# Robert Gramacy

#### 12 packages on CRAN

This package provides a flexible statistical framework for generating optimal epidemiological interventions that are designed to minimize the total expected cost of an emerging epidemic while simultaneously propagating uncertainty regarding underlying disease parameters through to the decision process via Bayesian posterior inference. The strategies produced through this framework are adaptive: vaccination schedules are iteratively adjusted to reflect the anticipated trajectory of the epidemic given the current population state and updated parameter estimates.

Inference by sequential Monte Carlo for dynamic tree regression and classification models with hooks provided for sequential design and optimization, fully online learning with drift, variable selection, and sensitivity analysis of inputs. Illustrative examples from the original dynamic trees paper are facilitated by demos in the package; see demo(package="dynaTree").

Performs approximate GP regression for large computer experiments and spatial datasets. The approximation is based on finding small local designs for prediction (independently) at particular inputs. OpenMP and SNOW parallelization are supported for prediction over a vast out-of-sample testing set; GPU acceleration is also supported for an important subroutine. OpenMP and GPU features may require special compilation. An interface to lower-level (full) GP inference and prediction is provided. Wrapper routines for blackbox optimization under mixed equality and inequality constraints via an augmented Lagrangian scheme, and for large scale computer model calibration, are also provided.

Functions with example data for graphing, pruning, and mapping models from hierarchical clustering, and classification and regression trees.

Estimation of multivariate normal (MVN) and student-t data of arbitrary dimension where the pattern of missing data is monotone. See Pantaleo and Gramacy (2010) <doi:10.1214/10-BA602>. Through the use of parsimonious/shrinkage regressions (plsr, pcr, lasso, ridge, etc.), where standard regressions fail, the package can handle a nearly arbitrary amount of missing data. The current version supports maximum likelihood inference and a full Bayesian approach employing scale-mixtures for Gibbs sampling. Monotone data augmentation extends this Bayesian approach to arbitrary missingness patterns. A fully functional standalone interface to the Bayesian lasso (from Park & Casella), Normal-Gamma (from Griffin & Brown), Horseshoe (from Carvalho, Polson, & Scott), and ridge regression with model selection via Reversible Jump, and student-t errors (from Geweke) is also provided.

Sequential Monte Carlo inference for fully Bayesian Gaussian process (GP) regression and classification models by particle learning (PL). The sequential nature of inference and the active learning (AL) hooks provided facilitate thrifty sequential design (by entropy) and optimization (by improvement) for classification and regression models, respectively. This package essentially provides a generic PL interface, and functions (arguments to the interface) which implement the GP models and AL heuristics. Functions for a special, linked, regression/classification GP model and an integrated expected conditional improvement (IECI) statistic is provides for optimization in the presence of unknown constraints. Separable and isotropic Gaussian, and single-index correlation functions are supported. See the examples section of ?plgp and demo(package="plgp") for an index of demos

Regularized (polychotomous) logistic regression by Gibbs sampling. The package implements subtly different MCMC schemes with varying efficiency depending on the data type (binary v. binomial, say) and the desired estimator (regularized maximum likelihood, or Bayesian maximum a posteriori/posterior mean, etc.) through a unified interface.

Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes (GPs) with jumps to the limiting linear model (LLM). Special cases also implemented include Bayesian linear models, CART, treed linear models, stationary separable and isotropic GPs, and GP single-index models. Provides 1-d and 2-d plotting functions (with projection and slice capabilities) and tree drawing, designed for visualization of tgp-class output. Sensitivity analysis and multi-resolution models are supported. Sequential experimental design and adaptive sampling functions are also provided, including ALM, ALC, and expected improvement. The latter supports derivative-free optimization of noisy black-box functions.

Bayesian Additive Regression Trees (BART) provide flexible nonparametric modeling of covariates for continuous, binary, categorical and time-to-event outcomes. For more information see Sparapani, Spanbauer and McCulloch <doi:10.18637/jss.v097.i01>.

Performs Gaussian process regression with heteroskedastic noise following Binois, M., Gramacy, R., Ludkovski, M. (2016) <arXiv:1611.05902>. The input dependent noise is modeled as another Gaussian process. Replicated observations are encouraged as they yield computational savings. Sequential design procedures based on the integrated mean square prediction error and lookahead heuristics are provided, and notably fast update functions when adding new observations.

Software for computing a log-concave (maximum likelihood) estimator for i.i.d. data in any number of dimensions. For a detailed description of the method see Cule, Samworth and Stewart (2010, Journal of Royal Statistical Society Series B, <doi:10.1111/j.1467-9868.2010.00753.x>).

Constructs a space-filling design under the criterion of maximum-minimum distance. Both discrete and continuous searches are provided.