Bayesian negative binomial regression model with unobserved covariates for predicting the frequency of north atlantic tropical storms

Abstract

Predicting the annual frequency of tropical storms is of interest because it can provide basic information towards improved preparation against these storms. Sea surface temperatures (SSTs) averaged over the hurricane season can predict annual tropical cyclone activity well. But predictions need to be made before the hurricane season when the predictors are not yet observed. Several climate models issue forecasts of the SSTs, which can be used instead. Such models use the forecasts of SSTs as surrogates for the true SSTs. We develop a Bayesian negative binomial regression model, which makes a distinction between the true SSTs and their forecasts, both of which are included in the model. For prediction, the true SSTs may be regarded as unobserved predictors and sampled from their posterior predictive distribution. We also have a small fraction of missing data for the SST forecasts from the climate models. Thus, we propose a model that can simultaneously handle missing predictors and variable selection uncertainty. If the main goal is prediction, an interesting question is should we include predictors in the model that are missing at the time of prediction? We attempt to answer this question and demonstrate that our model can provide gains in prediction.

Keywords:

• Bayesian model averaging
• Bayesian variable selection
• count data
• missing covariates
• Markov chain Monte Carlo
• prediction sets

Acknowledgments

The authors thank Drs. Kate Cowles and Luke Tierney for helpful comments on a previous version of the manuscript. The authors also thank the Editor, Associate Editor and two reviewers for helpful suggestions. Dr. Wei Zhang is gratefully acknowledged for his help with the data. This research was supported in part through computational resources provided by The University of Iowa, Iowa City, Iowa. The authors are grateful to Dr. Luke Tierney for access to nodes on the ARGON cluster at The University of Iowa. Joyee Ghosh's research was supported by NSF Grant DMS-1612763. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Joyee Ghosh's research was supported by NSF Grant DMS-1612763. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.