Preliminary Dissertation Proposal
نویسنده
چکیده
The topic of my dissertation research is Bayesian methods in the social sciences. There will be several parts to the dissertation. One part, the focus of this proposal, is a novel method called tuned Bayesian model averaging (tBMA) that modifies Bayesian model averaging (BMA) by using the data to inform the prior specification. BMA is a tool that accounts for model uncertainty in typical regression analyses (Hoeting et al., 1999). BMA requires that the analyst specify a prior distribution over the collection of models under consideration. Typically, users of BMA have put equal prior probability on all models. Since this specification puts nearly all of the prior mass on models with an intermediate number of terms, we find that this can result in poor predictive ability when the data generating model depends on a large proportion of the available covariates. The tBMA process specifies a method that results in a data-dependent prior over the model space. We define a hyper-parameter λ that favors small models when close to zero, and large models when close to one. This λ is chosen through leave-one-out methods like those that are used to select the tuning parameter in smoothing spline analyses (Wahba, 1990). We start with a generalized cross-validation (GCV) procedure that provides good results when the true data generating model contains a large proportion of the available predictors. We find that an approximation used in the derivation of this GCV criterion leads to poor performance in some cases, however. We then derive an ordinary cross-validation (OCV) version of tBMA that fixes this problem. Simulation results are presented that show out-of-sample prediction error can be reduced by a factor of two in some situations, relative to standard BMA. The second part is a Bayesian Heckman-type selection model for multinomial data. The Heckman model is commonly used in the social sciences
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