1,721,072 research outputs found
Probabilistic Relations Among Logically Dependent Conditional Events
No full textIn this paper the concepts of partial and complete logical dependence among conditional events are studied and a comparison is made with some definitions given by other authors. Then, some logical and probabilistic relations are considered in the framework of coherent probabilistic assessments. A particular class of logically dependent conditional events is considered and, based on some results on coherence of precise and imprecise probability assessments, the probabilistic relations implied by logical dependence are studied. It is shown that logical dependence does not necessarily imply probabilistic relations. Finally, given two logically independent events, we examine the coherence of some probability assessments which are relevant to the property of stochastic independence
Probabilistic reasoning under coherence in System P
No full textIn this paper we apply a probabilistic reasoning under coherence to System P.We consider a notion of strict probabilistic consistency, we show its equivalence to Adams’ probabilistic consistency, and we give a necessary and sufficient condition for probabilistic entailment. We consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our coherence-based approach, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony rule of System P+ proposed by Adams in his extended probabilistic logic. Finally, we examine the propagation of lower bounds with real ε-values and, to illustrate our probabilistic reasoning, we consider an example
Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilità
No full textIn this paper the coherence condition based on the penalty criterion, proposed by de Finetti in his subjective theory of probability, is examined. Then a 'slight' modification of this definition of coherence, which is equivalent, when applied to nonconditional events, to that of de Finetti, is studied. Contrary to the latter, our definition does not require, in the case of conditional events, any strengthening. This more 'natural' condition (called C_0 coherence) is also interpreted from a geometrical point of view by means of a generalization of the concept of constituent. Moreover, we show the equivalence between the strengthened coherence based on the betting criterion and C_0 coherence
Probabilità condizionate C_0 -coerenti
No full textIn this paper we deepen the study of C_0-coherence. In particular, we show that a conditional probability which is C_0-coherent satisfies all properties of a finitely additive one. Moreover we prove the equivalence among strengthened coherence of B. de Finetti, C_0-coherence and the coherence based on the betting criterion with strengthening
Aspetti algebrici e geometrici nell'insegnamento della probabilità soggettiva
No full textIn questo articolo di carattere didattico si mette in luce come l'insegnamento della probabilità basato sull'impostazione soggettiva fornisce in modo naturale un "ambiente" in cui si possono riprendere e sviluppare in un'ottica "fusionista" tipica di B. de Finetti vari aspetti e concetti logico/matematici, ad esempio logica delle proposizioni, funzioni lineari, geometria analitica, insiemi convessi, teoremi di alternativa, risultando così di notevole valore formativo
Un'applicazione del concetto di pseudodensità al problema della prima cifra significativa dei dati statistici
No full textThe well known 'first digit' problem is solved by introducing an ordering between intervals, that are interpreted as 'points' on which a pseudodensity is defined by a suitable set function
Probabilistic logic under coherence and default reasoning
No full textIn this paper we study a probabilistic logic based on the notion of coherence of de Finetti. We first recall the notion of coherence for precise conditional probability assessments, then we consider its generalization to the case of imprecise assessments. We examine conditional probabilistic knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. In our probabilistic logic the notion of probabilistic interpretation is directly defined in terms of precise conditional probability assessments. Then, we give in our approach new proofs of some results obtained in probabilistic default reasoning
Classi quasi additive di eventi e coerenza di probabilità condizionate
No full textBy using the C_0-coherence concept, we prove that, given a finitely additive conditional probability P on E x H, with E an algebra of events, if the class H of the conditioning events is P-almost additive then P is a coherent conditional probability. Moreover, the extension of P on E x H*, with H contained in H*, such that the class H* of the conditioning events is additive, is examined. Finally, some examples of P-almost additive classes are shown and a sufficient condition of almost additivity is given
Incomplete probability assessments in decision analysis
No full textIn analysing a decision problem, in a situation of partial knowledge, a decision maker may be reluctant to assign a complete probability distribution on the relevant states of nature. In order to face this difficulty, several methods, based on indeterminate probabilities or probability intervals, have been proposed in the literature. In this paper, arguing that it is meaningless to judge probabilistic assessments as correct or wrong, it is maintained that only coherence has an objective and significant role. Then to overcome practical difficulties, an approach based on the subjective methodology and on the use of numerical and qualitative probabilities, is outlined
Probabilità di eventi come previsione di numeri aleatori
No full textIn questo lavoro si adotta l'impostazione soggettiva della probabilità. Si consider l'esperimento di estrazioni senza restituzione da un'urna di composizione nota e, basandosi sul criterio della scommessa, si mostra che le probabilità di successo nelle diverse prove si possono rappresentare come previsioni di particolari numeri aleatori. Utilizzando, quindi, la proprietà di linearità della previsione si ottiene una semplice espressione che, applicata in modo iterativo, consente di mostrare che (a priori) la probabilità di successo in ogni prova è costante. Infine vengono esaminate altre applicazioni
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