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.

Ensemble Models for Lactation Curves

Lactation curves describe temporal changes in milk yield and are key to breeding and managing dairy animals more efficiently. The use of ensemble modeling, which consists of combining predictions from multiple models, has the potential to yields more accurate and robust estimates of lactation patterns than relying solely on single model estimates. The package EMOTIONS fits 47 models for lactation curves and creates ensemble models using model averaging based on Akaike information criterion (AIC), Bayesian information criterion (BIC), root mean square percentage error (RMSPE) and mean squared error (MAE), variance of the predictions, cosine similarity for each model's predictions, and Bayesian Model Average (BMA). The daily production values predicted through the ensemble models can be used to estimate resilience indicators in the package. The package allows the graphical visualization of the model ranks and the predicted lactation curves. Additionally, the packages allows the user to detect milk loss events and estimate residual-based resilience indicators.

Analyze Multiple Exposure Realizations in Association Studies

Analyze association studies with multiple realizations of a noisy or uncertain exposure. These can be obtained from e.g. a two-dimensional Monte Carlo dosimetry system (Simon et al 2015 ) to characterize exposure uncertainty. The implemented methods are regression calibration (Carroll et al. 2006 ), extended regression calibration (Little et al. 2023 ), Monte Carlo maximum likelihood (Stayner et al. 2007 ), frequentist model averaging (Kwon et al. 2023 ), and Bayesian model averaging (Kwon et al. 2016 ). Supported model families are Gaussian, binomial, multinomial, Poisson, proportional hazards, and conditional logistic.

Bayesian Variable Selection in High Dimensional Settings using Nonlocal Priors

Variable/Feature selection in high or ultra-high dimensional settings has gained a lot of attention recently specially in cancer genomic studies. This package provides a Bayesian approach to tackle this problem, where it exploits mixture of point masses at zero and nonlocal priors to improve the performance of variable selection and coefficient estimation. product moment (pMOM) and product inverse moment (piMOM) nonlocal priors are implemented and can be used for the analyses. This package performs variable selection for binary response and survival time response datasets which are widely used in biostatistic and bioinformatics community. Benefiting from parallel computing ability, it reports necessary outcomes of Bayesian variable selection such as Highest Posterior Probability Model (HPPM), Median Probability Model (MPM) and posterior inclusion probability for each of the covariates in the model. The option to use Bayesian Model Averaging (BMA) is also part of this package that can be exploited for predictive power measurements in real datasets.

Bayesian Variable Selection using Power-Expected-Posterior Prior

Performs Bayesian variable selection under normal linear models for the data with the model parameters following as prior distributions either the power-expected-posterior (PEP) or the intrinsic (a special case of the former) (Fouskakis and Ntzoufras (2022) , Fouskakis and Ntzoufras (2020) ). The prior distribution on model space is the uniform over all models or the uniform on model dimension (a special case of the beta-binomial prior). The selection is performed by either implementing a full enumeration and evaluation of all possible models or using the Markov Chain Monte Carlo Model Composition (MC3) algorithm (Madigan and York (1995) ). Complementary functions for hypothesis testing, estimation and predictions under Bayesian model averaging, as well as, plotting and printing the results are also provided. The results can be compared to the ones obtained under other well-known priors on model parameters and model spaces.

Evolutionary Mode Jumping Markov Chain Monte Carlo Expert Toolbox

Implementation of the Mode Jumping Markov Chain Monte Carlo algorithm from Hubin, A., Storvik, G. (2018) , Genetically Modified Mode Jumping Markov Chain Monte Carlo from Hubin, A., Storvik, G., & Frommlet, F. (2020) , Hubin, A., Storvik, G., & Frommlet, F. (2021) , and Hubin, A., Heinze, G., & De Bin, R. (2023) , and Reversible Genetically Modified Mode Jumping Markov Chain Monte Carlo from Hubin, A., Frommlet, F., & Storvik, G. (2021) , which allow for estimating posterior model probabilities and Bayesian model averaging across a wide set of Bayesian models including linear, generalized linear, generalized linear mixed, generalized nonlinear, generalized nonlinear mixed, and logic regression models.

Model Selection with Bayesian Methods and Information Criteria

Model selection and averaging for regression and mixtures, inclusing Bayesian model selection and information criteria (BIC, EBIC, AIC, GIC).

MCMC for Spike and Slab Regression

Spike and slab regression with a variety of residual error distributions corresponding to Gaussian, Student T, probit, logit, SVM, and a few others. Spike and slab regression is Bayesian regression with prior distributions containing a point mass at zero. The posterior updates the amount of mass on this point, leading to a posterior distribution that is actually sparse, in the sense that if you sample from it many coefficients are actually zeros. Sampling from this posterior distribution is an elegant way to handle Bayesian variable selection and model averaging. See for an explanation of the Gaussian case.

Bayesian Analysis of Generalized Linear Models with Historical Data

User-friendly functions for leveraging (multiple) historical data set(s) in Bayesian analysis of generalized linear models (GLMs) and survival models, along with support for Bayesian model averaging (BMA). The package provides functions for sampling from posterior distributions under various informative priors, including the prior induced by the Bayesian hierarchical model, power prior by Ibrahim and Chen (2000) , normalized power prior by Duan et al. (2006) , normalized asymptotic power prior by Ibrahim et al. (2015) , commensurate prior by Hobbs et al. (2011) , robust meta-analytic-predictive prior by Schmidli et al. (2014) , latent exchangeability prior by Alt et al. (2024) , and a normal (or half-normal) prior. The package also includes functions for computing model averaging weights, such as BMA, pseudo-BMA, pseudo-BMA with the Bayesian bootstrap, and stacking (Yao et al., 2018 ), as well as for generating posterior samples from the ensemble distributions to reflect model uncertainty. In addition to GLMs, the package supports survival models including: (1) accelerated failure time (AFT) models, (2) piecewise exponential (PWE) models, i.e., proportional hazards models with piecewise constant baseline hazards, and (3) mixture cure rate models that assume a common probability of cure across subjects, paired with a PWE model for the non-cured population. Functions for computing marginal log-likelihoods under each implemented prior are also included. The package compiles all the 'CmdStan' models once during installation using the 'instantiate' package.