The subjective Bayesian approach to the treatment of several models begins by assigning
a prior probability to each model, with the prior probabilities summing to one.
Since each model is already endowed with a prior probability distribution for its parameters
and for the probability distribution of observable data conditional on its parameters,
there is then a complete probability distribution over the space of models, parameters,
and observable data. (No particular problems arise from non-nesting of models in this
framework.) This probability space can then be augmented with the distribution of an
object or vector of objects of interest. For example, in a macroeconomic policy setting the
models could include VARs,. DSGEs, and traditional large-scale macroeconomic models,
and the vector of interest might include future output growth, interest rates, inflation and
unemployment, whose distribution is implied by each of the models considered. Implicit
in this formulation is the conditional distribution of the vector of interest conditional on
the observed data. Technically, this requires the integration (or marginalization) of parameters
in each model as well as the models themselves. As a practical matter this usually
proceeds by first computing the probability of each model conditional on the data, and
then using these probabilities as weights in averaging the posterior distribution of the
vector of interest in each model.