"Essential" Robust Statistics.
 Tools allowing to analyze data with robust methods.  This includes
 regression methodology including model selections and multivariate
 statistics where we strive to cover the book "Robust Statistics,
 Theory and Methods" by 'Maronna, Martin and Yohai'; Wiley 2006.

Fits the robust Bayesian Copas (RBC) selection model of Bai et al. (2020) <arXiv:2005.02930> for correcting and quantifying publication bias in univariate meta-analysis. Also fits standard random effects meta-analysis and the Copas-like selection model of Ning et al. (2017) <doi:10.1093/biostatistics/kxx004>.

Robust estimators for the beta regression, useful for modeling 
  bounded continuous data. Currently, four types of robust estimators are supported. 
  They depend on a tuning constant which may be fixed or selected by a 
  data-driven algorithm also implemented in the package. Diagnostic tools 
  associated with the fitted model, such as the residuals and goodness-of-fit 
  statistics, are implemented. Robust Wald-type tests are available. More details
  about robust beta regression are described in Maluf et al. (2022) <arXiv:2209.11315>.

Robust tests (RW and RF) are provided for testing the equality of two long-tailed symmetric (LTS) means when the variances are unknown and arbitrary. RW test is a robust version of Welch's two sample t test and the RF is a robust fiducial based test. The RW and RF tests are proposed using the adaptive modified maximum likelihood (AMML) estimators derived by Tiku and Surucu (2009) <doi:10.1016/j.spl.2008.12.001> and Donmez (2010) <https://open.metu.edu.tr/bitstream/handle/11511/19440/index.pdf>.

Bayesian robust fitting of linear mixed effects models through weighted likelihood equations and approximate Bayesian computation as proposed by Ruli et al. (2017) <arXiv:1706.01752>.

Implements full Bayesian analysis for calibrating mathematical models with new   methodology for modeling the discrepancy function. It allows for emulation, calibration and prediction using complex mathematical model outputs and experimental data. See the reference: Mengyang Gu and Long Wang, 2018, Journal of Uncertainty Quantification; Mengyang Gu, Fangzheng Xie and Long Wang, 2022, Journal of Uncertainty Quantification; Mengyang Gu, Kyle Anderson and Erika McPhillips, 2023, Technometrics.