Tools for Bayesian Analyses

Provides tools for conducting Bayesian analyses and Bayesian model averaging (Kass and Raftery, 1995, , Hoeting et al., 1999, ). The package contains functions for creating a wide range of prior distribution objects, mixing posterior samples from 'JAGS' and 'Stan' models, plotting posterior distributions, and etc... The tools for working with prior distribution span from visualization, generating 'JAGS' and 'bridgesampling' syntax to basic functions such as rng, quantile, and distribution functions.

Harmonic Mean p-Values and Model Averaging by Mean Maximum Likelihood

The harmonic mean p-value (HMP) test combines p-values and corrects for multiple testing while controlling the strong-sense family-wise error rate. It is more powerful than common alternatives including Bonferroni and Simes procedures when combining large proportions of all the p-values, at the cost of slightly lower power when combining small proportions of all the p-values. It is more stringent than controlling the false discovery rate, and possesses theoretical robustness to positive correlations between tests and unequal weights. It is a multi-level test in the sense that a superset of one or more significant tests is certain to be significant and conversely when the superset is non-significant, the constituent tests are certain to be non-significant. It is based on MAMML (model averaging by mean maximum likelihood), a frequentist analogue to Bayesian model averaging, and is theoretically grounded in generalized central limit theorem. For detailed examples type vignette("harmonicmeanp") after installation. Version 3.0 addresses errors in versions 1.0 and 2.0 that led function p.hmp to control the familywise error rate only in the weak sense, rather than the strong sense as intended.

Model Selection and Multimodel Inference Based on (Q)AIC(c)

Functions to implement model selection and multimodel inference based on Akaike's information criterion (AIC) and the second-order AIC (AICc), as well as their quasi-likelihood counterparts (QAIC, QAICc) from various model object classes. The package implements classic model averaging for a given parameter of interest or predicted values, as well as a shrinkage version of model averaging parameter estimates or effect sizes. The package includes diagnostics and goodness-of-fit statistics for certain model types including those of 'unmarkedFit' classes estimating demographic parameters after accounting for imperfect detection probabilities. Some functions also allow the creation of model selection tables for Bayesian models of the 'bugs', 'rjags', and 'jagsUI' classes. Functions also implement model selection using BIC. Objects following model selection and multimodel inference can be formatted to LaTeX using 'xtable' methods included in the package.

Robust Bayesian T-Test

An implementation of Bayesian model-averaged t-tests that allows users to draw inferences about the presence versus absence of an effect, variance heterogeneity, and potential outliers. The 'RoBTT' package estimates ensembles of models created by combining competing hypotheses and applies Bayesian model averaging using posterior model probabilities. Users can obtain model-averaged posterior distributions and inclusion Bayes factors, accounting for uncertainty in the data-generating process (Maier et al., 2024, ). The package also provides a truncated likelihood version of the model-averaged t-test, enabling users to exclude potential outliers without introducing bias (Godmann et al., 2024, ). Users can specify a wide range of informative priors for all parameters of interest. The package offers convenient functions for summary, visualization, and fit diagnostics.

The Bayesian Causal Effect Estimation Algorithm

A Bayesian model averaging approach to causal effect estimation based on the BCEE algorithm. Currently supports binary or continuous exposures and outcomes. For more details, see Talbot et al. (2015) Talbot and Beaudoin (2022) .

Bayesian Mortality Modelling with 'Stan'

Implementation of popular mortality models using the 'rstan' package, which provides the R interface to the 'Stan' C++ library for Bayesian estimation. The package supports well-known models proposed in the actuarial and demographic literature including the Lee-Carter (1992) and the Cairns-Blake-Dowd (2006) models. By a simple call, the user inputs deaths and exposures and the package outputs the MCMC simulations for each parameter, the log likelihoods and predictions. Moreover, the package includes tools for model selection and Bayesian model averaging by leave future-out validation.

Phase I Optimal Dose Assignment using the FBCRM and MFBCRM Methods

Performs dose assignment and trial simulation for the FBCRM (Fully Bayesian Continual Reassessment Method) and MFBCRM (Mixture Fully Bayesian Continual Reassessment Method) phase I clinical trial designs. These trial designs extend the Continual Reassessment Method (CRM) and Bayesian Model Averaging Continual Reassessment Method (BMA-CRM) by allowing the prior toxicity skeleton itself to be random, with posterior distributions obtained from Markov Chain Monte Carlo. On average, the FBCRM and MFBCRM methods outperformed the CRM and BMA-CRM methods in terms of selecting an optimal dose level across thousands of randomly generated simulation scenarios. Details on the methods and results of this simulation study are available on request, and the manuscript is currently under review.

Measures of Uncertainty for Model Selection

Following the common types of measures of uncertainty for parameter estimation, two measures of uncertainty were proposed for model selection, see Liu, Li and Jiang (2020) . The first measure is a kind of model confidence set that relates to the variation of model selection, called Mac. The second measure focuses on error of model selection, called LogP. They are all computed via bootstrapping. This package provides functions to compute these two measures. Furthermore, a similar model confidence set adapted from Bayesian Model Averaging can also be computed using this package.

Robust Bayesian Survival Analysis

A framework for estimating ensembles of parametric survival models with different parametric families. The RoBSA framework uses Bayesian model-averaging to combine the competing parametric survival models into a model ensemble, weights the posterior parameter distributions based on posterior model probabilities and uses Bayes factors to test for the presence or absence of the individual predictors or preference for a parametric family (Bartoš, Aust & Haaf, 2022, ). The user can define a wide range of informative priors for all parameters of interest. The package provides convenient functions for summary, visualizations, fit diagnostics, and prior distribution calibration.

Robust Bayesian Meta-Analyses

A framework for estimating ensembles of meta-analytic and meta-regression models (assuming either presence or absence of the effect, heterogeneity, publication bias, and moderators). The RoBMA framework uses Bayesian model-averaging to combine the competing meta-analytic models into a model ensemble, weights the posterior parameter distributions based on posterior model probabilities and uses Bayes factors to test for the presence or absence of the individual components (e.g., effect vs. no effect; Bartoš et al., 2022, ; Maier, Bartoš & Wagenmakers, 2022, ). Users can define a wide range of prior distributions for + the effect size, heterogeneity, publication bias (including selection models and PET-PEESE), and moderator components. The package provides convenient functions for summary, visualizations, and fit diagnostics.