Nicolas Chopin (CREST) just posted an entry on Statisfaction about the comparison of truncated Normal algorithms run by Alan Rogers, from the University of Utah. Nicolas wrote a paper in Statistics and Computing about a simulation method, which proposes a Ziggurat type of algorithm for this purpose, and which I do not remember reading, thanks to my diminishing memory buffer!  As shown in the picture below, when truncating to the half-line (a,∞), this method improves upon my accept-reject approach except in the far tails.

On the top graph, made by Alan Rogers, my uniform proposal (r) seems to be doing better for a Normal truncated to (a,b) when b<0, or when a gets large and close to b. Nicolas’ ziggurat (c) works better than the Gaussian accept-reject method (c) on the positive part. (I wonder what the exponential proposal (e) stands for, in terms of scale parameter.)