Simulation of truncated normal variables

@article{Robert1995SimulationOT,
  title={Simulation of truncated normal variables},
  author={Christian P. Robert},
  journal={Statistics and Computing},
  year={1995},
  volume={5},
  pages={121-125}
}
  • C. Robert
  • Published 23 July 2009
  • Mathematics
  • Statistics and Computing
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 space for any covariance structure. 

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References

SHOWING 1-10 OF 20 REFERENCES

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.

Order restricted statistical inference

Isotonic Regression. Tests of Ordered Hypotheses: The Normal Means Case. Tests of Ordered Hypotheses: Generalizations of the Likelihood Ratio Tests and Other Procedures. Inferences about a Set of

Estimation of parameters in hidden Markov models

  • W. QianD. Titterington
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
  • 1991
Parameter estimation from noisy versions of realizations of Markov models is extremely difficult in all but very simple examples. The paper identifies these difficulties, reviews ways of coping with

Markov Chain Monte Carlo Maximum Likelihood

Markov chain Monte Carlo (e. g., the Metropolis algorithm and Gibbs sampler) is a general tool for simulation of complex stochastic processes useful in many types of statistical inference. The basics

Markov Chains for Exploring Posterior Distributions

Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are

The calculation of posterior distributions by data augmentation

If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution of parameters of interest.

Explaining the Gibbs Sampler

A simple explanation of how and why the Gibbs sampler works is given and analytically establish its properties in a simple case and insight is provided for more complicated cases.

Practical Markov Chain Monte Carlo

The case is made for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature.

Inference from Iterative Simulation Using Multiple Sequences

The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and