September 22, 2017 11:30 AM / 12:30 PMBlocker Building (BLOC), Room 113979-845-3141
Department of Statistics Rice University
"Dynamic Shrinkage Processes"
We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon the global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we allow the local scale parameters to depend on the history of the shrinkage process. The resulting processes inherit the desirable shrinkage behavior of popular global-local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modeling time series data or regression functions with local features. We construct a highly efficient Gibbs sampling algorithm by adapting successful techniques from stochastic volatility modeling and deriving a Polya-Gamma scale mixture representation of the proposed process. We use dynamic shrinkage processes to produce superior Bayesian trend filtering estimates and posterior credible intervals for irregular curve-fitting of minute-by-minute Twitter CPU usage data, and develop an adaptive time-varying parameter regression model to assess the efficacy of the Fama-French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that with the exception of the market risk, no other risk factors are significant except for brief periods.
September 29, 2017 11:30 AM / 12:30 PMBlocker Building (BLOC), Room 113979-845-3141
JEFFREY D. HART
Department of Statistics Texas A&M University
"Prior-free Bayes Factors Based on Data Splitting"
Bayes factors that do not require prior distributions are proposed for testing one parametric model versus another. These Bayes factors are relatively simple to compute, relying only on maximum likelihood estimates, and are Bayes consistent at an exponential rate for nested models even when the smaller model is true. These desirable properties derive from the use of data splitting and the simplicity of Bayes factors for comparing fully specified models. A simulation study explores practical concerns, and the methodology is illustrated with civil engineering data involving compressive strength of concrete.