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.