2013;83(9):1671–1683.
Ridout M, Hinde J, Demétrio CG. A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics. 2001;57(1):219–223.
Rodrigues J. Bayesian analysis of zero-inflated distributions. Communications in Statistics-Theory and Methods. 2003;32(2):281–289.
Scott AJ, Knott M. A cluster analysis method for grouping means in the analysis of variance. Biometrics. 1974;p. 507–512.
Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association. 1987;82(398):528–540.
Tawiah K, Iddrisu WA, Asampana Asosega K. Zero-Inflated Time Series Modelling of COVID-19 Deaths in Ghana. Journal of Environmental and Public Health. 2021;2021(1):5543977.
Vostrikova LY; Russian Academy of Sciences. Detecting “disorder” in multidimensional random processes. 1981;259(2):270–274.
Wen CC, Baker N, Paul R, Hill E, Hunt K, Li H, et al. A Bayesian zero-inflated betabinomial model for longitudinal data with group-specific changepoints. Statistics in Medicine. 2024;43(1):125–140.
Zhang NR, Siegmund DO. A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data. Biometrics. 2007;63(1):22–32, 309.
Zhou W, Huang D, Liang Q, Huang T, Wang X, Pei H, et al. Early warning and predicting of COVID-19 using zero-inflated negative binomial regression model and negative binomial regression model. BMC Infectious Diseases. 2024;24(1):1006.
Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 04 September 2026

  • Receive Date 26 July 2025
  • Revise Date 21 May 2026
  • Accept Date 25 July 2026