Fast simulation of truncated Gaussian distributions

TL;DR

This paper introduces faster algorithms for simulating truncated Gaussian distributions, providing efficient methods for one- and two-dimensional cases with promising acceptance rates, and discusses extensions to higher dimensions.

Contribution

The paper presents novel, computationally efficient algorithms for simulating truncated Gaussian vectors in one and two dimensions, with potential extensions to higher dimensions.

Findings

One-dimensional algorithm is faster than existing methods.

Acceptance rate for the two-dimensional accept-reject algorithm is at least 0.5 for semi-finite truncation.

Acceptance rate is at least 0.47 for finite truncation intervals.

Abstract

We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [a_i,b_i], or a semi-finite interval [a_i,+infty). In the one-dimensional case, we design a table-based algorithm that is computationally faster than alternative algorithms. In the two-dimensional case, we design an accept-reject algorithm. According to our calculations and our numerical studies, the acceptance rate of this algorithm is bounded from below by 0.5 for semi-finite truncation intervals, and by 0.47 for finite intervals. Extension to 3 or more dimensions is discussed.