Flexible Evaluation of Surrogate Markers with Bayesian Model Averaging

Provides functions to estimate the proportion of treatment effect explained by the surrogate marker using a Bayesian Model Averaging approach. Duan and Parast (2023) .

Capture-Recapture Estimation using Bayesian Model Averaging

Performs Bayesian model averaging for capture-recapture. This includes code to stratify records, check the strata for suitable overlap to be used for capture-recapture, and some functions to plot the estimated population size.

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 Model Averaging for Univariate Link Latent Gaussian Models

Bayesian model averaging (BMA) algorithms for univariate link latent Gaussian models (ULLGMs). For detailed information, refer to Steel M.F.J. & Zens G. (2024) "Model Uncertainty in Latent Gaussian Models with Univariate Link Function" . The package supports various g-priors and a beta-binomial prior on the model space. It also includes auxiliary functions for visualizing and tabulating BMA results. Currently, it offers an out-of-the-box solution for model averaging of Poisson log-normal (PLN) and binomial logistic-normal (BiL) models. The codebase is designed to be easily extendable to other likelihoods, priors, and link functions.

Bayesian Model Averaging of Covariate Adjusted Negative-Binomial Dose-Response

Dose-response modeling for negative-binomial distributed data with a variety of dose-response models. Covariate adjustment and Bayesian model averaging is supported. Functions are provided to easily obtain inference on the dose-response relationship and plot the dose-response curve.

Estimate Ensemble Bayesian Model Averaging Forecasts using Gibbs Sampling or EM-Algorithms

Create forecasts from multiple predictions using ensemble Bayesian model averaging (EBMA). EBMA models can be estimated using an expectation maximization (EM) algorithm or as fully Bayesian models via Gibbs sampling. The methods in this package are Montgomery, Hollenbach, and Ward (2015) and Montgomery, Hollenbach, and Ward (2012) .

Bayesian Variable Selection and Model Averaging using Bayesian Adaptive Sampling

Package for Bayesian Variable Selection and Model Averaging in linear models and generalized linear models using stochastic or deterministic sampling without replacement from posterior distributions. Prior distributions on coefficients are from Zellner's g-prior or mixtures of g-priors corresponding to the Zellner-Siow Cauchy Priors or the mixture of g-priors from Liang et al (2008) for linear models or mixtures of g-priors from Li and Clyde (2019) in generalized linear models. Other model selection criteria include AIC, BIC and Empirical Bayes estimates of g. Sampling probabilities may be updated based on the sampled models using sampling w/out replacement or an efficient MCMC algorithm which samples models using a tree structure of the model space as an efficient hash table. See Clyde, Ghosh and Littman (2010) for details on the sampling algorithms. Uniform priors over all models or beta-binomial prior distributions on model size are allowed, and for large p truncated priors on the model space may be used to enforce sampling models that are full rank. The user may force variables to always be included in addition to imposing constraints that higher order interactions are included only if their parents are included in the model. This material is based upon work supported by the National Science Foundation under Division of Mathematical Sciences grant 1106891. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Efficient Leave-One-Out Cross-Validation and WAIC for Bayesian Models

Efficient approximate leave-one-out cross-validation (LOO) for Bayesian models fit using Markov chain Monte Carlo, as described in Vehtari, Gelman, and Gabry (2017) . The approximation uses Pareto smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. As a byproduct of the calculations, we also obtain approximate standard errors for estimated predictive errors and for the comparison of predictive errors between models. The package also provides methods for using stacking and other model weighting techniques to average Bayesian predictive distributions.

Flexible Bayesian Model Selection and Model Averaging

Implements the Mode Jumping Markov Chain Monte Carlo algorithm described in and its Genetically Modified counterpart described in as well as the sub-sampling versions described in for flexible Bayesian model selection and model averaging.

Bayesian Network Structure Learning, Parameter Learning and Inference

Bayesian network structure learning, parameter learning and inference. This package implements constraint-based (PC, GS, IAMB, Inter-IAMB, Fast-IAMB, MMPC, Hiton-PC, HPC), pairwise (ARACNE and Chow-Liu), score-based (Hill-Climbing and Tabu Search) and hybrid (MMHC, RSMAX2, H2PC) structure learning algorithms for discrete, Gaussian and conditional Gaussian networks, along with many score functions and conditional independence tests. The Naive Bayes and the Tree-Augmented Naive Bayes (TAN) classifiers are also implemented. Some utility functions (model comparison and manipulation, random data generation, arc orientation testing, simple and advanced plots) are included, as well as support for parameter estimation (maximum likelihood and Bayesian) and inference, conditional probability queries, cross-validation, bootstrap and model averaging. Development snapshots with the latest bugfixes are available from < https://www.bnlearn.com/>.