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.

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.

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 Change-Point Detection and Time Series Decomposition

Interpretation of time series data is affected by model choices. Different models can give different or even contradicting estimates of patterns, trends, and mechanisms for the same data--a limitation alleviated by the Bayesian estimator of abrupt change,seasonality, and trend (BEAST) of this package. BEAST seeks to improve time series decomposition by forgoing the "single-best-model" concept and embracing all competing models into the inference via a Bayesian model averaging scheme. It is a flexible tool to uncover abrupt changes (i.e., change-points, breakpoints, structural breaks, or join-points), cyclic variations (e.g., seasonality), and nonlinear trends in time-series observations. BEAST not just tells when changes occur but also quantifies how likely the detected changes are true. It detects not just piecewise linear trends but also arbitrary nonlinear trends. BEAST is applicable to real-valued time series data of all kinds, be it for remote sensing, economics, climate sciences, ecology, and hydrology. Example applications include its use to identify regime shifts in ecological data, map forest disturbance and land degradation from satellite imagery, detect market trends in economic data, pinpoint anomaly and extreme events in climate data, and unravel system dynamics in biological data. Details on BEAST are reported 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).

Bayesian Marginal Effects for 'brms' Models

Calculate Bayesian marginal effects, average marginal effects, and marginal coefficients (also called population averaged coefficients) for models fit using the 'brms' package including fixed effects, mixed effects, and location scale models. These are based on marginal predictions that integrate out random effects if necessary (see for example and ).

Adjust Longitudinal Regression Models Using Bayesian Methodology

Adjusts longitudinal regression models using Bayesian methodology for covariance structures of composite symmetry (SC), autoregressive ones of order 1 AR (1) and autoregressive moving average of order (1,1) ARMA (1,1).

Combining Subset MCMC Samples to Estimate a Posterior Density

See Miroshnikov and Conlon (2014) . Recent Bayesian Markov chain Monto Carlo (MCMC) methods have been developed for big data sets that are too large to be analyzed using traditional statistical methods. These methods partition the data into non-overlapping subsets, and perform parallel independent Bayesian MCMC analyses on the data subsets, creating independent subposterior samples for each data subset. These independent subposterior samples are combined through four functions in this package, including averaging across subset samples, weighted averaging across subsets samples, and kernel smoothing across subset samples. The four functions assume the user has previously run the Bayesian analysis and has produced the independent subposterior samples outside of the package; the functions use as input the array of subposterior samples. The methods have been demonstrated to be useful for Bayesian MCMC models including Bayesian logistic regression, Bayesian Gaussian mixture models and Bayesian hierarchical Poisson-Gamma models. The methods are appropriate for Bayesian hierarchical models with hyperparameters, as long as data values in a single level of the hierarchy are not split into subsets.