Sensitivity, Data Fitness and Parametric Uncertainty

Posterior uncertainty is a measure of the spread of the product of the prior distribution and the likelihood function. As shown previously in the 4th example of Section 2.1.6 (Chapter 2) a small posterior uncertainty is possible for poor data fitting. In this case, the normalizing constant will be large. 

On the other hand, the sensitivity is the change of model output X due to parameter perturbation and it can be quantified by the following matrix  

The slope of the posterior PDF depends on the sensitivity, which controls the rate of the change of the model output due to perturbation of the parameters. On the other hand, the posterior uncertainty of the parameters is controlled by the decaying rate (slope) of the posterior PDF in the neighborhood around the optimal point. Therefore, it is particularly important to investigate the sensitivity of a model around the optimal parameters. 

Bayesian Methods for Structural Dynamics and Civil Engineering 

In the next section, the Bayesian model class selection method is introduced for quantification and selection of model classes. It will be discussed for the globally identifiable case and the general case. The Ockham factor is introduced and it serves as the penalty for a complicated model, which appears naturally from the evidence. Computational issues will be discussed and 

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