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Constraints are a common feature of modern statistical models. Statistical inference for models with constraints using the usual methods based on the Wald and likelihood ratio statistics turns out to be problematical. Because the constraints constitute prior information, though, Bayesian statistical inference would seem to be appropriate.

Geweke (1995) describes methods for generating simulations of posterior distributions of the parameters of constrained models. These methods, the Markov chain Monte Carlo simulators, are significantly more computationally intensive than even the simple bootstrap methods. Moreover, each statistical model requires special attention, obviating a general computer program.

Newton and Raftery (1994) propose an SIR adjusted weighted likelihood bootstrap for generating a simulated posterior distribution of the parameters. Monte Carlo evidence was presented here showing the relative success of the method.

R. Schoenberg
Fri Sep 12 09:47:41 PDT 1997