  We develop a Bayesian framework for estimation and prediction of dynamic
models for observations from the two-parameter exponential family. Different
link functions are introduced to model both the mean and the precision in the
exponential family allowing the introduction of covariates and time series
components. We explore conjugacy and analytical approximations under the class
of partial specified models to keep the computation fast. The algorithm of
West, Harrison and Migon (1985) is extended to cope with the two-parameter
exponential family models. The methodological novelties are illustrated with
two applications to real data. The first, considers unemployment rates in
Brazil and the second some macroeconomic variables for the United Kingdom.
