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Activity Number:
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281
- Bayesian Methods for Complex Data Analysis
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Type:
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Topic-Contributed
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Date/Time:
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Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
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Sponsor:
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International Society for Bayesian Analysis (ISBA)
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Abstract #317272
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Title:
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Identifying Latent Groups in Spatial Panel Data Using a Markov Random Field Constrained Product Partition Model
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Author(s):
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Tianyu Pan* and Guanyu Hu and Weining Shen
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Companies:
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University of California, Irvine and University of Missouri - Columbia and University of California Irvine
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Keywords:
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Marginal Likelihood;
Nonparametric Bayesian Method;
Posterior Consistency;
Spatial Homogeneity
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Abstract:
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Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM) and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structures among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.
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Authors who are presenting talks have a * after their name.
