# Fast simulation of truncated Gaussian distributions

@article{Chopin2011FastSO, title={Fast simulation of truncated Gaussian distributions}, author={Nicolas Chopin}, journal={Statistics and Computing}, year={2011}, volume={21}, pages={275-288} }

We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [ai,bi], or a semi-finite interval [ai,+∞). 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 numerical studies, the acceptance rate of this algorithm is bounded from below by 0.5 for semi…

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## References

SHOWING 1-10 OF 40 REFERENCES

### Perfect simulation of positive Gaussian distributions

- Computer ScienceStat. Comput.
- 2003

An exact simulation algorithm that produces variables from truncated Gaussian distributions on R via a perfect sampling scheme, based on stochastic ordering and slice sampling, since accept-reject algorithms like the one of Geweke and Robert are difficult to extend to higher dimensions.

### Perfectly random sampling of truncated multinormal distributions

- MathematicsAdvances in Applied Probability
- 2007

The target measure μ is the distribution of a random vector in a box ℬ, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure μ. A ‘coupling from the…

### Automatic sampling with the ratio-of-uniforms method

- Computer ScienceTOMS
- 2000

It is shown, that the ratio-of-uniforms method is also useful for the design of a black-box algorithm suitable for a large class of distributions, including all with log-concave densities.

### A hybrid Markov chain for the Bayesian analysis of the multinomial probit model

- Mathematics, Computer ScienceStat. Comput.
- 1998

A modification of the sampling technique, by defining a hybrid Markov chain in which, after each Gibbs sampling cycle, a Metropolis step is carried out along a direction of constant likelihood.

### Generating Random Numbers from a Unimodal Density by Cutting Corners

- Computer Science
- 2007

The cutting corners algorithm can be used to generate random numbers from any unimodal density which is speciied only as a computer subroutine, giving a random number in the time that it takes to generate four or ve uniform random numbers.

### Algorithm 802: an automatic generator for bivariate log-concave distributions

- Computer Science, MathematicsTOMS
- 2000

The article describes the details how this main idea can be used to construct Algorithm ALC2D that can generate random pairs from all bivariate log-concave distributions with known domain, computable density, and computable partial derivatives.

### Non-Uniform Random Variate Generation

- Computer Science, Mathematics
- 1986

This chapter reviews the main methods for generating random variables, vectors and processes in non-uniform random variate generation, and provides information on the expected time complexity of various algorithms before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.

### Automatic Nonuniform Random Variate Generation

- Computer Science
- 2011

It is shown how random variate genration algorithms work and an interface for R is suggested as an example of a statistical library, which could be used for simulation or statistical computing.

### Bayesian Analysis of Constrained Parameter and Truncated Data Problems

- Computer Science, Mathematics
- 1991

This paper illustrates how the Gibbs sampler approach to Bayesian calculation avoids these difficulties and leads to straightforwardly implemented procedures, even for apparently very complicated model forms.