Methods for computing joint tests, controlling the Familywise Error Rate (FWER) and getting lower bounds on the number of false hypotheses in a set. The methods implemented here are described in Mogensen and Markussen (2021) <doi:10.48550/arXiv.2108.04731>.

Efficient sampling of truncated multivariate (scale) mixtures of normals under linear inequality constraints is nontrivial due to the analytically intractable normalizing constant. Meanwhile, traditional methods may subject to numerical issues, especially when the dimension is high and dependence is strong.    Algorithms proposed by Li and Ghosh (2015) <doi: 10.1080/15598608.2014.996690> are adopted for overcoming difficulties in simulating truncated distributions. Efficient rejection sampling for simulating truncated univariate normal distribution is included in the package, which shows superiority in terms of acceptance rate and numerical stability compared to existing methods and R packages. An efficient function for sampling from truncated multivariate normal distribution subject to convex polytope restriction regions based on Gibbs sampler for conditional truncated univariate distribution is provided. By extending the sampling method, a function for sampling truncated multivariate Student's t distribution is also developed.     Moreover, the proposed method and computation remain valid for high dimensional and strong dependence scenarios. Empirical results in Li and Ghosh (2015) <doi: 10.1080/15598608.2014.996690> illustrated the superior performance in terms of various criteria (e.g. mixing and integrated auto-correlation time).

Importance sampling from the truncated multivariate normal using the GHK (Geweke-Hajivassiliou-Keane) simulator.
  Unlike Gibbs sampling which can get stuck in one truncation sub-region depending on initial values, this package allows 
  truncation based on disjoint regions that are created by truncation of absolute values. The GHK algorithm uses simple Cholesky
  transformation followed by recursive simulation of univariate truncated normals hence there are also no convergence issues. 
  Importance sample is returned along with sampling weights, based on which, one can calculate integrals over truncated regions
  for multivariate normals.