Multi-Resolution Scanning for Cross-Sample and Cross-Group Differences

Implements the multi-resolution scanning (MRS) method for cross-sample distribution comparisons, as described in Soriano and Ma (2017) , and the analysis of distributional variation (ANDOVA) method for cross-group comparisons introduced in Ma and Soriano (2018) . Both methods use nonparametric models on multi-resolution partition trees to detect and characterize differences among distributions, with tools for visualizing the results.

Probabilistic multi-resolution scanning for cross-sample variation

This package fits the MRS algorithm for comparison across probability distributions. The model is based on a nonparametric process taking the form of a Markov model that transitions between a "null" and an "alternative" state on a multi-resolution partition tree of the sample space. MRS effectively detects and characterizes a variety of underlying differences. These differences can be visualized using several plotting functions.

Install

The development version can be installed from GitHub on Linux, macOS, or Windows:

install.packages("remotes")
remotes::install_github("MaStatLab/MRS")

Use

The main functions and their descriptions are provided in the help files:

ans = mrs(X, G)
ans = andova(X, G, H)
summary(ans)
plot1D(ans)
plot2D(ans)
plotTree(ans)
plot1DSigWindows(ans)

Visual demos

The package includes three reproducible demonstrations of the main workflows:

demo(package = "MRS")

demo("mrs_1d", package = "MRS", ask = FALSE)
demo("mrs_2d", package = "MRS", ask = FALSE)
demo("andova_replicates", package = "MRS", ask = FALSE)

The former standalone scripts in examples/ have been consolidated into these demos. Each workflow now has one purpose:

mrs_1d shows a localized difference, its signed effect, and Bayesian-FDR selection.
mrs_2d compares the observed grouping with a label-shuffled control before showing multiscale probability, effect, and tree views.
andova_replicates compares pooled MRS with both ANDOVA integration methods, uses an explicit baseline, and contrasts nested studies with 4, 10, and 20 replicates to show why pooled analysis can be overconfident.

All simulations use fixed random seeds. The obsolete mrs_nested() examples are represented by the supported andova() workflow, while developer-oriented numerical diagnostics are covered by the automated tests.

Reference

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B, 79(2), 547-572. https://doi.org/10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529-541. https://doi.org/10.1080/10618600.2017.1402774