Generalized Additive Models for Location Scale and Shape

Functions for fitting the Generalized Additive Models for Location Scale and Shape introduced by Rigby and Stasinopoulos (2005), . The models use a distributional regression approach where all the parameters of the conditional distribution of the response variable are modelled using explanatory variables.

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 Variable Selection and Model Averaging using Bayesian Adaptive Sampling

Package for Bayesian Variable Selection and Model Averaging in linear models and generalized linear models using stochastic or deterministic sampling without replacement from posterior distributions. Prior distributions on coefficients are from Zellner's g-prior or mixtures of g-priors corresponding to the Zellner-Siow Cauchy Priors or the mixture of g-priors from Liang et al (2008) for linear models or mixtures of g-priors from Li and Clyde (2019) in generalized linear models. Other model selection criteria include AIC, BIC and Empirical Bayes estimates of g. Sampling probabilities may be updated based on the sampled models using sampling w/out replacement or an efficient MCMC algorithm which samples models using a tree structure of the model space as an efficient hash table. See Clyde, Ghosh and Littman (2010) for details on the sampling algorithms. Uniform priors over all models or beta-binomial prior distributions on model size are allowed, and for large p truncated priors on the model space may be used to enforce sampling models that are full rank. The user may force variables to always be included in addition to imposing constraints that higher order interactions are included only if their parents are included in the model. This material is based upon work supported by the National Science Foundation under Division of Mathematical Sciences grant 1106891. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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++'.

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) .