MODELS, PRIOR INFORMATION, AND BAYESIAN-ANALYSIS

Formulation of models for observations and prior densities for their p arameters is an important activity in many sciences. In the present pa per, after a discussion of this area of activity, entropy-based method s are employed to derive many central econometric and statistical mode ls and noninformative and informative prior densities for their parame ters in an explicit, reproducible manner. Examples are provided to ill ustrate the general procedures. In particular, maxent is employed to p roduce linear and nonlinear regression and autoregression models, hier archical models, time-varying parameter models, etc. Then maximal data information prior (MDIP) densities for hyperparameters, common parame ters in different likelihood functions, multinomial parameters, etc, a re derived. Also the MDIP approach is utilized to produce prior odds f or alternative hypotheses or models.