priorGauss
object, which represents the
hyperparameters of the normal inverted-Wishart distribution used
as a prior distribution for the Gaussian model. Below, the prior
may be specified either by a character string, or by explicitly
setting the values of the parameters.
priorGauss(type = "general", tau = 0, mean = 0, df = 1, scale = df)
a general prior. In this case you must specify all hyperparameters,
including a vector for argument
mean
, a matrix for argument
scale
, and the
tau
and
df
parameters. This is the default.
priorGauss
are ignored. priorGauss
are
ignored. tau
and
mean
arguments to
priorGauss
are ignored, and the default for the
scale
and
df
arguments are both 1. When a scalar value of
scale
is input, it is
used to define the final
scale
matrix, see the description of the
scale
argument.
mean
in the Bayes estimates. The larger
the degrees of freedom, the stronger the belief in the prior
distribution of the mean. For both
"noninformative"
and
"ridge"
priors,
tau
is zero, the minimum possible value for
tau
. This
gives an improper uniform prior on the means. For maximum likelihood
estimation (
"ml"
),
tau
is set to
Machine$double.xmax
.
mean
is set to zero for
"ml"
,
"noninformative"
, and
"ridge"
priors.
df
is set to -1, the minimum value. This means that the mode
for the posterior distribution of the covariance matrix given the data
will be the usual unbiased estimate of the multivariate normal
covariance matrix. For
"ridge"
estimates,
df = 1
by default, but it
is also possible to specify any value greater than -1. Parameter
df
is ignored for maximum likelihood estimation.
scale
parameter in the inverse Wishart prior. This is the
expected sums of squares and cross-products for the multivariate
normal data when there are
df
degrees of freedom. For a
"noninformative"
prior,
scale
is set to zero. Argument
scale
is
not used in maximum likelihood estimation. For
type = "ridge"
, you
can give any scale matrix of the correct dimensionality for your
problem. Alternatively, if a scalar value is input for scale, then
the final scale matrix is taken as the diagonal matrix containing the
scalar value times the variances of the observations for the
nonmissing data (i.e., for each variable, variances are computed on
the observed values). In this case, the usual biased maximum likelihood
estimates are computed, see
. For
type = "general"
, any positive definite square
matrix of the appropriate dimension may be used.
"priorGauss"
. This is a list containing the
components
type
,
tau
,
mean
,
df
, and
scale
.
For
"ridge"
priors, the prior can be computed
using routine
dataDepPrior
. See
.
Schafer, J. L. (1997), Analysis of Incomplete Multivariate Data, Chapman & Hall, London.
priorGauss(type = "noninformative")