• Corpus ID: 613672

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

@inproceedings{Geweke1991EfficientSF,
  title={Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities},
  author={John Geweke},
  year={1991}
}
John GewekeDepartment of EconomicsUniversity of MinnesotaMinneapolis, MN 55455First draft: April, 1991Phone: (612)625-7563 Fax: (612)624-0209E-mail: geweke@atlas.socsci.umn.eduAbstractThe construction and implementation of a Gibbs sampler for efficient simulation from thetruncated multivariate normal and Student-t distributions is described. It is shown how theaccuracy and convergence of integrals based on the Gibbs sample may be constructed, andhow an estimate of the probability of the… 

Efficient Gibbs Sampling of Truncated Multivariate Normal with Application to Constrained Linear Regression

In this paper we propose an efficient Gibbs sampler for simulation of a multivariate normal random vector subject to inequality linear constraints. Inference in a Bayesian linear model, where the

Efficient sampling methods for truncated multivariate normal and student-t distributions subject to linear inequality constraints

Sampling from a truncated multivariate distribution subject to multiple linear inequality constraints is a recurring problem in many areas in statistics and econometrics, such as the order-restricted

MCMC Estimation of Restricted Covariance Matrices

This article is motivated by the difficulty of applying standard simulation techniques when identification constraints or theoretical considerations induce covariance restrictions in multivariate

Simulating Normal Rectangle Probabilities and Their Derivatives: Effects of Vectorization

  • V. Hajivassiliou
  • Mathematics, Computer Science
    Int. J. High Perform. Comput. Appl.
  • 1993
Judged in terms of simulation root-mean-squared-er ror for a given investment in computation time, it is found that the importance sampling recursive triangulariza tion simulator GHK remains the best method for simu lating probabilities irrespective of vectorization; the crude Monte Carlo simulator CFS offers the greatest benefits from vectorization and the Gibbs resampling algorithm GSS emerges as one of the preferred meth ods for simulating logarithmic derivatives.

2 An Alternative Parameterization of the Covariance Matrix

This article is motivated by the difficulty of applying standard simulation techniques when identification constraints or theoretical considerations induce covariance restrictions in multivariate

A Bayesian Model of Sample Selection with a Discrete Outcome Variable

Relatively few published studies apply Heckman’s (1979) sample selection model to the case of a discrete endogenous variable and those are limited to a single outcome equation. However, there are

MCMC perspectives on simulated likelihood estimation

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves

Efficient algorithms for generating truncated multivariate normal distributions

Numerical comparisons show that the proposed iterative data augmentation algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.

Sequential Monte Carlo EM for multivariate probit models

...

References

SHOWING 1-10 OF 13 REFERENCES

Linear Statistical Inference and Its Applications

"C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of

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.

The method of simulated scores for the estimation of LDV models

The method of simulated scores (MSS) is presented for estimating limited dependent variables models (LDV) with flexible correlation structure in the unobservables. We propose simulators that are

Bayesian Inference in Econometric Models Using Monte Carlo Integration

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost

Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments

Methods for spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence in the normal linear model with informative priors, and in the Tobit-censored regression model.

Exact Inference in the Inequality Constrained Normal Linear Regression Model

Inference in the inequality constrained normal linear regression model is approached as a problem in Bayesian inference, using a prior that is the product of a conventional uninformative distribution

A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration

This paper proposes a simple modification of a conventional generalized method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration

Sampling-Based Approaches to Calculating Marginal Densities

Abstract Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the

Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

  • S. GemanD. Geman
  • Physics
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1984
The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.

1965: Linear Statistical Inference and Its Applications

  • 1965: Linear Statistical Inference and Its Applications