Abstract:
In this thesis, we present solutions for the
controlled calibration problem under the Bayesian perspective to
statistical inference. The first problem considered is related to the
linear case with elliptically distributed errors. For the elliptical
dependent model it is shown that the posterior distribution for the
quantity of interest coincides with the posterior distribution obtained
under the normality assumption with an improper prior distribution. A
conjugate prior analysis is also considered. The coincidence of the
inference is not noted for the independent elliptical model. As
consequences of some prior specifications and representability of the
elliptical model, general expressions are obtained for the posterior
distributions, which are characterized as mixtures of known
distributions. Moreover, simple conditional posterior distributions of
one parameter given the others were obtained which allowed the use of
the Gibbs sampler to obtain approximations to the posterior
distributions of the quantities of interest. Subsequently, the
calibration problem for nonlinear situations was considered under the
assumption that the response variable is categorized. A generalization
of the well know probity model was considered, by taking an elliptical
distribution function as the link function. For this case, an
asymptotic approximation was obtained for the posterior distribution.
A MCMC (Monte Carlo Markov Chain) solution is considered for the
binomial model. For the multinomial model, a MCMC solution is present
and the conditional distributions required for implementing the
approach are obtained.