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Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques. (English) Zbl 1330.62108
Summary: Computationally efficient simulation methods for hierarchical Bayesian analysis of the seemingly unrelated regression (SUR) and simultaneous equations models (SEM) are proposed and applied. These methods combine a direct Monte Carlo (DMC) approach and an importance sampling procedure to calculate Bayesian estimation and prediction results, namely, Bayesian posterior densities for parameters, predictive densities for future values of variables and associated moments, intervals and other quantities. The results obtained by our approach are compared to those yielded by use of MCMC techniques. Finally, we show that our algorithm can be applied to the Bayesian analysis of state space models.

MSC:
62F15 Bayesian inference
65C05 Monte Carlo methods
65C60 Computational problems in statistics (MSC2010)
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