Search results for "Prevision"

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 …

Logical Operations among Conditional Events: theoretical aspects and applications

2019

We generalize the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. These notions are defined, in the setting of coherence, by means of suitable conditional random quantities with values in the interval $[0,1]$. We also define the notion of negation, by verifying De Morgan's Laws. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals and we show that some well known properties which are satisfied by conjunctions and disjunctions of unconditional events are also satisfied by conjunctions and disjunction of conditional events. We also examine in detail the coherence of the prevision a…

Generalized coherence and connection property of imprecise conditional previsions.

2008

In this paper we consider imprecise conditional prevision assessments on random quantities with finite set of possible values. We use a notion of generalized coherence which is based on the coherence principle of de Finetti. We consider the checking of g-coherence, by extending some previous results obtained for imprecise conditional probability assessments. Then, we study a connection property of interval-valued gcoherent prevision assessments, by extending a result given in a previous paper for precise assessments.

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…

Coherent Conditional Previsions and Proper Scoring Rules

2012

In this paper we study the relationship between the notion of coherence for conditional prevision assessments on a family of finite conditional random quantities and the notion of admissibility with respect to bounded strictly proper scoring rules. Our work extends recent results given by the last two authors of this paper on the equivalence between coherence and admissibility for conditional probability assessments. In order to prove that admissibility implies coherence a key role is played by the notion of Bregman divergence.

On general conditional random quantities

2009

In the first part of this paper, recalling a general discussion on iterated conditioning given by de Finetti in the appendix of his book, vol. 2, we give a representation of a conditional random quantity $X|HK$ as $(X|H)|K$. In this way, we obtain the classical formula $\pr{(XH|K)} =\pr{(X|HK)P(H|K)}$, by simply using linearity of prevision. Then, we consider the notion of general conditional prevision $\pr(X|Y)$, where $X$ and $Y$ are two random quantities, introduced in 1990 in a paper by Lad and Dickey. After recalling the case where $Y$ is an event, we consider the case of discrete finite random quantities and we make some critical comments and examples. We give a notion of coherence fo…

MODELLO DI PREVISIONE DELLA STATURA FINALE IN PAZIENTI PEDIATRICI ITALIANI AFFETTI DA DEFICIT DI GH TRATTATI CON SOMATROPINA

2021

Obiettivi: elaborare un modello di previsione della statura finale in pazienti pediatrici con deficit di GH trattati con somatropina ricombinante, valutando quali siano le variabili più importanti nel determinismo della statura finale. Metodi: 1043 pazienti trattati per deficit di GH (picco di GH <10 ng/dl a 2 test di stimolo) giunti ad altezza finale. Mediana età a inizio trattamento 11 (IQR 8.7/12.8) anni; mediana altezza a inizio trattamento -2.43 (IQR -2.80/-2.01) SDS; mediana altezza bersaglio -1.09 (IQR -1.63/-0.48) SDS; dose iniziale di somatropina mediana altezza finale -1.08 SDS (IQR -1.64/-0.50 SDS, vs altezza a inizio trattamento p <0.001, vs altezza bersaglio p=ns). Analis…

Analisi delle serie storiche economiche

2009

Reassessing Accuracy Rates of Median Decisions

2007

We show how Bruno de Finetti''s fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the radiological diagnosis of asbestosis. Conditional exchangeability of individual radiologists'' diagnoses is recognized as more appropriate than independence which is commonly presumed. The FTP yields coherent bounds on probabilities of interest when available information is insufficient to determine a complete distribution. Further assertions that are natural to the problem motivate a partial ordering of conditional probabilities, extending the computation …

A temperature-type model for describing the relationship between fungal growth and water activity

2001

Growth of Penicillium chrysogenum, Aspergillus flavus, Cladosporium cladosporioides and Alternaria alternata at their respective optimum temperatures was studied in Potato Dextrose Agar (PDA) medium at different water activities (a(w)) adjusted with glycerol. The growth rate (mu) was expressed as the increase in colony radius per unit of time. This paper extends the model that showed the relationship between temperature and bacterial growth rate developed by Rosso et al. [J. Theor. Biol. 162 (1993) 447] to describe the influence of a(w) on fungal development. An excellent correlation between the experimental data and the model predictions was obtained, the regression coefficients (r2) were …