Bayesian Estimation of Neyman–Scott Rectangular Pulse Model Parameters in Comparison with Other Parameter Estimation Methods

Abstract

Neyman–Scott rectangular pulse is a stochastic rainfall model with five parameters. The impacts of initial values and optimization methods on the parameter estimation of the Neyman–Scott rectangular pulse model were investigated using both the method of moments and the method of maximum likelihood. The estimates using the method of moments were influenced by the optimization method and were sensitive to the initial values and the aggregation scale of the data. Thus, by using frequentist estimation methods, we cannot guarantee the unique values as estimates. The aim of this study is to find more reliable unique values as estimates using a Bayesian approach. In this approach, parameters are estimated from the posterior distribution, and model performance is assessed by comparing observed values with fitted values. Slice sampling within the Gibbs sampler algorithm demonstrates superior convergence and model fitting, yielding unique estimates for the model parameters. The main conclusion of this study is that Bayesian estimation methods outperform other estimation methods in terms of providing reliable and stable estimates that improve rainfall generation accuracy.