SeminÃrio
PIPGEs - UFSCar/USP Â 29/08/2013 (quinta-feira) -
14h00
LOCAL:
Sala
de seminÃrios  DEs-UFSCar
TÃTULO:
A classical measure
of evidence for general null hypotheses
Alexandre GalvÃo
Patriota Â
IME-USP
RESUMO:
In
science, the most widespread statistical quantities are perhaps p-values. A
typical advice is to reject the null hypothesis H0 if the corresponding p-value
is sufficiently small (usually smaller than 0.05). Many criticisms regarding
p-values have arisen in the scientific literature. The main issue is that in
general optimal p-values (based on likelihood ratio statistics) are not measures
of evidence over the parameter space Î. Here, we propose an objective measure of
evidence for very general null hypotheses that satisfies logical requirements
(i.e., operations on the subsets of Î) that are not met by p-values (e.g., it is
a possibility measure). We study the proposed measure in the light of the
abstract belief calculus formalism and we conclude that it can be used to
establish objective states of belief on the subsets of Î. Based on its
properties, we strongly recommend this measure as an additional summary of
significance tests. At the end of the paper we give a short listing of possible
open problems.
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