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 Statistics36 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)