Bayesian inference on sparse multinomial data using smoothed Dirichlet distribution with an application to COVID-19 data

Article type: Research Article

Authors: Wickramasinghe, Lahiru^{a; *} | Leblanc, Alexandre^b | Muthukumarana, Saman^b

Affiliations: [a] Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Canada | [b] Department of Statistics, University of Manitoba, Winnipeg, Canada

Correspondence: [*] Corresponding author: Lahiru Wickramasinghe. Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Canada. E-mail: l.wickramasinghe@uwinnipeg.ca.

Abstract: We develop a Bayesian approach for estimating multinomial cell probabilities using a smoothed Dirichlet prior. The most important feature of the smoothed Dirichlet prior is that it forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet prior. We propose a shrinkage-type estimator using this Bayesian approach to estimate multinomial cell probabilities. The proposed estimator allows us to borrow information across other multinomial populations and cell categories simultaneously to improve the estimation of cell probabilities, especially in a context of sparsity with ordered categories. We demonstrate the proposed approach using COVID-19 data and estimate the distribution of positive COVID-19 cases across age groups for Canadian health regions. Our approach allows improved estimation in smaller health regions where few cases have been observed.

Keywords: Multinomial distribution, sparse data; smoothed Dirichlet distribution, shrinkage estimators, COVID-19

DOI: 10.3233/MAS-221411

Journal: Model Assisted Statistics and Applications, vol. 18, no. 3, pp. 207-226, 2023