Date of Completion
Brian Hartman, Yung S. Choi
Field of Study
Master of Science
Eliciting appropriate prior information from experts for a statistical model is no easy task. Expressing this information in terms of hyperparameters of prior distributions on abstract model parameters can be nearly impossible, especially after data augmentation or transformation. In previous work on logistic and binomial regression models, Hanson et al. (2014) assert that ``experts are confident only in their assessment of the population as a whole'' and propose a version of the g-prior which effectively places a standard beta distributed prior on the overall population probability of success. We explore the efficacy of using the informed g-prior in a real prediction problem involving electrical utility asset damages due to hurricanes in Connecticut. Prior information is elicited from a group of engineers at the electrical utility and several methods are used to select hyper-parameters for the g-prior. The out-of-sample predictive accuracy of these informed models is compared to the performance of models constructed under common reference priors (Jeffreys's, Gelman et al. (2008), and a noninformative specification of the g-prior) using IS-LOO (Vehtari et al., 2014; Vehtari and Gelman, 2014), root mean squared error (RMSE), and other statistics. In this application, with carefully selected hyper-parameters, binomial regression models using the informed g-prior match the predictive accuracy of common reference priors and offer no distinct advantage. Careless selection of hyper-parameters can however, lead to substantial reduction in predictive accuracy. Surprisingly, the noninformative specification of the g-prior performed marginally better than all other models tested in this paper; contradicting one of the findings in Hanson et al. (2014) In addition, we show the predictive accuracy gained by modeling spatial correlation in the residuals and prove that such models substantially outperform some statistical learning models growing in popularity in this field.
Lally, Nathan R., "The Informative g-Prior vs. Common Reference Priors for Binomial Regression With an Application to Hurricane Electrical Utility Asset Damage Prediction" (2015). Master's Theses. 813.