Fast Bayesian inference for spatial mean-parameterized Conway-Maxwell-Poisson models
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909198548205568 |
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| author | Kang, Bokgyeong Hughes, John Haran, Murali |
| author_facet | Kang, Bokgyeong Hughes, John Haran, Murali |
| contents | Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are two classes of models that allow for these features -- he mode-parameterized Conway--Maxwell--Poisson (COMP) distribution and the generalized Poisson model. However both require the use of either constraints on the parameter space or a parameterization that leads to challenges in interpretability. We propose a spatial mean-parameterized COMP model that retains the flexibility of these models while resolving the above issues. We use a Bayesian spatial filtering approach in order to efficiently handle high-dimensional spatial data and we use reversible-jump MCMC to automatically choose the basis vectors for spatial filtering. The COMP distribution poses two additional computational challenges -- an intractable normalizing function in the likelihood and no closed-form expression for the mean. We propose a fast computational approach that addresses these challenges by, respectively, introducing an efficient auxiliary variable algorithm and pre-computing key approximations for fast likelihood evaluation. We illustrate the application of our methodology to simulated and real datasets, including Texas HPV-cancer data and US vaccine refusal data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11472 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast Bayesian inference for spatial mean-parameterized Conway-Maxwell-Poisson models Kang, Bokgyeong Hughes, John Haran, Murali Methodology Applications Computation Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are two classes of models that allow for these features -- he mode-parameterized Conway--Maxwell--Poisson (COMP) distribution and the generalized Poisson model. However both require the use of either constraints on the parameter space or a parameterization that leads to challenges in interpretability. We propose a spatial mean-parameterized COMP model that retains the flexibility of these models while resolving the above issues. We use a Bayesian spatial filtering approach in order to efficiently handle high-dimensional spatial data and we use reversible-jump MCMC to automatically choose the basis vectors for spatial filtering. The COMP distribution poses two additional computational challenges -- an intractable normalizing function in the likelihood and no closed-form expression for the mean. We propose a fast computational approach that addresses these challenges by, respectively, introducing an efficient auxiliary variable algorithm and pre-computing key approximations for fast likelihood evaluation. We illustrate the application of our methodology to simulated and real datasets, including Texas HPV-cancer data and US vaccine refusal data. |
| title | Fast Bayesian inference for spatial mean-parameterized Conway-Maxwell-Poisson models |
| topic | Methodology Applications Computation |
| url | https://arxiv.org/abs/2301.11472 |