Support theory: A nonextensional representation of subjective probability.

I show that de Finetti’s coherence theorem is equivalent to the Hahn-Banach theorem and discuss some consequences of this result. First, the result unites two aspects of de Finetti’s thought in a nice way: a corollary of the result is that the coherence theorem implies the existence of a fair countable lottery, which de Finetti appealed to in his arguments against countable additivity. Another corollary of the result is the existence of sets that are not Lebesgue measurable. I offer a subjectivist interpretation of this corollary that is concordant with de Finetti’s views. I conclude by pointing out that my result shows that there is a sense in which de Finetti’s theory of subjective probability is necessarily nonconstructive. This raises questions about whether the coherence theorem can underwrite a legitimate theory of rational belief.

Tversky and Kahneman (1983) found that a relationship of positive conditional dependence between the components of a conjunction of two events increases the prevalence of the conjunction fallacy. Consistent with this finding, the results of two experiments reveal that dependence leads to higher estimates for the conjunctive probability and a higher incidence of the fallacy. However, contrary to the theoretical account proposed by Tversky and Kahneman, the actual magnitude of the conditional relationship does not directly affect the extent of the fallacy; all that is necessary is for a positive conditional relationship to exist. The pattern of results obtained can be accounted for in terms of Shackle's (1969) “potential surprise” theory of subjective probability. Surprise theory predicts that the impact of the conditional event will be at its maximum where the relationship is a negative one. Tversky and Kahneman's model, on the other hand, predicts the maximum effect when the relationship is positive. In all 12 scenarios tested, multiple regression analysis revealed that the standardized beta weight associated with the conditional event was greater when the relationship was a negative one. Thus the outcome was supportive of the surprise model rather than Tversky and Kahneman's account.

Incremental conditioning of lower and upper probabilities

Muth’s Rational Expectations Hypothesis, That “…The Subjective Probability Distributions Are Distributed Around an Objective Probability Distribution, for a given Information Set…” is an Oxymoron. It Can Be Corrected by Amending It to Read “…The Subjective Probability Distributions Are Distributed Around a Subjective Consensus Probability Distribution, for a given Information Set…”

Comparison of the Unstructured Clinician Gestalt, the Wells Score, and the Revised Geneva Score to Estimate Pretest Probability for Suspected Pulmonary Embolism

Accurate diagnostic and prognostic probabilities are important for physicians and their patients because of their impact on decisions. For individual patient decision making, physicians have to rely on their own judgement. Research has shown that physicians’ probability assessments are often not of high quality and that a variety of factors have a detrimental influence on their judgements. Using a formula or a model may produce superior assessments. Most treatment decisions involve uncertainty and value conflict in the sense that there is a trade off between the possible harms of alternative treatments and their benefits. The communication of diagnostic and prognostic probabilities to patients occurs largely in verbal terms, which can lead to ambiguity in communication. The precise words and context chosen for communication are very important and can have a major effect on patients’ decisions.

The prognosis of patients in whom pulmonary embolism (PE) is suspected but ruled out is poorly understood. We evaluated whether the initial assessment of clinical probability of PE could help to predict the prognosis for these patients. Retrospective analysis of data obtained during a prospective multicentre management study. Six general and teaching hospitals in Belgium, France and Switzerland. In 1334 patients in whom PE was ruled out, 3-month mortality data were available (hospital readmission status was unknown for three patients) and clinical probability was evaluated with the revised Geneva score (RGS). Three-month mortality and readmission rates. Three-month mortality and readmissions rates were 3% and 19%, respectively and differed significantly depending on the RGS-determined PE probability group (P<0.001). When compared with patients presenting with a low probability, the risk of death after 3 months was higher in cases of intermediate or high RGS-based probability {odds ratio: 8.7 [95% confidence interval (CI): 2.7-28.5] and 22.6 (95%CI: 2.1-241.2), respectively}. The readmission risk increased with PE probability group (P<0.001). The main causes of death were cancer, respiratory failure and cardiovascular failure. In total, 86% of patients with low RGS-based probability were alive and had not been readmitted to hospital, whereas other patients had a twofold increased risk of death or readmission during the 3-month follow-up. The simplified Geneva score, calculated a posteriori, gave similar results. Initial assessment of clinical probability may help to stratify prognosis of patients in whom PE has been ruled out. Patients with a low probability of PE have a good prognosis. Whether patients with higher probability might benefit from more vigilant care should be evaluated.

