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.

Spatially and Temporally Varying Coefficient Models Using Generalized Additive Models

A framework for specifying spatially, temporally and spatially-and-temporally varying coefficient models using Generalized Additive Models with Gaussian Process smooths. The smooths are parameterised with location and / or time attributes. Importantly the framework supports the investigation of the presence and nature of any space-time dependencies in the data, allows the user to evaluate different model forms (specifications) and to pick the most probable model or to combine multiple varying coefficient models using Bayesian Model Averaging. For more details see: Brunsdon et al (2023) , Comber et al (2023) and Comber et al (2024) .

Distributions for Generalized Additive Models for Location Scale and Shape

A set of distributions which can be used for modelling the response variables in Generalized Additive Models for Location Scale and Shape, Rigby and Stasinopoulos (2005), . The distributions can be continuous, discrete or mixed distributions. Extra distributions can be created, by transforming, any continuous distribution defined on the real line, to a distribution defined on ranges 0 to infinity or 0 to 1, by using a 'log' or a 'logit' transformation respectively.

R Interface to Stan

User-facing R functions are provided to parse, compile, test, estimate, and analyze Stan models by accessing the header-only Stan library provided by the 'StanHeaders' package. The Stan project develops a probabilistic programming language that implements full Bayesian statistical inference via Markov Chain Monte Carlo, rough Bayesian inference via 'variational' approximation, and (optionally penalized) maximum likelihood estimation via optimization. In all three cases, automatic differentiation is used to quickly and accurately evaluate gradients without burdening the user with the need to derive the partial derivatives.

Survival Analysis in Health Economic Evaluation

Contains a suite of functions for survival analysis in health economics. These can be used to run survival models under a frequentist (based on maximum likelihood) or a Bayesian approach (both based on Integrated Nested Laplace Approximation or Hamiltonian Monte Carlo). To run the Bayesian models, the user needs to install additional modules (packages), i.e. 'survHEinla' and 'survHEhmc'. These can be installed using 'remotes::install_github' from their GitHub repositories: (< https://github.com/giabaio/survHEhmc> and < https://github.com/giabaio/survHEinla/> respectively). 'survHEinla' is based on the package INLA, which is available for download at < https://inla.r-inla-download.org/R/stable/>. The user can specify a set of parametric models using a common notation and select the preferred mode of inference. The results can also be post-processed to produce probabilistic sensitivity analysis and can be used to export the output to an Excel file (e.g. for a Markov model, as often done by modellers and practitioners). .

Fitting Shared Atoms Nested Models via Markov Chains Monte Carlo

Estimate Bayesian nested mixture models via Markov Chain Monte Carlo methods. Specifically, the package implements the common atoms model (Denti et al., 2023), its finite version (D'Angelo et al., 2023), and a hybrid finite-infinite model. All models use Gaussian mixtures with a normal-inverse-gamma prior distribution on the parameters. Additional functions are provided to help analyzing the results of the fitting procedure. References: Denti, Camerlenghi, Guindani, Mira (2023) , D’Angelo, Canale, Yu, Guindani (2023) .

Estimate Pollinator Body Size and Co-Varying Ecological Traits

Tools to estimate pollinator body size and co-varying traits. This package contains novel Bayesian predictive models of pollinator body size (for bees and hoverflies) as well as preexisting predictive models for pollinator body size (currently implemented for ants, bees, butterflies, flies, moths and wasps) as well as bee tongue length and foraging distance, total field nectar loads and wing loading. An additional GitHub repository < https://github.com/liamkendall/pollimetrydata> provides model objects to use the bodysize function internally. All models are described in Kendall et al (2018) .

Estimating the Degrees of Freedom of the Student's t-Distribution under a Bayesian Framework

A Bayesian framework to estimate the Student's t-distribution's degrees of freedom is developed. Markov Chain Monte Carlo sampling routines are developed as in to sample from the posterior distribution of the degrees of freedom. A random walk Metropolis algorithm is used for sampling when Jeffrey's and Gamma priors are endowed upon the degrees of freedom. In addition, the Metropolis-adjusted Langevin algorithm for sampling is used under the Jeffrey's prior specification. The Log-normal prior over the degrees of freedom is posed as a viable choice with comparable performance in simulations and real-data application, against other prior choices, where an Elliptical Slice Sampler is used to sample from the concerned posterior.

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.

Tcl/Tk Additions

A series of additional Tcl commands and Tk widgets with style and various functions (under Windows: DDE exchange, access to the registry and icon manipulation) to supplement the tcltk package