On the Determination of

Models derived from scientific considerations often exhibit four characteristics: (1) a likelihood is not available; (2) prior information is available; (3) a portion of the prior information is expressed in terms of functionals of the model that cannot be converted into an analytic prior on model parameters; (4) the model can be simulated. In addition, (5) either a parametric statistical model for the data is known from the literature or can be determined. The latter is nearly always the case because sieves are admissible. We develop a computationally intensive Bayesian modelling strategy for estimation and inference for scientific models that meet this description including methods for assessing model adequacy. An important adjunct to the method is that the implied map from the parameters of the scientific model to the parameters of the statistical model and to functionals of the scientific model becomes available. This map is a powerful tool for eliciting the properties of the scientific model and understanding the reasons for model success or failure. The methods are applied to a consumption based asset pricing model that uses habit persistence to overcome the known statistical inadequacies of the classical consumption based asset pricing model