Multivariate Calibration and Yield Estimation

Abstract

Abstract : Calibration of the linear magnitude-yield relation and estimation of yields from subsequent vector magnitudes is studied from the classical and Bayesian points of view. Calibration regressions are developed using (1) sampled magnitude-yield pairs, (2) sampled pairs and prior information and (3) sampled magnitudes and CORRTEX measurements. Yield estimates and confidence intervals are derived under all three assumptions using the predictive distribution of the observed magnitude. Prior information, such as might be provided by expert panels, is incorporated through distributional assumptions made on the slope- intercept vectors and the yield-adjusted magnitude covariance matrix. A maximum likelihood estimation procedure is derived for the case where CORRTEX yields are available. All methods are illustrated on a population of 16 magnitude pairs (m sub b, L sub g) and associated announced yields from Semipalatinsk.