Penalty function for the log-likelihood of
Qpenalty is the default function;
MPpenalty is an example of a user-defined function effectively
corresponding to a prior distributio on
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in the univariate case, a single value
degrees of freedom, only required if
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
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
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
alpha=+/-Inf, this choice also penalizes
Q=Inf, effectively removing
alpha=0 from the parameter
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
attr(Q, "der1") and
depending onthe input value
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.
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