Evaluates posterior density for \(\mu\), the mean of a MVN distribution, with a MVN prior on \(\mu\)
mvnmvnp(y, m0 = 0, V0 = 1, Sigma = NULL, ...)a vector of observations from a MVN distribution with unknown mean and known variance-covariance.
the mean vector of the MVN prior, or a scalar constant so that the prior
vector of length \(k\) with the same element repeated k times, e.g. m0 = 0
the variance-covariance matrix of the MVN prior, or the diagonal of the variance-covariance matrix of the MVN prior, or a scalar constant, say \(n_0\), so the prior is \(n_0\times \mathbf{I}_k\) where \(\mathbf{I}_k\) is the \(k\) by \(k\) identity matrix.
the known variance covariance matrix of the data. If this value is NULL, which it is by default, then the sample covariance is used. NOTE: if this is the case then the cdf and quantile functions should really be multivariate t, but they are not - in which case the results are only (approximately) valid for large samples.
any other values to be passed to Bolstad.control
A list will be returned with the following components:
the posterior mean of the MVN posterior distribution
the posterior variance-covariance matrix of the MVN posterior distribution
a function that will evaluation the posterior cdf at a given point. This function calls mvtnmorm::pmvnorm.
a function that will find quantiles from the posterior given input probabilities. This function calls mvtnorm::qmvnorm.