R packages

• BASS: Bayesian Adaptive Spline Surfaces BASS implements a fully Bayesian version of adaptive spline surface models and performs global sensitivity analyses of these models. The BASS framework is similar to that of Bayesian multivariate adaptive regression splines (BMARS) from Denison, Mallick, and Smith (1998), but with many added features. The software is built to efficiently handle significant amounts of data with many continuous or categorical predictors and with functional response. Under our Bayesian framework, most priors are automatic but these can be modified by the user to focus on parsimony and the avoidance of overfitting. If directed to do so, the software uses parallel tempering to improve the reversible jump Markov chain Monte Carlo (RJMCMC) methods used to perform inference.

• exdqlm: Extended Dynamic Quantile Linear Models The R package exdqlm is a tool for dynamic quantile regression. The main focus of the package is to provide a framework for Bayesian inference and forecasting of flexible dynamic quantile linear models (exDQLMs). exDQLMs utilize a new family of error distributions for parametric quantile regression, the extended asymmetric Laplace (exAL), a generalization of the asymmetric Laplace (AL) which is commonly used in parametric quantile regression. Estimation of a dynamic quantile linear model, which utilizes the AL, is included in the package as a special case. Non-time-varying quantile regression models are also a special case of our methods. Further, routines for estimation of a nonlinear relationship between the response and a given input variable at a specified quantile via a transfer function model are available. The software provides the choice of two different algorithms for posterior inference: Markov chain Monte Carlo (MCMC), and importance sampling variational Bayes (ISVB). While MCMC provides an efficient sample-based exploration of the posterior distribution, the approximation obtained by the ISVB algorithm enables fast inference for long time series at a fraction of the memory and computational costs of the MCMC. A routine for forecasting the dynamic quantile is available in the package, as well as several quantitative and visual diagnostics for model evaluation. Vignette.

• MTD: Mixture Transition Distribution Models. Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. This set of routines implement the examples in Zheng, Kottas and Sansó, JCGS (2022).

• MSSS: Multi-Scale Shotgun Stochastic Search for Spatial Datasets'' MSSS implements a multi-scale spatial kernel convolution model where fine scale local features are captured by high resolution knots while lower resolution terms are used to describe large scale features. MSSS does not require Markov chain Monte Carlo to produce a fully probabilistic quantification of the prediction uncertainty. In addition, the model does not require a maximum resolution to be specified in advance. The model fitting approach, based on Bayesian model averaging, is computationally feasible on large datasets, as computations for shotgun stochastic search can be performed in parallel, leveraging the availability of convenient formulas for fast updating the coefficients when adding a single knot. This package requires OpenMP, so it may not compile on MACOS X with a default C compiler.

• NNRCM: Nearest-Neighbors Gaussian Process with Random Covariance Matrix'' NNRCM implements a non-stationary spatial model based on a normal-inverse-Wishart framework, conditioning on a set of nearest-neighbors. The model implements both univariate and bivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. This package requires OpenMP, so it may not compile on MACOS X with a default C compiler.