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}
}
  • N. Chopin
  • Published 1 April 2011
  • Computer Science, Mathematics
  • Statistics and Computing
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… 

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

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

A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets

A new algorithm is proposed that outperforms crude rejection method for the simulation of truncated multivariate Gaussian random variables and is based on a generalization of Von Neumann’s rejection technique which requires the determination of the mode of the truncation multivariate density function.

Simulation from the Tail of the Univariate and Multivariate Normal Distribution

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

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

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

Sampling from a multivariate Gaussian distribution truncated on a simplex: A review

This paper reviews recent Monte Carlo methods for sampling from multivariate Gaussian distributions restricted to the standard simplex and describes and analyzes two Hamiltonian Monte Carlo Methods.

Finite-dimensional approximation of Gaussian processes with inequality constraints

A finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators is developed, based on a linear combination between Gaussian random coefficients and deterministic basis functions.

Fast Simulation of Hyperplane-Truncated Multivariate Normal Distributions

We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently

Numerical Computation of Multivariate Normal Probabilities Using Bivariate Conditioning

New methods are derived for the computation of multivariate normal probabilities defined for hyper-rectangular probability regions. The methods use conditioning with a sequence of truncated bivariate

0 N ov 2 01 7 Finite-dimensional approximation of Gaussian processes with inequality constraints November 21 , 2017

A finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators is developed, based on a linear combination between Gaussian random coefficients and deterministic basis functions.

Cutoff for a class of auto-regressive models with large initialization

. We analyze the convergence rate of auto-regressive Markov chains p X k q k ě 0 on R d , where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others.
...

References

SHOWING 1-10 OF 40 REFERENCES

Perfect simulation of positive Gaussian distributions

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

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

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

  • A. Nobile
  • Mathematics, Computer Science
    Stat. 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

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

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.

An exact likelihood analysis of the multinomial probit model

Non-Uniform Random Variate Generation

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

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

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.