Penalty function for the log-likelihood of selm
models
when method="MPLE"
. Qpenalty
is the default function;
MPpenalty
is an example of a user-defined function effectively
corresponding to a prior distributio on alpha
.
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alpha_etc, alpha |
in the univariate case, a single value |
nu |
degrees of freedom, only required if |
der |
a numeric value in the set 0,1,2 which indicates the
required numer of derivatives of the function. In the multivariate case
the function will only be called with |
The penalty is a function of alpha
, but its expression may
depend on other ingredients, specifically nu
and cov2cor(Omega)
.
See ‘Details’ of selm
for additional information.
The penalty mechanism allows to introduce a prior distribution π for α by setting Q=-log(π), leading to a maximum a posteriori estimate in the stated sense.
As a simple illustration of this mechanism, function MPpenalty
implements the ‘matching prior’ distribution for the univariate SN
distribution studied by Cabras et al. (2012); a brief summary of the
proposal is provided in Section 3.2 of Azzalini and Capitanio (2014). Note
that, besides alpha=+/-Inf
, this choice also penalizes alpha=0
with Q=Inf
, effectively removing alpha=0
from the parameter
space.
Starting from the code of function MPpenalty
, a user should be able
to introduce an alternative prior distribution if so desired.
A positive number Q
representing the penalty, possibly
with attributes attr(Q, "der1")
and attr(Q, "der2")
,
depending onthe input value der
.
Adelchi Azzalini
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
Cabras, S., Racugno, W., Castellanos, M. E., and Ventura, L. (2012). A matching prior for the shape parameter of the skew-normal distribution. Scand. J. Statist. 39, 236–247.
selm
function
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