Biased Urn Model Distributions

Statistical models of biased sampling in the form of univariate and multivariate noncentral hypergeometric distributions, including Wallenius' noncentral hypergeometric distribution and Fisher's noncentral hypergeometric distribution. See vignette("UrnTheory") for explanation of these distributions. Literature: Fog, A. (2008a). Calculation Methods for Wallenius' Noncentral Hypergeometric Distribution, Communications in Statistics, Simulation and Computation, 37(2) . Fog, A. (2008b). Sampling methods for Wallenius’ and Fisher’s noncentral hypergeometric distributions, Communications in Statistics—Simulation and Computation, 37(2) .

Random Cluster Generation (with Specified Degree of Separation)

We developed the clusterGeneration package to provide functions for generating random clusters, generating random covariance/correlation matrices, calculating a separation index (data and population version) for pairs of clusters or cluster distributions, and 1-D and 2-D projection plots to visualize clusters. The package also contains a function to generate random clusters based on factorial designs with factors such as degree of separation, number of clusters, number of variables, number of noisy variables.

Randomized Singular Value Decomposition

Low-rank matrix decompositions are fundamental tools and widely used for data analysis, dimension reduction, and data compression. Classically, highly accurate deterministic matrix algorithms are used for this task. However, the emergence of large-scale data has severely challenged our computational ability to analyze big data. The concept of randomness has been demonstrated as an effective strategy to quickly produce approximate answers to familiar problems such as the singular value decomposition (SVD). The rsvd package provides several randomized matrix algorithms such as the randomized singular value decomposition (rsvd), randomized principal component analysis (rpca), randomized robust principal component analysis (rrpca), randomized interpolative decomposition (rid), and the randomized CUR decomposition (rcur). In addition several plot functions are provided.

Generate Attractive Random Colors

Simple methods to generate attractive random colors. The random colors are from a wrapper of 'randomColor.js' < https://github.com/davidmerfield/randomColor>. In addition, it also generates optimally distinct colors based on k-means (inspired by 'IWantHue' < https://github.com/medialab/iwanthue>).

The Multivariate Normal and t Distributions, and Their Truncated Versions

Functions are provided for computing the density and the distribution function of d-dimensional normal and "t" random variables, possibly truncated (on one side or two sides), and for generating random vectors sampled from these distributions, except sampling from the truncated "t". Moments of arbitrary order of a multivariate truncated normal are computed, and converted to cumulants up to order 4. Probabilities are computed via non-Monte Carlo methods; different routines are used in the case d=1, d=2, d=3, d>3, if d denotes the dimensionality.

Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

Generates random assignments for common experimental designs and random samples for common sampling designs.

Generate Random Identifiers

Generate random or human readable and pronounceable identifiers.

Space-Filling Random and Quasi-Random Sequences

Generates random and quasi-random space-filling sequences. Supports the following sequences: 'Halton', 'Sobol', 'Owen'-scrambled 'Sobol', 'Owen'-scrambled 'Sobol' with errors distributed as blue noise, progressive jittered, progressive multi-jittered ('PMJ'), 'PMJ' with blue noise, 'PMJ02', and 'PMJ02' with blue noise. Includes a 'C++' 'API'. Methods derived from "Constructing Sobol sequences with better two-dimensional projections" (2012) S. Joe and F. Y. Kuo, "Progressive Multi-Jittered Sample Sequences" (2018) < https://graphics.pixar.com/library/ProgressiveMultiJitteredSampling/paper.pdf> Christensen, P., Kensler, A. and Kilpatrick, C., and "A Low-Discrepancy Sampler that Distributes Monte Carlo Errors as a Blue Noise in Screen Space" (2019) E. Heitz, B. Laurent, O. Victor, C. David and I. Jean-Claude, .

Markov Chain Monte Carlo (MCMC) Package

Contains functions to perform Bayesian inference using posterior simulation for a number of statistical models. Most simulation is done in compiled C++ written in the Scythe Statistical Library Version 1.0.3. All models return 'coda' mcmc objects that can then be summarized using the 'coda' package. Some useful utility functions such as density functions, pseudo-random number generators for statistical distributions, a general purpose Metropolis sampling algorithm, and tools for visualization are provided.

Tools for Social Network Analysis

A range of tools for social network analysis, including node and graph-level indices, structural distance and covariance methods, structural equivalence detection, network regression, random graph generation, and 2D/3D network visualization.