# Simulation from the Tail of the Univariate and Multivariate Normal Distribution

@inproceedings{Botev2019SimulationFT, title={Simulation from the Tail of the Univariate and Multivariate Normal Distribution}, author={Zdravko I. Botev and Pierre L'Ecuyer}, booktitle={Systems Modeling: Methodologies and Tools}, year={2019} }

We study and compare various methods to generate a random variate or vector from the univariate or multivariate normal distribution truncated to some finite or semi-infinite region, with special attention to the situation where the regions are 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…

## 2 Citations

### Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo

- Computer ScienceArXiv
- 2021

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex polytope. We prove that, starting from a warm start,…

### Analysis of Optical Brain Signals Using Connectivity Graph Networks

- PsychologyCD-MAKE
- 2020

It is found that motion imagery and mental arithmetic share a background network structure, and that the right prefrontal cortex, in AFp8, is an invariable destination for information flows in every stimuli and participant.

## References

SHOWING 1-10 OF 27 REFERENCES

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

- MathematicsVALUETOOLS
- 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…

### 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…

### 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.

### Tail distribution of the maximum of correlated Gaussian random variables

- Mathematics2015 Winter Simulation Conference (WSC)
- 2015

This article shows that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient estimator of the true variance.

### 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…

### 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.

### Simulation of truncated normal variables

- Mathematics
- 1995

We provide simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with convex restricted parameter…

### Model uncertainty and variable selection in Bayesian lasso regression

- Computer ScienceStat. Comput.
- 2010

This paper describes how the marginal likelihood can be accurately computed when the number of predictors in the model is not too large, allowing for model space enumeration when the total number of possible predictors is modest.

### 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.