# Simulation from the Normal Distribution Truncated to an Interval in the Tail

@inproceedings{Botev2016SimulationFT, title={Simulation from the Normal Distribution Truncated to an Interval in the Tail}, author={Zdravko I. Botev and Pierre L'Ecuyer}, booktitle={ValueTools}, year={2016} }

We study and compare various methods to generate a random variate from the normal distribution truncated to some finite or semi-infinite interval, with special attention to the situation where the interval is far in the tail. This is required in particular for certain applications in Bayesian statistics, such as to perform exact posterior simulations for parameter inference, but could have many other applications as well. We distinguish the case in which inversion is warranted, and that in…

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## References

SHOWING 1-10 OF 26 REFERENCES

### Fast simulation of truncated Gaussian distributions

- Computer Science, MathematicsStat. Comput.
- 2011

This work designs a table-based algorithm that is computationally faster than alternative algorithms and an accept-reject algorithm for simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval, or a semi-finite interval.

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

- Mathematics
- 2016

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…

### Efficient probability estimation and simulation of the truncated multivariate student-t distribution

- Mathematics2015 Winter Simulation Conference (WSC)
- 2015

An exponential tilting method for the accurate estimation of the probability that a random vector with multivariate student-t distribution falls in a convex polytope is proposed, providing an alternative to approximate Markov Chain Monte Carlo simulation.

### Efficient estimation and simulation of the truncated multivariate student-\(t\) distribution

- Mathematics
- 2015

We propose an exponential tilting method for exact simulation from the truncated multivariate student-t distribution in high dimensions as an alternative to approximate Markov Chain Monte Carlo…

### 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.

### Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities

- Mathematics
- 1991

It is shown how the accuracy and convergence of integrals based on the Gibbs sample may be constructed, and how an estimate of the probability of the constraint set under the unrestricted distribution may be produced.

### 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.

### Variance Reduction's Greatest Hits

- Computer Science
- 2007

A guided tour of five different methods that can make a huge difference in the accuracy of simulation estimators, which can reduce the variance (or improve the efficiency) by an arbitrary large factor.

### Quasi-Monte Carlo methods with applications in finance

- MathematicsFinance Stochastics
- 2009

We review the basic principles of quasi-Monte Carlo (QMC) methods, the randomizations that turn them into variance-reduction techniques, the integration error and variance bounds obtained in terms of…