In principle, the Bayesian approach to model selection is straightforward. Prior probability distributions are used to describe the uncertainty surrounding all unknowns. After observing the data, the posterior distribution provides a coherent post data summary of the remaining uncertainty which is relevant for model selection. However, the practical implementation of this approach often requires carefully tailored priors and novel posterior calculation methods. In this article, we illustrate some of the fundamental practical issues that arise for two different model selection problems: the variable selection problem for the linear model and the CART model selection problem.

We investigate the issue of model uncertainty in cross-country growth regressions using Bayesian Model Averaging (BMA). We find that the posterior probability is spread widely among many models, suggesting the superiority of BMA over choosing any single model. Out-of-sample predictive results support this claim. In contrast to Levine and Renelt (1992), our results broadly support the more ‘optimistic ’ conclusion of Salai-Martin (1997b), namely that some variables are important regressors for explaining cross-country growth patterns. However, care should be taken in the methodology employed. The approach proposed here is firmly grounded in statistical theory and immediately leads to posterior and predictive inference. Copyright © 2001 John Wiley & Sons, Ltd. 1.

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Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-con dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of

Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this paper is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure-of-fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the S&P100 index.

In 2008 all ECB publications feature a motif taken from the €10 banknote.

Zellner’s g-prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this paper, we study mixtures of g-priors as an alternative to default g-priors that resolve many of the problems with the original formulation, while maintaining the computational tractability that has made the g-prior so popular. We present theoretical properties of the mixture g-priors and provide real and simulated examples to compare the mixture formulation with fixed g-priors, Empirical Bayes approaches and other default procedures.

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Model averaging provides an alternative to model selection. An algorithm ARM rooted in information theory is proposed to combine different regression models/methods. A simulation is conducted in the context of linear regression to compare its performance with familiar model selection criteria AIC and BIC, and also with some Bayesian model averaging (BMA) methods. The simulation suggests

This paper proposes a Bayesian procedure for combining forecasts from multivariate forecasting models, e.g. VAR models. Standard applications of Bayesian model averaging suffer from a basic difficulty in this context, when additional variables are included and modelled the connection between the overall measure of fit for the model and the expected forecasting performance for the variables of interest is lost. We circumvent this problem by focusing on the predictive performance for the variables of interest and base the forecast combination on the predictive likelihood. Specifically we consider forecast combination and, indirectly, model selection for VAR models when there is uncertainty about which variables to include in the model in addition to the forecast variables. For this purpose we consider all possible combinations of variables and lag lengths and the models that arise from these. The procedure is evaluated in a small simulation study and found to perform competitively in applications to real world data.