Gaussian processes Correlated Bayesian Additive Regression Trees

In recent years, Bayesian Additive Regression Trees (BART) has garnered increased attention, leading to the development of various extensions for diverse applications. However, there has been limited exploration of its utility in analyzing correlated data. This paper introduces a novel extension of BART, named Correlated BART (CBART). Unlike the original BART with independent errors, CBART is specifically designed to handle correlated (dependent) errors. Additionally, we propose the integration of CBART with Gaussian processes (GP) to create a new model termed GP-CBART. This innovative model combines the strengths of the Gaussian processes and CBART, making it particularly well-suited for analyzing time series or spatial data. In the GP-CBART framework, CBART captures the nonlinearity in the mean regression (covariates) function, while the Gaussian processes adeptly models the correlation structure within the response. Additionally, given the high flexibility of both CBART and GP models, their combination may lead to identification issues. We provide methods to address these challenges. To demonstrate the effectiveness of CBART and GP-CBART, we present corresponding simulated and real-world examples

A Program for Multivariate Normal Bayesian Allocation and Examples of Wide Discrepancies for Dimension Reducing Optimal Allocation and Separation Procedures in Multivariate Normal Populations

1 online resource (PDF, 46 pages

Information Asymptotics and Inequalities for Posterior and Predictive Distributions

1 online resource (PDF, 19 pages

Local Prior Influence

1 online resource (PDF, 36 pages

Bayesian Inference for Periodic Regime-Switching Models

Nous présentons une classe générale de modèles non-linéaires avec changement de régime Markovienne. Les modèles proposés permettent d'avoir une structure périodique pour la chaîne de Markov ainsi que des effets saisonniers dans chaqu'un des régimes. La classe de structure proposée permet d'avoir des interdépendences entre les fluctuationssaisonnières, les cycles d'affaire et la composante de croissance. Une méthode Baysienne basée sur le principe de l'échantillonage de Gibbs est utilisée pour estimation et interférence. Deux exemples empiriques sont fournis, un premier utilisant des séries de mise en chantier de0501sons, tandis que le second couvre la production industrielle aux États-Unis.We present a general class of nonlinear time series Markov regime-switching models for seasonal data which may exhibit periodic features in the hidden Markov process as well as in the laws of motion in each of the regimes. This class of models allows for nontrivial dependencies between seasonal, cyclical and long-term patterns in the data. To overcome the competitional burden we adopt a Bayesian approach to estimation and inference. This paper contains two empirical examples as illustration, one using housing starts data while the other covers U.S. post WWII individual production

Effect of Blood Pressure Control on Long-Term Risk of End-Stage Renal Disease and Death Among Subgroups of Patients With Chronic Kidney Disease.

Background Our objective was to explore the effect of intensive blood pressure (BP) control on kidney and death outcomes among subgroups of patients with chronic kidney disease divided by baseline proteinuria, glomerular filtration rate, age, and body mass index. Methods and Results We included 840 MDRD (Modification of Diet in Renal Disease) trial and 1067 AASK (African American Study of Kidney Disease and Hypertension) participants. We used Cox models to examine whether the association between intensive BP control and risk of end-stage renal disease (ESRD) or death is modified by baseline proteinuria (≥0.44 versus <0.44 g/g), glomerular filtration rate (≥30 versus <30 mL/min per 1.73 m2), age (≥40 versus <40 years), or body mass index (≥30 versus <30 kg/m2). The median follow-up was 14.9 years. Strict (versus usual) BP control was protective against ESRD (hazard ratio [HR]ESRD, 0.77; 95% CI, 0.64-0.92) among those with proteinuria ≥0.44 g/g but not proteinuria <0.44 g/g. Strict (versus usual) BP control was protective against death (HRdeath, 0.73; 95% CI, 0.59-0.92) among those with glomerular filtration rate <30 mL/min per 1.73 m2 but not glomerular filtration rate ≥30 mL/min per 1.73 m2 (HRdeath, 0.98; 95% CI, 0.84-1.15). Strict (versus usual) BP control was protective against ESRD among those ≥40 years (HRESRD, 0.82; 95% CI, 0.71-0.94) but not <40 years. Strict (versus usual) BP control was also protective against ESRD among those with body mass index ≥30 kg/m2 (HRESRD, 0.75; 95% CI, 0.61-0.92) but not body mass index <30 kg/m2. Conclusions The ESRD and all-cause mortality benefits of intensive BP lowering may not be uniform across all subgroups of patients with chronic kidney disease. But intensive BP lowering was not associated with increased risk of ESRD or death among any subgroups that we examined

Bayesian Ensemble Learning

We develop a Bayesian “sum-of-trees” model, named BART, where each tree is constrained by a prior to be a weak learner. Fitting and inference are accomplished via an iterative backfitting MCMC algorithm. This model is motivated by ensemble methods in general, and boosting algorithms in particular. Like boosting, each weak learner (i.e., each weak tree) contributes a small amount to the overall model. However, our procedure is defined by a statistical model: a prior and a likelihood, while boosting is defined by an algorithm. This model-based approach enables a full and accurate assessment of uncertainty in model predictions, while remaining highly competitive in terms of predictive accuracy

Bayesian Inference for Periodic Regime-Switching Models

We present a general class of nonlinear time series Markov regime-switching models for seasonal data which may exhibit periodic features in the hidden Markov process as well as in the laws of motion in each of the regimes. This class of models allows for nontrivial dependencies between seasonal, cyclical and long-term patterns in the data. To overcome the competitional burden we adopt a Bayesian approach to estimation and inference. This paper contains two empirical examples as illustration, one using housing starts data while the other covers U.S. post WWII individual production. Nous présentons une classe générale de modèles non-linéaires avec changement de régime Markovienne. Les modèles proposés permettent d'avoir une structure périodique pour la chaîne de Markov ainsi que des effets saisonniers dans chaqu'un des régimes. La classe de structure proposée permet d'avoir des interdépendences entre les fluctuationssaisonnières, les cycles d'affaire et la composante de croissance. Une méthode Baysienne basée sur le principe de l'échantillonage de Gibbs est utilisée pour estimation et interférence. Deux exemples empiriques sont fournis, un premier utilisant des séries de mise en chantier de0501sons, tandis que le second couvre la production industrielle aux États-Unis.Markov switching; Periodic models; Seasonality; Gibbs sampler, Modèles à changement de régime ; Structure périodique ; Saisonnalité ; Échantillonage de Gibbs