Two practical tests are provided for assessing whether multiple covariates in a treatment group and a matched control group are balanced in observational studies.

Select balanced and spatially balanced probability samples in multi-dimensional spaces
    with any prescribed inclusion probabilities. It contains fast (C++ via Rcpp) implementations of
    the included sampling methods. The local pivotal method by Grafström, Lundström and Schelin (2012)
    <doi:10.1111/j.1541-0420.2011.01699.x> and spatially correlated Poisson sampling by Grafström (2012)
    <doi:10.1016/j.jspi.2011.07.003> are included. Also the cube method (for balanced sampling) and
    the local cube method (for doubly balanced sampling) are included, see Grafström and Tillé (2013)
    <doi:10.1002/env.2194>.

Statistical decision in proteomics data using a hierarchical
    Bayesian model. There are two regression models for describing the 
    mean-variance trend, a gamma regression or a latent gamma mixture
    regression. The regression model is then used as an Empirical Bayes
    estimator for the prior on the variance in a peptide. Further, it assumes
    that each measurement has an uncertainty (increased variance) associated
    with it that is also inferred. Finally, it tries to estimate the posterior
    distribution (by Hamiltonian Monte Carlo) for the differences in means for
    each peptide in the data. Once the posterior is inferred, it integrates the
    tails to estimate the probability of error from which a statistical decision
    can be made.
    See Berg and Popescu for details (<doi:10.1016/j.mcpro.2023.100658>).

Hypothesis tests and sure independence screening (SIS) procedure based on ball statistics, including ball divergence <doi:10.1214/17-AOS1579>, ball covariance <doi:10.1080/01621459.2018.1543600>, and ball correlation <doi:10.1080/01621459.2018.1462709>, are developed to analyze complex data in metric spaces, e.g, shape, directional, compositional and symmetric positive definite matrix data. The ball divergence and ball covariance based distribution-free tests are implemented to detecting distribution difference and association in metric spaces <doi:10.18637/jss.v097.i06>. Furthermore, several generic non-parametric feature selection procedures based on ball correlation, BCor-SIS and all of its variants, are implemented to tackle the challenge in the context of ultra high dimensional data. A fast implementation for large-scale multiple K-sample testing with ball divergence <doi: 10.1002/gepi.22423> is supported, which is particularly helpful for genome-wide association study.