ArXiv:0907.4010v1 [stat.CO] 23 Jul 2009.pdf

## arXiv:0907.4010v1 [stat.CO] - Simulation of Truncated Normal Variables

This paper presents algorithms for simulating one-sided and two-sided truncated normal variables, addressing a common need in Bayesian inference for problems with restricted parameter spaces.

Key Points:

One-Sided Truncation: The authors propose an efficient accept-reject algorithm based on the exponential distribution. This algorithm outperforms repeated sampling from a standard normal distribution, especially for larger truncation points.
Optimal Scale Factor: The optimal scale factor in the exponential distribution is derived analytically, leading to higher acceptance probabilities.
Two-Sided Truncation: Simulation from the two-sided truncated normal distribution is achieved by modifying the one-sided algorithm, considering both lower and upper bounds.
Markov Chain Monte Carlo (MCMC) Application: The algorithms are integrated into MCMC methods for simulating multivariate normal variables with restricted parameter spaces.

Contribution:

The paper offers:

A simple and efficient method for simulating from one-sided truncated normal distributions.
An acceptance-rejection algorithm that significantly improves upon standard techniques, especially for moderate to large truncation points.
* A foundation for extending the methods to two-sided truncations and multivariate scenarios using MCMC.