Bayesian predictive analysis of natural disaster losses

Different types of natural events hit the United States every year. The data of natural hazards from 1900 to 2016 in the US shows that there is an increasing trend in annul natural disaster losses after 1980. Climate change is recognized as one of the factors causing this trend, and predictive analysis of natural losses becomes important in loss prediction and risk prevention as this trend continues. In this paper, we convert natural disaster losses to the year 2016 dollars using yearly average Consumers Price Index (CPI), and conduct several tests to verify that the CPI adjusted amounts of loss from individual natural disasters are independent and identically distributed. Based on these test results, we use various model selection quantities to find the best model for the natural loss severity among three composite distributions, namely Exponential-Pareto, Inverse Gamma-Pareto, and Lognormal-Pareto. These composite distributions model piecewise small losses with high frequency and large losses with low frequency. Remarkably, we make the first attempt to derive analytical Bayesian estimate of the Lognormal-Pareto distribution based on the selected priors, and show that the Lognormal-Pareto distribution outperforms the other two composite distributions in modeling natural disaster losses. Important risk measures for natural disasters are thereafter derived and discussed.