1,720,972 research outputs found
Probabilistic inconsistency correction for misclassification in statistical matching, with an example in health care
No full textA recently proposed procedure for correcting inconsistent (i.e. incoherent) probability assessments is specifically tailored for the statistical matching problem with misclassification component. Such procedure is based on L1 distance minimization encoded in mixed integer programming (MIP) problems and it results particularly apt to deal with assessments stemming from different sources of information. The statistical matching problem is one of those cases. The statistical matching problem has been recently studied also inside a misclassification setting. To proceed with a correction in such a framework, if marginal assessments on the conditioning event are wanted to remain fixed, the only possible solutions are the closest Fréchet–Hoeffding bounds for the misclassification probabilities. On the contrary, if also the marginal probabilities are allowed to be modified, the L1-based procedure can be applied by a straightforward translation in an MIP problem. Such procedure is applied to a healthcare expenditures and health conditions data example
Implicit Degree of Support for Finite Lower-Upper Conditional Probabilities Extensions
No full textIn this paper we propose a measure for the implicit degree of support for
coherent extensions of probabilistic models based on partial conditional
lower-upper assessments. This degree of support is induced by the different extension bounds that arise
operationally in automated computational inference procedures. These different bounds are induced by the "extreme" distributions compatible with an initial assessment, i.e. those
that strictly attain at least one of the constraints imposed by the modeler.
The minimum and the maximum of these extension bounds determine
the so called "least commitment" coherent extension interval, while the
intermediate values can be used to grade the support of the initial assessment for tighter intervals. The
appropriateness of the degree of support is determined by coherence of
particular sub-intervals of the wider "least commitment" coherent exten-
sion range. The proposed degree of support can be helpful in the pro-
cess of finding appropriate extension bounds whenever the standard pro-
cedure results in bounds that are too wide to be useful
Locally strong coherence in inferential processes
No full textIn this paper we deal with probabilistic inference in the most general form of coherent conditional probability assessments. In particular, our aim is to reduce computational difficulties that could arise with a direct application of the main characterization results. We reach our goal by introducing the notion of locally strong coherence and characterizing it by logical conditions. Hence, some of the numerical constraints are replaced by Boolean satisfiability conditions. An automatic procedure is proposed and its efficiency is proved. Some examples are reported to make easier the understanding of the machinery and to show its effectiveness
Coherent restrictions of vague conditional lower-upper probability extensions
No full textIn this paper we propose a way to restrict extension bounds
induced by coherent conditional lower-upper probability assessments.
Such shrinkage turns out to be helpful whenever the natural bounds
are too vague to be used. Since coherence of a conditional lower-upper
probability assessment can be characterized through a class of conditional probability distributions, the idea is to take the intersection of the extension bounds induced by each single element of the class instead of
the convex combination, as it is usually done. Coherence of such method
is proved for extensions performed on both conditional events logical dependent and not-dependent on the initial domain
Non Additive Ordinal Relations Representable by Lower and Upper Probabilities
No full textWe characterize (in terms of necessary and sufficient conditions) binary relations representable
by a lower probability. Such relations can be non-additive (as the relations
representable by a probability) and also not "partially monotone" (as the relations representable
by a belief function).
Moreover we characterize relations representable by upper probabilities and those representable
by plausibility. In fact the conditions characterizing these relations are not
immedi~tely deducible by means of "dual" conditions given on the contrary events, like in
the numerical case
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