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.

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.

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.

All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

Multivariate Time Series (MTS) is a general package for analyzing multivariate linear time series and estimating multivariate volatility models. It also handles factor models, constrained factor models, asymptotic principal component analysis commonly used in finance and econometrics, and principal volatility component analysis. (a) For the multivariate linear time series analysis, the package performs model specification, estimation, model checking, and prediction for many widely used models, including vector AR models, vector MA models, vector ARMA models, seasonal vector ARMA models, VAR models with exogenous variables, multivariate regression models with time series errors, augmented VAR models, and Error-correction VAR models for co-integrated time series. For model specification, the package performs structural specification to overcome the difficulties of identifiability of VARMA models. The methods used for structural specification include Kronecker indices and Scalar Component Models. (b) For multivariate volatility modeling, the MTS package handles several commonly used models, including multivariate exponentially weighted moving-average volatility, Cholesky decomposition volatility models, dynamic conditional correlation (DCC) models, copula-based volatility models, and low-dimensional BEKK models. The package also considers multiple tests for conditional heteroscedasticity, including rank-based statistics. (c) Finally, the MTS package also performs forecasting using diffusion index , transfer function analysis, Bayesian estimation of VAR models, and multivariate time series analysis with missing values.Users can also use the package to simulate VARMA models, to compute impulse response functions of a fitted VARMA model, and to calculate theoretical cross-covariance matrices of a given VARMA model.

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.

Bayesian Change-Point Detection and Time Series Decomposition

BEAST is a Bayesian estimator of abrupt change, seasonality, and trend for decomposing univariate time series and 1D sequential data. Interpretation of time series depends on model choice; different models can yield contrasting or contradicting estimates of patterns, trends, and mechanisms. BEAST alleviates this by abandoning the single-best-model paradigm and instead using Bayesian model averaging over many competing decompositions. It detects and characterizes abrupt changes (changepoints, breakpoints, structural breaks, joinpoints), cyclic or seasonal variation, and nonlinear trends. BEAST not only detects when changes occur but also quantifies how likely the changes are true. It estimates not just piecewise linear trends but also arbitrary nonlinear trends. BEAST is generically applicable to any real-valued time series, such as those from remote sensing, economics, climate science, ecology, hydrology, and other environmental and biological systems. Example applications include identifying regime shifts in ecological data, mapping forest disturbance and land degradation from satellite image time series, detecting market trends in economic indicators, pinpointing anomalies and extreme events in climate records, and analyzing system dynamics in biological time series. Details are given in Zhao et al. (2019) .

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).