Longitudinal Gaussian Process Regression

Interpretable nonparametric modeling of longitudinal data using additive Gaussian process regression. Contains functionality for inferring covariate effects and assessing covariate relevances. Models are specified using a convenient formula syntax, and can include shared, group-specific, non-stationary, heterogeneous and temporally uncertain effects. Bayesian inference for model parameters is performed using 'Stan'. The modeling approach and methods are described in detail in Timonen et al. (2021) .

Robust Bayesian Variable Selection via Expectation-Maximization

Variable selection methods have been extensively developed for analyzing highdimensional omics data within both the frequentist and Bayesian frameworks. This package provides implementations of the spike-and-slab quantile (group) LASSO which have been developed along the line of Bayesian hierarchical models but deeply rooted in frequentist regularization methods by utilizing Expectation–Maximization (EM) algorithm. The spike-and-slab quantile LASSO can handle data irregularity in terms of skewness and outliers in response variables, compared to its non-robust alternative, the spike-and-slab LASSO, which has also been implemented in the package. In addition, procedures for fitting the spike-and-slab quantile group LASSO and its non-robust counterpart have been implemented in the form of quantile/least-square varying coefficient mixed effect models for high-dimensional longitudinal data. The core module of this package is developed in 'C++'.

Empirical Bayesian Tobit Matrix Estimation

Estimation tools for multidimensional Gaussian means using empirical Bayesian g-modeling. Methods are able to handle fully observed data as well as left-, right-, and interval-censored observations (Tobit likelihood); descriptions of these methods can be found in Barbehenn and Zhao (2023) . Additional, lower-level functionality based on Kiefer and Wolfowitz (1956) and Jiang and Zhang (2009) is provided that can be used to accelerate many empirical Bayes and nonparametric maximum likelihood problems.

An Implementation of the Bayesian Markov (Renewal) Mixed Models

The Bayesian Markov renewal mixed models take sequentially observed categorical data with continuous duration times, being either state duration or inter-state duration. These models comprehensively analyze the stochastic dynamics of both state transitions and duration times under the influence of multiple exogenous factors and random individual effect. The default setting flexibly models the transition probabilities using Dirichlet mixtures and the duration times using gamma mixtures. It also provides the flexibility of modeling the categorical sequences using Bayesian Markov mixed models alone, either ignoring the duration times altogether or dividing duration time into multiples of an additional category in the sequence by a user-specific unit. The package allows extensive inference of the state transition probabilities and the duration times as well as relevant plots and graphs. It also includes a synthetic data set to demonstrate the desired format of input data set and the utility of various functions. Methods for Bayesian Markov renewal mixed models are as described in: Abhra Sarkar et al., (2018) and Yutong Wu et al., (2022) .

Spatial Bayesian Methods for Task Functional MRI Studies

Performs a spatial Bayesian general linear model (GLM) for task functional magnetic resonance imaging (fMRI) data on the cortical surface. Additional models include group analysis and inference to detect thresholded areas of activation. Includes direct support for the 'CIFTI' neuroimaging file format. For more information see A. F. Mejia, Y. R. Yue, D. Bolin, F. Lindgren, M. A. Lindquist (2020) and D. Spencer, Y. R. Yue, D. Bolin, S. Ryan, A. F. Mejia (2022) .

Machine Learning Experiments

Provides 'R6' objects to perform parallelized hyperparameter optimization and cross-validation. Hyperparameter optimization can be performed with Bayesian optimization (via 'ParBayesianOptimization' < https://cran.r-project.org/package=ParBayesianOptimization>) and grid search. The optimized hyperparameters can be validated using k-fold cross-validation. Alternatively, hyperparameter optimization and validation can be performed with nested cross-validation. While 'mlexperiments' focuses on core wrappers for machine learning experiments, additional learner algorithms can be supplemented by inheriting from the provided learner base class.

Methods to Analyse Seasonal Radial Tree Growth Data

Methods for comparing different regression algorithms for describing the temporal dynamics of secondary tree growth (xylem and phloem). Users can compare the accuracy of the most common fitting methods usually used to analyse xylem and phloem data, i.e., Gompertz function, Double Gompertz function, General Additive Models (GAMs); and an algorithm newly introduced to the field, i.e., Bayesian Regularised Neural Networks (brnn). The core function of the package is XPSgrowth(), while the results can be interpreted using implemented generic S3 methods, such as plot() and summary().

Bayesian Network-Based Clustering of Multi-Omics Data

Unsupervised Bayesian network-based clustering of multi-omics data. Both binary and continuous data types are allowed as inputs. The package serves a dual purpose: it clusters (patient) samples and learns the multi-omics networks that characterize discovered clusters. Prior network knowledge (e.g., public interaction databases) can be included via blacklisting and penalization matrices. For clustering, the EM algorithm is employed. For structure search at the M-step, the Bayesian approach is used. The output includes membership assignments of samples, cluster-specific MAP networks, and posterior probabilities of all edges in the discovered networks. In addition to likelihood, AIC and BIC scores are returned. They can be used for choosing the number of clusters. References: P. Suter et al. (2021) , J. Kuipers and P. Suter and G. Moffa (2022) , J. Kuipers et al. (2018) .

Complete Environment for Bayesian Inference

Provides a complete environment for Bayesian inference using a variety of different samplers (see ?LaplacesDemon for an overview).

Hierarchical Bayesian Small Area Estimation

Functions to compute small area estimates based on a basic area or unit-level model. The model is fit using restricted maximum likelihood, or in a hierarchical Bayesian way. In the latter case numerical integration is used to average over the posterior density for the between-area variance. The output includes the model fit, small area estimates and corresponding mean squared errors, as well as some model selection measures. Additional functions provide means to compute aggregate estimates and mean squared errors, to minimally adjust the small area estimates to benchmarks at a higher aggregation level, and to graphically compare different sets of small area estimates.