Peter McCullagh
On Bayes' theorem for improper mixtures.
Thu, 12/15/2011 - 15:01 — SomNambulAuthors: Peter McCullagh, Han Han
Subjects: Statistics
AbstractAlthough Bayes's theorem demands a prior that is a probability distribution
on the parameter space, the calculus associated with Bayes's theorem sometimes
generates sensible procedures from improper priors, Pitman's estimator being a
good example. However, improper priors may also lead to Bayes procedures that
are paradoxical or otherwise unsatisfactory, prompting some authors to insist
that all priors be proper. This paper begins with the observation that an
improper measure on Theta satisfying Kingman's countability condition is in
fact a probability distribution on the power set.The Ewens process on spaces of even and balanced partitions.
Wed, 10/19/2011 - 15:01 — SomNambulAuthors: Harry Crane, Peter McCullagh
Subjects: Statistics
AbstractWe discuss a generalization of the Ewens partition process to $\partitionsj$,
the space of partitions whose block sizes are divisible by $j\in\mathbb{N}$,
called even partitions of order $j$, or $j$-even partitions, and
$\partitionsneut$, the subspace of $\partitionsj$ whose elements are labeled in
$[j]$ and whose blocks contain an equal number of elements with each label,
called $j$-balanced partitions. As in the Ewens process, these processes can be
constructed sequentially according to a random seating rule.Classification Based on Permanental Process with Cyclic Approximations.
Thu, 08/25/2011 - 15:01 — SomNambulAuthors: Jie Yang, Klaus Miescke, Peter McCullagh
Subjects: Methodology
AbstractIn this paper we introduce a statistical model based on a permanental process
for supervised classification problems. Unlike many research work in the
literature, we assume only exchangeability instead of independence on
observations. Regardless of the number of classes or the dimension of the
feature variables, the model may require only 2-3 parameters for fitting the
covariance structure within clusters. It works well even if each class occupies
non-convex, disjoint regions, or regions overlapped with other classes in the
feature space.
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