Joint Hierarchical Gaussian Process Model with Application to Forecast in Medical Monitoring

A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is minimized through the hierarchical design. The method is further extended to joint modeling of continuous measurements and survival events. The baseline hazard, covariate and joint effects are conveniently modeled in this hierarchical structure. The estimation and inference are implemented in fully Bayesian framework using the objective and shrinkage priors. In simulation studies, this model shows robustness in latent estimation, correlation detection and high accuracy in forecasting. The model is illustrated with medical monitoring data from cystic fibrosis (CF) patients. Estimation and forecasts are obtained in the measurement of lung function and records of acute respiratory events. Keyword: Extrapolation, Joint Model, Longitudinal Model, Hierarchical Gaussian Process, Cystic Fibrosis, Medical Monitoring

BET: Bayesian Ensemble Trees for Clustering and Prediction in Heterogeneous Data

We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble trees (BET) and model them as an infinite mixture Dirichlet process. We show that BET adapts to data heterogeneity and accurately estimates each component. Compared with the bootstrap-aggregating approach, BET shows improved prediction performance with fewer trees. We develop an efficient estimating procedure with improved sampling strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations, classification of breast cancer and regression of lung function measurement of cystic fibrosis patients. Keywords: Bayesian CART; Dirichlet Process; Ensemble Approach; Heterogeneity; Mixture of Trees.