I am guessing that it would could make sense to expand the convex hull one point
at a time (starting with the point closest to the center of gravity?) and see if
the error estimates remain approximately the same in order to make arbitrary
causal inferences.
Would it really be totally unreasonable to use the sum of the log-
likelihood-ratios (on each of the parameters of the model) as it expands from
few points to many in order to determine log-likelihood of model given the
data?
Quoting John Gasper <jtgasper(a)gmail.com>om>:
this isn't quite right. it includes all of
elements in the interior
of the set, and - for everything we care about - is a closed set.
i.e., it includes the boundary.
in other words, the convex hull is defined about a set, A, and is the
smallest convex set including A. (alternatively, if you deal well
thinking in terms of intersections, it is also the intersection of all
convex sets that include A.)
when in doubt, see aliprantis and border: the convex hull of A is defined
as:
$\set{x : \exists x_i \in A, \alpha_i \geq 0, \sum_{i=1}^{n} \alpha_i,
and x = \sum_{i=1}^{n}\alpha_i x_i}$
john
On 4/13/06, ghumphr(a)fas.harvard.edu <ghumphr(a)fas.harvard.edu> wrote:
If any of this doesn't make sense, please
let me know.
The _convex hull_ is the set of points at the border of the _convex set_
(which
is a set of space and does not appear to be
defined in the current version
of
the Oxford English dictionary). The convex hull
occupies no space, but
contains all of the points.
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--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
John Gasper, PhD Candidate
Dept: Social & Decision Sciences
Carnegie Mellon University
www.hss.cmu.edu/departments/sds
Spring 2006:
The Institute for Quantitative Social Science
Cambridge, MA 02138
www.iq.harvard.edu
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