Subhadip Pal

In this work, we develop new data augmentation algorithms for Bayesian analysis of directional data using the von Mises-Fisher distribution in arbitrary dimensions. The approach leads to a new class of distributions, called the Modified Pólya-Gamma distribution, which we construct in detail. The proposed data augmentation strategies circumvent the need for analytic approximations to integration, numerical integration, or Metropolis-Hastings for the corresponding posterior inference. Simulations and real data examples are presented to demonstrate the applicability and to apprise the performance of the proposed procedures.

Background: Prediction and classification algorithms are commonly used in clinical research for identifying patients susceptible to clinical conditions such as diabetes, colon cancer, and Alzheimer’s disease. Developing accurate prediction and classification methods benefits personalized medicine. Building an excellent predictive model involves selecting the features that are most significantly associated with the outcome. These features can include several biological and demographic characteristics, such as genomic biomarkers and health history. Such variable selection becomes challenging when the number of potential predictors is large. Bayesian shrinkage models have emerged as popular and flexible methods of variable selection in regression settings. This work discusses variable selection with three shrinkage priors and illustrates its application to clinical data such as Pima Indians Diabetes, Colon cancer, ADNI, and OASIS Alzheimer’s real-world data.Methods: A unified Bayesian hierarchical framework that implements and compares shrinkage priors in binary and multinomial logistic regression models is presented. The key feature is the representation of the likelihood by a Polya-Gamma data augmentation, which admits a natural integration with a family of shrinkage priors, specifically focusing on Horseshoe, Dirichlet Laplace, and Double Pareto priors. Extensive simulation studies are conducted to assess the performances under different data dimensions and parameter settings. Measures of accuracy, AUC, brier score, L1 error, cross-entropy, and ROC surface plots are used as evaluation criteria comparing the priors with frequentist methods as Lasso, Elastic-Net, and Ridge regression.Results: All three priors can be used for robust prediction on significant metrics, irrespective of their categorical response model choices. Simulation studies could achieve the mean prediction accuracy of 91.6% (95% CI: 88.5, 94.7) and 76.5% (95% CI: 69.3, 83.8) for logistic regression and multinomial logistic models, respectively. The model can identify significant variables for disease risk prediction and is computationally efficient.Conclusions: The models are robust enough to conduct both variable selection and prediction because of their high shrinkage properties and applicability to a broad range of classification problems.