esentation 2 Information Criteria. Generally, most information criteria select the model that minimize a quantity similar to ICm = \Gamma2log ` f (yj `m ; m) ' + dmF (1) ffl ` m is the parameter vector and ` m are the the MLE. ffl F is the penalty for each additional parameter used in the model. In linear regression models: ffl ` T m = [fi T (m) ; oe 2 ]. ffl Minimizing \Gamma2log ` f (yj ` m ; m) ' is equivalent to minimizing nlog(RSSm<F43.1

We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley’s paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and log-linear regressions under our proposed prior densities with a series of simulated and real data examples.

This document reviews and applies recently developed techniques for Bayesian estimation and model selection in the context of Time Series modeling for Stochastic Volatility. After the literature review on Generalized Conditional Autoregressive models, Stochastic Volatility models, and the relevant results on Markov Chain Monte Carlo methods (MCMC), an example applying such techniques is shown. The methodology is used with a series of Weekly Colombian-USA Exchange Rate on seven different models. The GARCH model, which uses Type-IV Pearson distribution, is favored for the selecting technique,