Simulation from the Tail of the Univariate and Multivariate Normal Distribution

We study and compare various methods to generate a random variate or vector from the univariate or multivariate normal distribution truncated to some finite or semi-infinite region, with special attention to the situation where the regions are far in the tail. This is required in particular for certain applications in Bayesian statistics, such as to perform exact posterior simulations for parameter inference, but could have many other applications as well. We distinguish the case in which inversion is warranted, and that in which rejection methods are preferred.

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