On Keynes's Realization That His Concept of Uncertainty in the General Theory, Defined as an Inverse Function of Weight from the 'A Treatise on Probability', Would Not Have Any Impact at All on Economists Thinking

Weakly consistent extensions of lower previsions

Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker′s subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision‐making processing is implemented after Pareto optimality. In this paper, we attempted to incorporate the decider′s subjective sense with Pareto optimality for chromosomes ranking. A new ranking method based on subjective probability theory was thus proposed in order to explore and comprehend the true nature of the chromosomes on the Pareto optimal front. The properties of the ranking rule were proven, and its transitivity was presented as well. Simulation results compared the performance of the proposed ranking approach with the Pareto‐based ranking method for two multiobjective optimization cases, which demonstrated the effectiveness of the new ranking approach.

SUMMARYService selection in service‐oriented computing has emerged to be an increasingly important research area. From the client's point of view, in addition to the QoS of a service or a service composition, the trust level becomes an important part. As the complexity of invocation in service composition has been greatly increased, a comprehensive mechanism, which could evaluate both the subjective aspect as trust expression and the objective aspect as QoS, is needed. In this paper, we provide a formal service composition architecture for service selection. In addition, we propose a trust evaluation method for the service composition plan based on the subjective probability theory, based on them, our trust‐oriented genetic algorithm (TOGA) is proposed to find a near‐optimal service composition plan with QoS constraints. Experimental results have illustrated that our proposed approach can discover the near‐optimal solution efficiently. Copyright © 2013 John Wiley &amp; Sons, Ltd.

The methods and advantages of integrating knowledge-based and geographical information system techniques for the analysis of provenance and diagenesis in sedimentary basins are demonstrated by examples from the Cheshire Basin located in north-west England. Approximate reasoning techniques to handle the vagueness and uncertainty inherent in a large amount of geological data, knowledge and reasoning are reviewed with particular emphasis on provenance analysis using subjective probability theory, Dempster-Shafer theory and fuzzy logic techniques. Object-oriented methods for analysing diagenetic history in user specified volumes of the basin are discussed.

The subjective Bayesian approach to PRA: Theoretical and practical perspectives

In Service-Oriented Computing (SOC) environments, the trustworthiness of each service provider is critical for a service client when selecting one from a large pool of service providers. The trust value of a service provider is usually in the range of [0, 1] and is evaluated from the ratings given by service clients, which represent the subjective belief of service clients on the satisfaction of delivered services. So a trust value can be taken as a subjective probability, by which one party believes that another party can perform an action in a certain situation. Hence, subjective probability theory should be adopted in trust evaluation. In addition, in SOC environments, a service provider usually can invoke the services from other service providers forming a composite service. Thus, the global trust of a composite service should be evaluated based on both the subjective probability property of trust and complex invocation structures. In this paper, we first interpret the trust dependency caused by direct service invocations as conditional probability. Then, on the basis of trust dependency, we propose a Subjective probability based deductive (SELECTIVE) approach to evaluate the subjective global trustworthiness of a composite service. All these processes follow subjective probability theory and keep the subjective probability property of trust in evaluations. Our experimental results demonstrate that when compared with existing approaches our proposed SELECTIVE approach can yield more reasonable results.

In this paper, we present a brief version of de Finetti-Ramsey's subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section, we take up the case of some "Paradoxes in Expected Utility Theory" and try to reconcile them with the help of subjective probabilities.