Bayesian prediction of temperature records using the Pareto model

Statistical prediction of record values has potential environmental applications dealing, for example, with abrupt climate jumps, such as the prediction of rainfall extremes, highest water levels and sea surface or air record temperatures. In this article, and on the basis of observed Pareto records drawn from a sequential sample of independent and identically distributed random variables, we address the problem of Bayesian prediction of future records. The Bayesian predictive distribution is developed for future records and the corresponding highest posterior density (HPD)-prediction intervals are established. A data set representing the record values of average July temperatures in Neuenburg, Switzerland, is used to illustrate the proposed prediction procedure's environmental application.