Open Access
June 2023 Bayesian Spatial Homogeneity Pursuit of Functional Data: An Application to the U.S. Income Distribution
Guanyu Hu, Junxian Geng, Yishu Xue, Huiyan Sang
Author Affiliations +
Bayesian Anal. 18(2): 579-605 (June 2023). DOI: 10.1214/22-BA1320


An income distribution describes how an entity’s total wealth is distributed amongst its population. A problem of interest to regional economics researchers is to understand the spatial homogeneity of income distributions among different regions. In economics, the Lorenz curve is a well-known functional representation of income distribution. In this article, we propose a mixture of finite mixtures (MFM) model as well as a Markov random field constrained mixture of finite mixtures (MRFC-MFM) model in the context of spatial functional data analysis to capture spatial homogeneity of Lorenz curves. We design efficient Markov chain Monte Carlo (MCMC) algorithms to simultaneously infer the posterior distributions of the number of clusters and the clustering configuration of spatial functional data. Extensive simulation studies are carried out to show the effectiveness of the proposed methods compared with existing methods. We apply the proposed spatial functional clustering method to state level income Lorenz curves from the American Community Survey Public Use Microdata Sample (PUMS) data. The results reveal a number of important clustering patterns of state-level income distributions across the US.

Funding Statement

The research of Huiyan Sang was partially supported by NSF grant no. NSF DMS-1854655.


The authors would like to thank the editor in chief, the editor, the associate editor, and two reviewers for their valuable comments, which helped improve the presentation of this paper. In addition, the authors thank Dr. Fred Huffer for his help in writing.


Download Citation

Guanyu Hu. Junxian Geng. Yishu Xue. Huiyan Sang. "Bayesian Spatial Homogeneity Pursuit of Functional Data: An Application to the U.S. Income Distribution." Bayesian Anal. 18 (2) 579 - 605, June 2023.


Published: June 2023
First available in Project Euclid: 17 June 2022

MathSciNet: MR4578065
Digital Object Identifier: 10.1214/22-BA1320

Primary: 62P20
Secondary: 91B72

Keywords: Lorenz curve , Markov random field , mixture of finite mixtures , spatial functional data clustering

Vol.18 • No. 2 • June 2023
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