Efficient Sampling Methods for Truncated Multivariate Normal and Student-t Distributions Subject to Linear Inequality Constraints

• Published in: Journal of statistical theory and practice Vol. 9; no. 4; pp. 712 - 732
• Main Authors: Li, Yifang, Ghosh, Sujit K.
• Format: Journal Article
• Language: English
• Published: Cham Taylor & Francis 02.10.2015; Springer International Publishing
• Subjects: Gibbs sampler; Mathematics and Statistics; Probability Theory and Stochastic Processes; Rejection sampling; Statistical Theory and Methods; Statistics; Truncated multivariate normal distribution; Truncated multivariate Student-t distribution; Truncated scale mixture of multivariate normal distribution; Gibbs sampler; Rejection sampling; Truncated multivariate Student; Truncated scale mixture of multivariate normal distribution; Truncated multivariate normal distribution; 62E99; distribution
• DOI: 10.1080/15598608.2014.996690
• ISSN: 1559-8608

Sampling from a truncated multivariate distribution subject to multiple linear inequality constraints is a recurring problem in many areas in statistics and econometrics, such as the order-restricted regressions, censored data models, and shape-restricted nonparametric regressions. However, the sampling problem remains nontrivial due to the analytically intractable normalizing constant of the truncated multivariate distribution. We first develop an efficient rejection sampling method for the truncated univariate normal distribution, and analytically establish its superiority in terms of acceptance rates compared to some of the popular existing methods. We then extend our methodology to obtain samples from a truncated multivariate normal distribution subject to convex polytope restriction regions. Finally, we generalize the sampling method to truncated scale mixtures of multivariate normal distributions. Empirical results are presented to illustrate the superior performance of our proposed Gibbs sampler in terms of various criteria (e.g., mixing and integrated auto-correlation time).