mvn.bayes {miscF}

Estimate the Parameters of a Multivariate Normal Model by the Bayesian Methods

Description

Estimate the parameters of a multivariate normal model under different priors.

Usage

  mvn.bayes(X, nsim, prior=c("Jeffreys", "Conjugate"))

Arguments

X

a matrix of observations with one subject per row.

nsim

number of simulations.

prior

a character string specifying the prior distribution. It must be either "Jeffreys" or "Conjugate" and may be abbreviated. The default is "Jeffreys".

Details

Both the Jeffreys prior and normal-inverse-Wishart conjugate prior are available. The conjugate prior of variance covariance matrix is inverse-Wishart. To use a noninformative proper prior, the degree of freedom of Wishart prior was set as the number of dimensions and the scale matrix was chosen based on the unbiased estimate. The number of prior measurements was taken as one and the prior mean was set as its unbiased estimate.

Value

Mu.save

a matrix of mean vector of the model, one row per iteration.

Sigma.save

a three dimensional array of variance of the model. Sigma.save[,,i] is the result from the ith iteration.

Note

When the number of dimensions is two, under Jeffreys prior, it is straightforward to obtain independent samples from the posteriors.

References

Berger, J. O., Sun, D. (2008) Objective Priors for the Bivariate Normal Model. The Annals of Statistics 36 963-982.

Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B. (2003) Bayesian Data Analysis. 2nd ed. London: Chapman and Hall

Sun, D., Berger, J. O. (2009) Objective Priors for the Multivariate Normal Model. In Bayesian Statistics 8, Ed. J. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith and M. West. Oxford: Oxford University Press.

Examples

  Sigma <- matrix(c(100, 0.99*sqrt(100*100),
                      0.99*sqrt(100*100), 100),
                      nrow=2)
  X <- mvrnorm(1000, c(100, 100), Sigma)
  result <- mvn.bayes(X, 10000)
  Mu <- colMeans(result$Mu.save)
  Sigma <- apply(result$Sigma.save, c(1,2), mean)