Improved log-Gaussian approximation for over-dispersed Poisson regression: application to spatial analysis of COVID-19

by   Daisuke Murakami, et al.

In the era of open data, Poisson and other count regression models are increasingly important. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression, especially for (over-dispersed) Bayesian Poisson wherein the exact inference is unobtainable. The approach is derived via mode-based log-Gaussian approximation. Unlike closed-form alternatives, it remains accurate even for zero-inflated count data. Besides, our approach has no arbitrary parameter that must be determined a priori. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.



There are no comments yet.


page 1

page 2

page 3

page 4


Conjugate priors for count and rounded data regression

Discrete data are abundant and often arise as counts or rounded data. Ye...

Efficient posterior sampling for Bayesian Poisson regression

Poisson log-linear models are ubiquitous in many applications, and one o...

Bayesian Modeling of Nonlinear Poisson Regression with Artificial Neural Networks

Being in the era of big data, modeling and prediction of count data have...

Sensitivity optimization of multichannel searches for new signals

The frequentist definition of sensitivity of a search for new phenomena ...

On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models

This article is concerned with the fitting of multinomial regression mod...

Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data

As with the advancement of geographical information systems, non-Gaussia...

A spatial Poisson hurdle model with application to wildfires

Modelling wildfire occurrences is important for disaster management incl...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.