Search results for " Matematica"
showing 10 items of 1345 documents
Generalized Logical Operations among Conditional Events
2018
We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan's Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular we examine the Fr'echet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $mathc…
Compounds of conditionals and iterated conditioning under coherence
2017
We discuss the problem of defining logical operations among conditional events. Differently from many authors, we define the conjunction and disjunction in the setting of conditional random quantities. In probability theory and in probability logic a relevant problem, largely discussed by many authors, is that of defining logical operations among conditional events. In the many works concerning these operations, the conjunction and disjunction have been usually defined as suitable conditional events. In Kaufmann 2009 it has been proposed a theory for the compounds of conditionals which has been framed in the setting of coherence in (Gilio and Sanfilippo , 2013, 2014) In this framework, whic…
On compound and iterated conditionals
2021
We illustrate the notions of compound and iterated conditionals introduced, in recent papers, as suitable conditional random quantities, in the framework of coherence. We motivate our definitions by examining some concrete examples. Our logical operations among conditional events satisfy the basic probabilistic properties valid for unconditional events. We show that some, intuitively acceptable, compound sentences on conditionals can be analyzed in a rigorous way in terms of suitable iterated conditionals. We discuss the Import-Export principle, which is not valid in our approach, by also examining the inference from a material conditional to the associated conditional event. Then, we illus…
Sequentially Forecasting Economic Indices Using Mixture Linear Combinations of EP Distributions
2021
This article displays an application of the statistical method moti- vated by Bruno de Finetti's operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear com- binations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis test- ing. In its place, proper scoring rules for forecast distributions are used to assess the values o…
Completing the logarithmic scoring rule for assessing probability distributions
2012
We propose and motivate an expanded version of the logarithmic score for forecasting distributions, termed the Total Log score. It incorporates the usual logarithmic score, which is recognised as incomplete and has been mistakenly associated with the likelihood principle. The expectation of the Total Log score equals the Negentropy plus the Negextropy of the distribution. We examine both discrete and continuous forms of the scoring rule, and we discuss issues of scaling for scoring assessments. The analysis suggests the dual tracking of the quadratic score along with the usual log score when assessing the qualities of probability distributions. An application to the sequential scoring of f…
Interpreting Connexive Principles in Coherence-Based Probability Logic
2021
We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If \(\mathord {\thicksim }A\), then A, should not hold, since the conditional’s antecedent \(\mathord {\thicksim }A\) contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event \(A|\bar{A}\) is \(p(A|\bar{A})=0\). Moreover, connexive logics aim to capture the intuition that conditionals should express some “connection” between the antecedent and the consequent or, in terms of inferences, valid…
SCORING ALTERNATIVE FORECAST DISTRIBUTIONS: COMPLETING THE KULLBACK DISTANCE COMPLEX
2018
We develop two surprising new results regarding the use of proper scoring rules for evaluating the predictive quality of two alternative sequential forecast distributions. Both of the proponents prefer to be awarded a score derived from the other's distribution rather than a score awarded on the basis of their own. A Pareto optimal exchange of their scoring outcomes provides the basis for a comparison of forecast quality that is preferred by both forecasters, and also evades a feature of arbitrariness inherent in using the forecasters' own achieved scores. The well-known Kullback divergence, used as a measure of information, is evaluated via the entropies in the two forecast distributions a…
Quasi conjunction and p-entailment in nonmonotonic reasoning
2010
We study, in the setting of coherence, the extension of a probability assessment defined on n conditional events to their quasi conjunction. We consider, in particular, two special cases of logical dependencies; moreover, we examine the relationship between the notion of p-entailment of Adams and the inclusion relation of Goodman and Nguyen. We also study the probabilistic semantics of the QAND rule of Dubois and Prade; then, we give a theoretical result on p-entailment.
Probabilistic inference and syllogisms
2014
Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All S are P ” and “At least one S is P ” and their respective negated versions. We will discuss probabilistic notions of the existential import and the basic sentences type. We will develop an intuitively plausible version of the syllogisms that is able to deal with uncertainty, exceptions and nonmonotonicity. We will develop a new semantics for categorical syllogisms that is based on subjective probability. Specifically, we propose de Finetti’s principle of coherence and its generalization to lower and upper conditional probabilities as the fundamental corner ston…
La Ruota della Fortuna
2017
Nell’anno scolastico 2013-2014 presso l’I. C. Boccadifalco Tomasi di Lampedusa di Palermo abbiamo realizzato un progetto PON finalizzato all’ampliamento della matematica per le classi seconde della scuola primaria. In una delle attività realizzate, che descriviamo in questo lavoro, ci siamo occupati del problema dell’elicitazione delle probabilità basata sul criterio della scommessa [1]. Nell’attività proposta si richiede la formulazione delle probabilità mediante dei gradi di fiducia su alcuni eventi relativi al gioco della ruota della fortuna. In particolare, si propone allo studente di formulare delle valutazioni di probabilità mediante delle scommesse nel ruolo di giocatore in un g…