quack - R tools for UQ and calibration

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Description

The quack package contains several tools for UQ and Bayesian model calibration, with an emphasis on inference for physical parameters in complex physical systems. Many of the tools found in this package are implementations of the ideas found here

Note (7/17/23)

The R package MHadaptive has been removed from CRAN. As of 7/17/2023, in order to install the quack package, users will first need to install MHadaptive from the Archive as

#install.packages("devtools")
link <- "https://cran.r-project.org/src/contrib/Archive/MHadaptive/MHadaptive_1.1-8.tar.gz"
devtools::install_url(link)

Installation

To install the quack package, type

# install.packages("devtools")
devtools::install_github("knrumsey/quack")

Tools

See manual for details.

• Moment penalization: functions for the moment penalization (MP) prior, which are useful for improving identifiability and reducing bias when a physical system contains a set of nuisance parameters which can be viewed as iid samples from a specified distribution. Also contains methods for computing the probability of prior coherency, a useful diagnostic tool.
• Emulating the conditional posterior: A fast approach for approximating the cut distribution in low to moderate dimensions.
• Fast matrix algebra for BMC: Near-quadratic time approximations to the inverse of the covariance matrix given a particular structure. Useful for model calibration when a large number of sequential inversions are needed.
• Sequential local approximate GPs: Implementations of slapGP and leapGP which are two “global-model” extensions of the laGP framework.
• Accelerated bootstrap: An implementation of the accelerated bootstrap.
• Joint credible regions: Function to find elliptical joint credible regions given a sample of points $x \in \mathbb R^p$.
• Mixture of MVNs: Regularized estimator for high-dimensional mixtures (using the EM algorithm).
• KL Divergence Estimator An estimator for the KLD given independent samples x ~ P and y ~ Q.

References

Rumsey, Kellin N. Methods of uncertainty quantification for physical parameters. Diss. The University of New Mexico, 2020.

Rumsey, Kellin, et al. “Dealing with measurement uncertainties as nuisance parameters in Bayesian model calibration.” SIAM/ASA Journal on Uncertainty Quantification 8.4 (2020): 1287-1309.

Plummer, Martyn. “Cuts in Bayesian graphical models.” Statistics and Computing 25.1 (2015): 37-43.

Rumsey, Kellin N., and Gabriel Huerta. “Fast matrix algebra for Bayesian model calibration.” Journal of Statistical Computation and Simulation 91.7 (2021): 1331-1341.

Gramacy, Robert B. “laGP: large-scale spatial modeling via local approximate Gaussian processes in R.” Journal of Statistical Software 72 (2016): 1-46

Chen, Jiahua, and Xianming Tan. “Inference for multivariate normal mixtures.” Journal of Multivariate Analysis 100.7 (2009): 1367-1383.

Pérez-Cruz, Fernando. “Kullback-Leibler divergence estimation of continuous distributions.” 2008 IEEE international symposium on information theory. IEEE, 2008.