Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

Abstract

This paper develops a Bayesian approach to analysis of a generalized least squares(GLS) regression model for regional analyses of hydrologic data. The new approachallows computation of the posterior distributions of the parameters and the model errorvariance using a quasi-analytic approach. Two regional skew estimation studies illustratethe value of the Bayesian GLS approach for regional statistical analysis of a shapeparameter and demonstrate that regional skew models can be relatively precise witheffective record lengths in excess of 60 years. With Bayesian GLS the marginal posteriordistribution of the model error variance and the corresponding mean and variance of theparameters can be computed directly, thereby providing a simple but important extension ofthe regional GLS regression procedures popularized by Tasker and Stedinger (1989), whichis sensitive to the likely values of the model error variance when it is small relative to thesampling error in the at-site estimator.