Chapter 9 Bayesian analysis of simultaneous equation systems

This chapter discusses the Bayesian inference and identification. A Bayesian analysis of the scanning electron microscope (SEM) proceeds along the same lines as any other Bayesian analysis. Thus, if the analyst has chosen to work in a given parameter space, a prior density on that space is defined and Bayes theorem is applied to revise this prior density in the light of available data. The resulting posterior density is then used to solve problems of decision and inference. Predictive densities for future observations can also be derived. The chapter discusses numerical methods for evaluating key characteristics of posterior and predictive density functions. For models with many parameters, such as most simultaneous equation models, analytical methods remain indispensable to evaluate these densitieseither fully, or conditionally on a few parameters amenable to numerical treatment, or approximately to construct importance functions for Monte Carlo integration. The classes of prior densities permitting analytical evaluation of the posterior density are limited. In most Bayesian analyses they comprise essentially the so-called noninformative and natural-conjugate families.