info:eu-repo/semantics/report
Functions of Singular Random Matrices : A Bayesian Application
Autor
JOSE ANTONIO DIAZ GARCIA
Institución
Resumen
The
presen
t article
describ
es how the
Jacobian
is found
for
certain
functions
of
a singular
random
matrix,
both
in the
general
case
and
in that
of a non-negativ
e
de nite
random
matrix.
In particular,
we nd
the
Jacobian
of the
V
=
S
2
transfor-
mation
when
S
is non-negativ
e de nite,
and
in general,
the
Jacobian
of the
Y
=
X
+
transformation,
in whic
h
X
+
is the
generalised,
or Mo
ore-P
enrose,
inverse
of
X
.
Expressions
for
the
densities
of the
generalised
inverse
of the
cen
tral
Beta
and
F
singular
random
matrices
are
prop
osed.
Finally
, two applications
in the
eld
of
Bayesian
inference
are
presented.
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