Nonparametric Failure Time Bayesian Additive Regression Trees

Nonparametric Failure Time (NFT) Bayesian Additive Regression Trees (BART): Time-to-event Machine Learning with Heteroskedastic Bayesian Additive Regression Trees (HBART) and Low Information Omnibus (LIO) Dirichlet Process Mixtures (DPM). An NFT BART model is of the form Y = mu + f(x) + sd(x) E where functions f and sd have BART and HBART priors, respectively, while E is a nonparametric error distribution due to a DPM LIO prior hierarchy. See the following for a complete description of the model at .

Co-Data Learning for Bayesian Additive Regression Trees

Estimate prior variable weights for Bayesian Additive Regression Trees (BART). These weights correspond to the probabilities of the variables being selected in the splitting rules of the sum-of-trees. Weights are estimated using empirical Bayes and external information on the explanatory variables (co-data). BART models are fitted using the 'dbarts' 'R' package. See Goedhart and others (2023) for details.

Bayesian Additive Regression Trees using Bayesian Model Averaging

"BART-BMA Bayesian Additive Regression Trees using Bayesian Model Averaging" (Hernandez B, Raftery A.E., Parnell A.C. (2018) ) is an extension to the original BART sum-of-trees model (Chipman et al 2010). BART-BMA differs to the original BART model in two main aspects in order to implement a greedy model which will be computationally feasible for high dimensional data. Firstly BART-BMA uses a greedy search for the best split points and variables when growing decision trees within each sum-of-trees model. This means trees are only grown based on the most predictive set of split rules. Also rather than using Markov chain Monte Carlo (MCMC), BART-BMA uses a greedy implementation of Bayesian Model Averaging called Occam's Window which take a weighted average over multiple sum-of-trees models to form its overall prediction. This means that only the set of sum-of-trees for which there is high support from the data are saved to memory and used in the final model.

Bayesian Additive Regression Trees with Stan-Sampled Parametric Extensions

Fits semiparametric linear and multilevel models with non-parametric additive Bayesian additive regression tree (BART; Chipman, George, and McCulloch (2010) ) components and Stan (Stan Development Team (2021) < https://mc-stan.org/>) sampled parametric ones. Multilevel models can be expressed using 'lme4' syntax (Bates, Maechler, Bolker, and Walker (2015) ).

Iterative Bayesian Additive Regression Trees Descriptor Selection Method

A statistical method based on Bayesian Additive Regression Trees with Global Standard Error Permutation Test (BART-G.SE) for descriptor selection and symbolic regression. It finds the symbolic formula of the regression function y=f(x) as described in Ye, Senftle, and Li (2023) .

Bayesian Applied Regression Modeling via Stan

Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Users specify models via the customary R syntax with a formula and data.frame plus some additional arguments for priors.

Bayesian Variable Selection and Model Choice for Generalized Additive Mixed Models

Bayesian variable selection, model choice, and regularized estimation for (spatial) generalized additive mixed regression models via stochastic search variable selection with spike-and-slab priors.

Bayesian Generalized Additive Model Selection

Generalized additive model selection via approximate Bayesian inference is provided. Bayesian mixed model-based penalized splines with spike-and-slab-type coefficient prior distributions are used to facilitate fitting and selection. The approximate Bayesian inference engine options are: (1) Markov chain Monte Carlo and (2) mean field variational Bayes. Markov chain Monte Carlo has better Bayesian inferential accuracy, but requires a longer run-time. Mean field variational Bayes is faster, but less accurate. The methodology is described in He and Wand (2023) .

Modelling Multivariate Data with Additive Bayesian Networks

The 'abn' R package facilitates Bayesian network analysis, a probabilistic graphical model that derives from empirical data a directed acyclic graph (DAG). This DAG describes the dependency structure between random variables. The R package 'abn' provides routines to help determine optimal Bayesian network models for a given data set. These models are used to identify statistical dependencies in messy, complex data. Their additive formulation is equivalent to multivariate generalised linear modelling, including mixed models with independent and identically distributed (iid) random effects. The core functionality of the 'abn' package revolves around model selection, also known as structure discovery. It supports both exact and heuristic structure learning algorithms and does not restrict the data distribution of parent-child combinations, providing flexibility in model creation and analysis. The 'abn' package uses Laplace approximations for metric estimation and includes wrappers to the 'INLA' package. It also employs 'JAGS' for data simulation purposes. For more resources and information, visit the 'abn' website.

Bayesian Regression Models using 'Stan'

Fit Bayesian generalized (non-)linear multivariate multilevel models using 'Stan' for full Bayesian inference. A wide range of distributions and link functions are supported, allowing users to fit -- among others -- linear, robust linear, count data, survival, response times, ordinal, zero-inflated, hurdle, and even self-defined mixture models all in a multilevel context. Further modeling options include both theory-driven and data-driven non-linear terms, auto-correlation structures, censoring and truncation, meta-analytic standard errors, and quite a few more. In addition, all parameters of the response distribution can be predicted in order to perform distributional regression. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their prior knowledge. Models can easily be evaluated and compared using several methods assessing posterior or prior predictions. References: Bürkner (2017) ; Bürkner (2018) ; Bürkner (2021) ; Carpenter et al. (2017) .