| In this dissertation, we discuss three new prior distributions that are useful for applied Bayesian analyses. The first of these is a prior distribution for the covariance matrix of a multinomial probit model. This prior restricts the trace of the covariance matrix instead of the standard identifying restriction which fixes a single element of the covariance. We find that this approach avoids forcing the reseacher to make an arbitrary choice that can have large ramifications on the posterior predictions. The resulting Markov chain Monte Carlo algorithm compares favorably to the methods currently in use.;The next prior distribution we discuss is a prior for the covariance of an endogenous switching model (or selection model) with a multinomial response. This prior distribution can be estimated with a Gibbs sampler, whereas previous related work required Metropolis-Hastings steps to sample the covariance matrix. Further, we are able to incorporate the use of working parameters, which improve the mixing properties of the resulting Markov chains. We use these methods to model data from the Wisconsin Longitudinal Study.;Finally, we suggest a data-dependent prior distribution for the model space of Bayesian model averaging (BMA). We suggest a leave-one-out cross-validation process that chooses a prior from a class of prior distributions. We call our method "tuned Bayesian model averaging" or tBMA. In simulated examples, we find that tBMA provides significant gains in out-of-sample prediction compared to standard BMA. We apply these methods to an application which seeks to identify determinants of economic growth in African countries and the rest of the world. |
