Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

Gaussian finite mixture models fitted via EM algorithm for model-based clustering, classification, and density estimation, including Bayesian regularization, dimension reduction for visualisation, and resampling-based inference.

Hierarchical Bayesian ANOVA Models

It covers several Bayesian Analysis of Variance (BANOVA) models used in analysis of experimental designs in which both within- and between- subjects factors are manipulated. They can be applied to data that are common in the behavioral and social sciences. The package includes: Hierarchical Bayes ANOVA models with normal response, t response, Binomial (Bernoulli) response, Poisson response, ordered multinomial response and multinomial response variables. All models accommodate unobserved heterogeneity by including a normal distribution of the parameters across individuals. Outputs of the package include tables of sums of squares, effect sizes and p-values, and tables of predictions, which are easily interpretable for behavioral and social researchers. The floodlight analysis and mediation analysis based on these models are also provided. BANOVA uses 'Stan' and 'JAGS' as the computational platform. References: Dong and Wedel (2017) ; Wedel and Dong (2020) .

Bayesian Hierarchical Analysis of Cognitive Models of Choice

Fit Bayesian (hierarchical) cognitive models using a linear modeling language interface using particle Metropolis Markov chain Monte Carlo sampling with Gibbs steps. The diffusion decision model (DDM), linear ballistic accumulator model (LBA), racing diffusion model (RDM), and the lognormal race model (LNR) are supported. Additionally, users can specify their own likelihood function and/or choose for non-hierarchical estimation, as well as for a diagonal, blocked or full multivariate normal group-level distribution to test individual differences. Prior specification is facilitated through methods that visualize the (implied) prior. A wide range of plotting functions assist in assessing model convergence and posterior inference. Models can be easily evaluated using functions that plot posterior predictions or using relative model comparison metrics such as information criteria or Bayes factors. References: Stevenson et al. (2024) .

Univariate and Multivariate Spatial Modeling of Species Abundance

Fits single-species (univariate) and multi-species (multivariate) non-spatial and spatial abundance models in a Bayesian framework using Markov Chain Monte Carlo (MCMC). Spatial models are fit using Nearest Neighbor Gaussian Processes (NNGPs). Details on NNGP models are given in Datta, Banerjee, Finley, and Gelfand (2016) and Finley, Datta, and Banerjee (2022) . Fits single-species and multi-species spatial and non-spatial versions of generalized linear mixed models (Gaussian, Poisson, Negative Binomial), N-mixture models (Royle 2004 ) and hierarchical distance sampling models (Royle, Dawson, Bates (2004) ). Multi-species spatial models are fit using a spatial factor modeling approach with NNGPs for computational efficiency.

Ensemble Quadratic and Affine Invariant Markov Chain Monte Carlo

The Ensemble Quadratic and Affine Invariant Markov chain Monte Carlo algorithms provide an efficient way to perform Bayesian inference in difficult parameter space geometries. The Ensemble Quadratic Monte Carlo algorithm was developed by Militzer (2023) . The Ensemble Affine Invariant algorithm was developed by Goodman and Weare (2010) and it was implemented in Python by Foreman-Mackey et al (2013) . The Quadratic Monte Carlo method was shown to perform better than the Affine Invariant method in the paper by Militzer (2023) and the Quadratic Monte Carlo method is the default method used. The Chen-Shao Highest Posterior Density Estimation algorithm is used for obtaining credible intervals and the potential scale reduction factor diagnostic is used for checking the convergence of the chains.

Bayesian Applied Regression Modeling via Stan

Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Users specify models via the customary R syntax with a formula and data.frame plus some additional arguments for priors.

Multivariate Meta-Analysis

Multiple 2 by 2 tables often arise in meta-analysis which combines statistical evidence from multiple studies. Two risks within the same study are possibly correlated because they share some common factors such as environment and population structure. This package implements a set of novel Bayesian approaches for multivariate meta analysis when the risks within the same study are independent or correlated. The exact posterior inference of odds ratio, relative risk, and risk difference given either a single 2 by 2 table or multiple 2 by 2 tables is provided. Luo, Chen, Su, Chu, (2014) , Chen, Luo, (2011) , Chen, Chu, Luo, Nie, Chen, (2015) , Chen, Luo, Chu, Su, Nie, (2014) , Chen, Luo, Chu, Wei, (2013) .

Bindings for Bayesian TidyModels

Fit Bayesian models using 'brms'/'Stan' with 'parsnip'/'tidymodels' via 'bayesian' . 'tidymodels' is a collection of packages for machine learning; see Kuhn and Wickham (2020) < https://www.tidymodels.org>). The technical details of 'brms' and 'Stan' are described in Bürkner (2017) , Bürkner (2018) , and Carpenter et al. (2017) .

Production Function Output Gap Estimation

The output gap indicates the percentage difference between the actual output of an economy and its potential. Since potential output is a latent process, the estimation of the output gap poses a challenge and numerous filtering techniques have been proposed. 'RGAP' facilitates the estimation of a Cobb-Douglas production function type output gap, as suggested by the European Commission (Havik et al. 2014) < https://ideas.repec.org/p/euf/ecopap/0535.html>. To that end, the non-accelerating wage rate of unemployment (NAWRU) and the trend of total factor productivity (TFP) can be estimated in two bivariate unobserved component models by means of Kalman filtering and smoothing. 'RGAP' features a flexible modeling framework for the appropriate state-space models and offers frequentist as well as Bayesian estimation techniques. Additional functionalities include direct access to the 'AMECO' < https://economy-finance.ec.europa.eu/economic-research-and-databases/economic-databases/ameco-database_en> database and automated model selection procedures. See the paper by Streicher (2022) < http://hdl.handle.net/20.500.11850/552089> for details.

Fractional Factorial Designs with 2-Level Factors

Regular and non-regular Fractional Factorial 2-level designs can be created. Furthermore, analysis tools for Fractional Factorial designs with 2-level factors are offered (main effects and interaction plots for all factors simultaneously, cube plot for looking at the simultaneous effects of three factors, full or half normal plot, alias structure in a more readable format than with the built-in function alias).