ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Learning for Contingency Tables and Survival Data using Imprecise Probabilities

Bayesian inference is a method of statistical inference in which all forms of uncertainty are expressed in terms of probability. Classical Bayesian inference has some limitations. One of these situations is when we have little to no information about the experiment; another situation is when we have computational or time limitations. Also problematic is a situation where there are conflicts in choosing a prior distribution where we have experts giving different prior information, which results in less precise posterior probabilities. Because of these limitations, imprecise Bayesian approach takes place in Bayesian inference. Upper and lower posterior expectations are computed in order to calculate the degree of imprecision of the log-odds ratio. This is implemented in two-way contingency tables and then generalized to three-way tables by using different families of prior distributions, is which the core of this work. Survival data including right-censored observations are generated and converted to a sequence of 2 x 2 tables, three-way contingency tables, each 2 x 2 is built at each observed death time. Here, we assume only one death happens at each time and no ties. To implement imprecise Bayesian inference, two choices of imprecise priors are chosen. A set of four Normal priors and a set of four Beta priors are used with a non-central hypergeometric likelihood to update the posterior families and then the degree of imprecision is calculated for both cases. An example of real data is applied on Ovarian Cancer Survival data where upper and lower posterior expectations are estimated in order to calculate the degree of imprecision. We conduct simulation studies to sample from posterior distribution and estimate the log-odds ratio by using upper and lower posterior expectations. In the situation of three-way contingency tables, updating a set of priors to a set of posterior is done sequentially at each table by running MCMC method through using JAGS from R via rjags and runjags packages. Also, four factors (sample size, censoring rate, true parameter, and balancing rate) are studied to see how these four factors a ect the degree of imprecision with the two choices of imprecise priors. A fractional factorial design of 27 runs is constructed to see which one of these four factors is more signi cant. For each one of these 27 combination, upper and lower posterior expectations and the degree of imprecision of the log-odds ratio are calculated. The findings show that the smallest value of the degree of imprecision appears at the combination where the sample size is large (n = 200) and small number of censored times. In contrast, the largest value of the degree of imprecision is observed at the combination where the sample size is small (n = 40) and large number of censored times. These conclusions are supported by the findings of ANOVA that show that main e ects of the four factors are significant. The conclusion that can be summarized from the results of this work is having more information (more data) leads to less uncertainty about the parameter of interest

Représentation et combinaison d'informations incertaines : nouveaux résultats avec applications aux études de sûreté nucléaires

It often happens that the value of some parameters or variables of a system are imperfectly known, either because of the variability of the modelled phenomena, or because the availableinformation is imprecise or incomplete. Classical probability theory is usually used to treat these uncertainties. However, recent years have witnessed the appearance of arguments pointing to the conclusion that classical probabilities are inadequate to handle imprecise or incomplete information. Other frameworks have thus been proposed to address this problem: the three main are probability sets, random sets and possibility theory. There are many open questions concerning uncertainty treatment within these frameworks. More precisely, it is necessary to build bridges between these three frameworks to advance toward a unified handlingof uncertainty. Also, there is a need of practical methods to treat information, as using these framerowks can be computationally costly. In this work, we propose some answers to these two needs for a set of commonly encountered problems. In particular, we focus on the problems of:- Uncertainty representation- Fusion and evluation of multiple source information- Independence modellingThe aim being to give tools (both of theoretical and practical nature) to treat uncertainty. Some tools are then applied to some problems related to nuclear safety issues.Souvent, les valeurs de certains paramètres ou variables d'un système ne sont connues que de façon imparfaite, soit du fait de la variabilité des phénomènes physiques que l'on cherche à représenter,soit parce que l'information dont on dispose est imprécise, incomplète ou pas complètement fiable.Usuellement, cette incertitude est traitée par la théorie classique des probabilités. Cependant, ces dernières années ont vu apparaître des arguments indiquant que les probabilités classiques sont inadéquates lorsqu'il faut représenter l'imprécision présente dans l'information. Des cadres complémentaires aux probabilités classiques ont donc été proposés pour remédier à ce problème : il s'agit, principalement, des ensembles de probabilités, des ensembles aléatoires et des possibilités. Beaucoup de questions concernant le traitement des incertitudes dans ces trois cadres restent ouvertes. En particulier, il est nécessaire d'unifier ces approches et de comprendre les liens existants entre elles, et de proposer des méthodes de traitement permettant d'utiliser ces approches parfois cher en temps de calcul. Dans ce travail, nous nous proposons d'apporter des réponses à ces deux besoins pour une série de problème de traitement de l'incertain rencontré en analyse de sûreté. En particulier, nous nous concentrons sur les problèmes suivants :- Représentation des incertitudes- Fusion/évaluation de données venant de sources multiples- Modélisation de l'indépendanceL'objectif étant de fournir des outils, à la fois théoriques et pratiques, de traitement d'incertitude. Certains de ces outils sont ensuite appliqués à des problèmes rencontrés en sûreté nucléaire

Convenient Interactive Computing for Coherent Imprecise Prevision Assessments

A generalization of deFinetti's Fundamental Theorem of Probability facilitates coherent assessment, by iterated natural extension, of imprecise probabilities or expectations, conditional and unconditional. Point values are generalized to assessed bounds, accepted under weak coherence, that is, allowing the input of redundant loose bounds. The method is realized in a convenient interactive computer program, which is demonstrated here, and made available as open source code. This work suggests that a consulting expert's fees should not be paid unless his/her assessed probabilities cohere

CORPORATE SOCIAL RESPONSIBILITY IN ROMANIA

The purpose of this paper is to identify the main opportunities and limitations of corporate social responsibility (CSR). The survey was defined with the aim to involve the highest possible number of relevant CSR topics and give the issue a more wholesome perspective. It provides a basis for further comprehension and deeper analyses of specific CSR areas. The conditions determining the success of CSR in Romania have been defined in the paper on the basis of the previously cumulative knowledge as well as the results of various researches. This paper provides knowledge which may be useful in the programs promoting CSR.Corporate social responsibility, Supportive policies, Romania