Search results for "upper bound"

showing 2 items of 12 documents

Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities

2022

We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for …

Settore MAT/06 - Probabilita' E Statistica MatematicaCoherence Conditional events Conditional random quantities Conditional previsions Conjoined and disjoined conditionals Iterated conditionals Compound probability theorem Lower and upper bounds Import-export principle
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Prediction of the next value of a function

1981

The following model of inductive inference is considered. Arbitrary set tau = {tau_1, tau_2, ..., tau_n} of n total functions N->N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function f from the set tau. Processing these values by some algorithm (a strategy) we try to predict f(m+1) from f(0), f(1), ..., f(m). Upper and lower bounds for average error numbers are obtained for prediction by using deterministic and probabilistic strategies.

upper boundslower boundsdeterministicinductive inferencepredictionaveragenext valuestrategyerror numberprobabilistic
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