Alternative sampling methods for estimating multivariate normal probabilities

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Factor analysis with (mixed) observed and latent variables in the exponential family (2001, methodology): “See for an overview and comparison of these methods Sándor and András (2000).”
The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, background): “…and Lin (2012, 2013) and Nomura (2014b) consider approximation methods for special cases (orthant, bivariate, or trivariate probabilities) and Geweke (1991); Genz (1992); Joe (1995); Vijverberg (1997); S´andor and Andr´as (2004); Nomura (2014a) consider estimation schemes applicable for general ℓ .”
An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs (2009, methodology): “In several cases, estimates using these methods are more efficient than Monte Carlo estimates so that it is possible to employ smaller samples to obtain the same accuracy (Sándor and András 2004; Sándor and Train 2004).”
Estimation of Nonstationary Heterogeneous Panels (2007, background): “) Train (2003) argued that Halton draws are more effective for MSL estimation than pseudorandom draws because they can provide the same accuracy with fewer draws, thereby saving computer time.”