The normal law under linear restrictions: simulation and estimation via minimax tilting

By Zdravko I. Botev. 2016

276 citations recorded by the source corpus.

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set‐ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/533bf3ad398b299cc120f17ce2bd7674adb308ef

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In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Bayesian forecasting in economics and finance: A modern review (2022, background): “Although MCMC is able to solve this integral, it does so by generating the utility vector for each individual from a multivariate truncated normal, which is a computationally costly exercise (McCulloch and Rossi, 1994; Botev, 2017).”