Models, prior information, and Bayesian analysis

Formulation of models for observations and prior densities for their parameters is an important activity in many sciences. In the present paper, after a discussion of this area of activity, entropy-based methods are employed to derive many central econometric and statistical models and noninformative and informative prior densities for their parameters in an explicit, reproducible manner. Examples are provided to illustrate the general procedures. In particular, maxent is employed to produce linear and nonlinear regression and autoregression models, hierarchical models, time-varying parameter models, etc. Then maximal data information prior (MDIP) densities for hyperparameters, common parameters in different likelihood functions, multinomial parameters, etc, are derived. Also the MDIP approach is utilized to produce prior odds for alternative hypotheses or models.