A Bayesian nonparametric model for upper record data

Abstract

• This paper proposes a nonparametric Bayesian approach for record values with the Pareto kernels. • Two sampling algorithms are compared in posterior computation. • The nonparametric model with the blocked Gibbs sampling is outperformed in two real problems. This paper proposes a nonparametric Bayesian approach using a Dirichlet process mixture model with Pareto kernels to estimate the density of observed upper record values and predict future upper record values. A reference distribution, G 0 , in the nonparametric Bayesian model is provided on the basis of an objective prior for unknown parameters of the Pareto distribution to avoid difficulties caused by finding values of hyperparameters in G 0 . For the posterior computation, two sampling algorithms are employed and compared. Finally, the approach provides the estimated distribution of observed upper record values and prediction of future upper record values in two real problems, average annual temperatures and carbon dioxide emissions.