Additive Partitions of Integers

Additive partitions of integers. Enumerates the partitions, unequal partitions, and restricted partitions of an integer; the three corresponding partition functions are also given. Set partitions and now compositions and riffle shuffles are included.

Spatial Implementation of Bayesian Networks and Mapping

Allows spatial implementation of Bayesian networks and mapping in geographical space. It makes maps of expected value (or most likely state) given known and unknown conditions, maps of uncertainty measured as coefficient of variation or Shannon index (entropy), maps of probability associated to any states of any node of the network. Some additional features are provided as well: parallel processing options, data discretization routines and function wrappers designed for users with minimal knowledge of the R language. Outputs can be exported to any common GIS format.

Bayesian Inference with Laplace Approximations and P-Splines

Laplace approximations and penalized B-splines are combined for fast Bayesian inference in latent Gaussian models. The routines can be used to fit survival models, especially proportional hazards and promotion time cure models (Gressani, O. and Lambert, P. (2018) ). The Laplace-P-spline methodology can also be implemented for inference in (generalized) additive models (Gressani, O. and Lambert, P. (2021) ). See the associated website for more information and examples.

Bayesian Monotonic Regression Using a Marked Point Process Construction

An extended version of the nonparametric Bayesian monotonic regression procedure described in Saarela & Arjas (2011) , allowing for multiple additive monotonic components in the linear predictor, and time-to-event outcomes through case-base sampling. The extension and its applications, including estimation of absolute risks, are described in Saarela & Arjas (2015) . The package also implements the nonparametric ordinal regression model described in Saarela, Rohrbeck & Arjas .

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++'.

Complete Environment for Bayesian Inference

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

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) .