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Benchmark Priors for Bayesian Model Averaging

Date: Thu, 2 Apr 1998 12:20:59 -0600
Date (revised): Sat, 31 Jul 1999 11:41:07 -0500 (CDT)
Date (revised): Sun, 7 Oct 2001 10:39:37 -0500
Date (revised): Mon, 8 Oct 2001 08:57:00 -0500
Date (revised): Mon, 8 Oct 2001 09:06:13 -0500

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, "diffuse'' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an ``automatic'' or ``benchmark'' prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate $g$-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter $g_{0j}$. The consequences of different choices for $g_{0j}$ are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of $g_{0j}$ in a simulation study. The use of the MC$^3$ algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a "benchmark'' prior specification in a linear regression context with model uncertainty.

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EconWPA began as a conversation between Bob Parks and Larry Blume on January 28, 1993. I located Paul Ginsparg's archive (then and he graciously installed his software on a Sun Sparc system which was supporting the department of economics email and computation. EconWPA began accepting papers July 1, 1993 and had ftp, email, gopher and web interfaces. The web interface for submissions was engineered into existence in July 1995. A complete and catastrophic machine failure in 1999 caused the loss of EconWPA's email new paper announcment service at which time there were over 15,000 subscriptions with over 8,000 unique email addresses.

In 2005, Arts and Sciences commandeered the computing services that I had provided to the Department of Economics since 1987. Some might say that the department was sold out, others would (erroneously) claim that centralization is efficient, and still others would claim that I have few marketing skills.

I was told that I could keep operating EconWPA (as well as many other services including,, and three RePEc servers) but I would receive no support (hardware, software, or anthing else) and (as had been the case) no compensation. At that point, given the apparent low valuation of my activities by the department, and university, it made no sense for me to continue operating EconWPA or other services.

Thanks to all who have supported EconWPA in the past.

A Chinese curse states May you live in intersting times. I have. Bob Parks - Jan 2006