1,258 research outputs found
Situations and Evidence for Identity Using Dempster-Shafer Theory
We present a computational framework for identity based on Barwise and Devlin’s situation theory. We present an example with constellations of situations identifying an individual to create what we call id-situations, where id-actions are performed, along with supporting situations. We use Semantic Web standards to represent and reason about the situations in our example. We show how to represent the strength of the evidence, within the situations, as a measure of the support for judgments reached in the id-situation. To measure evidence of an identity from the supporting situations, we use the Dempster-Shafer theory of evidence. We enhance Dempster- Shafer theory in two ways to leverage the information available in a constellation of situations. One way exploits the structure within the situations, and the other way interprets the information-relationships in terms of argument schemes
Assessing forensic evidence by computing belief functions
We first discuss certain problems with the classical probabilistic approach
for assessing forensic evidence, in particular its inability to distinguish
between lack of belief and disbelief, and its inability to model complete
ignorance within a given population. We then discuss Shafer belief functions, a
generalization of probability distributions, which can deal with both these
objections. We use a calculus of belief functions which does not use the much
criticized Dempster rule of combination, but only the very natural
Dempster-Shafer conditioning. We then apply this calculus to some classical
forensic problems like the various island problems and the problem of parental
identification. If we impose no prior knowledge apart from assuming that the
culprit or parent belongs to a given population (something which is possible in
our setting), then our answers differ from the classical ones when uniform or
other priors are imposed. We can actually retrieve the classical answers by
imposing the relevant priors, so our setup can and should be interpreted as a
generalization of the classical methodology, allowing more flexibility. We show
how our calculus can be used to develop an analogue of Bayes' rule, with belief
functions instead of classical probabilities. We also discuss consequences of
our theory for legal practice.Comment: arXiv admin note: text overlap with arXiv:1512.01249. Accepted for
publication in Law, Probability and Ris
Evidence functions: a compositional approach to information
The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer ReviewedPostprint (author's final draft
Evidence functions: a compositional approach to information
The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer Reviewe
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