Théorie de la décision

Résumé

La théorie de la décision est une théorie de mathématiques appliquées ayant pour objet la prise de décision par une entité unique. (Les questions liées à la décision collective relèvent de la théorie du choix social.) Théorie de la décision intertemporelle La notion de décision intertemporelle découle de la prise en compte du facteur temps dans les problématiques reliant l'offre et la demande, les disponibilités et les contraintes. Ces problématiques sont celles qui découlent des combinaisons possibles entre les disponibilités et les décisions pouvant les impliquer. Les diverses fluctuations susceptibles d'être mesurées et prévues par ailleurs permettent ainsi de nourrir des modèles dynamiques. Modèle à utilité escomptée L'économiste Paul Samuelson propose en 1937 dans un article intitulé « A Note on Measurement of Utility » un modèle simple de décision intertemporelle connu sous le nom de modèle à utilité escomptée. Dans ce modèle, les préférences intertem

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Robust parameter estimation for the Ornstein-Uhlenbeck process

Sonja Rieder

In this paper, we derive elementary M- and optimally robust asymptotic linear (AL)-estimates for the parameters of an Ornstein-Uhlenbeck process. Simulation and estimation of the process are already well-studied, see Iacus (Simulation and inference for stochastic differential equations. Springer, New York, 2008). However, in order to protect against outliers and deviations from the ideal law the formulation of suitable neighborhood models and a corresponding robustification of the estimators are necessary. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. In a first step, we extend the method of M-estimation from Huber (Robust statistics. Wiley, New York, 1981). In a second step, we apply the general theory based on local asymptotic normality, AL estimates, and shrinking neighborhoods due to Kohl et al. (Stat Methods Appl 19:333-354, 2010), Rieder (Robust asymptotic statistics. Springer, New York, 1994), Rieder (2003), and Staab (1984). This leads to optimally robust ICs whose graph exhibits surprising behavior. In the end, we discuss the estimator construction, i.e. the problem of constructing an estimator from the family of optimal ICs. Therefore we carry out in our context the One-Step construction dating back to LeCam (Asymptotic methods in statistical decision theory. Springer, New York, 1969) and compare it by means of simulations with MLE and M-estimator.

Springer-Verlag2012

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Quantum-based approach for laboratory risk assessment and decision-making

Ruoxing Liao

With the rising focus on academic safety, there has been an effort to improve the academic safety climate and develop lab-specific risk assessment tools. Despite the progress made in recent years, there is still a deficit of reliable data statistics on safety events and risk assessment in academia, making it difficult to perform full-scale analysis. Moreover, the rapid turnover of personnel and the highly dynamic research tasks in a laboratory environment impede the implementation of classical and well-established risk management strategies, which are usually time-consuming and resource-intensive. Laboratory safety management is always challenging due to lack of data and effective methods. The end of safety management is usually the selection of risk mitigation measures. In the laboratory risk management process, decisions are often made through discussion and compromise. In this regard, it would be beneficial to provide a tool that can support in resource allocation and prioritization of actions. The goal of this project is to develop a decision support tool to assist in the selection of optimal and appropriate preventive or corrective measures in the lab safety management process. The use of decision tools such as Multi-Criteria Decision Making (MCDM) can effectively abstract complex laboratory management problems into a decision framework. This study focuses on the ranking process of competitive corrective measures. Combining the results of interviews and questionnaires, five evaluation criteria were proposed for the normative process of multi-criteria decision making. They are: Residual Risk, Risk reduction, Personnel reliability, Technical reliability, and Cost. classical methods TOPSIS and WSM have been evaluated during the study, and emerging quantum decision making methods have been explored. All three methods are used to simulate the laboratory safety decision making process, and they all present good consistency. Different weighting methods have also been applied to the model and two case studies have been conducted. The first case study is designed to construct the model and verify its feasibility, and the second model is used to investigate the process of group decision making. By applying different MCDM methods, the obtained results are discussed and compared to verify the stability and accuracy of the model. The approach proposed in this research is a promising tool. It offers the possibility to be compatible with different MCDM methods and risk assessment methods, and the proposed decision model could be used as a decision support system to help lab managers make better decisions, or it can provide a neutral point of view as an aid. Future work may include fine-tuning the model. In the following stage, decision criteria should be precisely defined, and corresponding quantitative formulas should be proposed to serve the flexible and dynamic laboratory environment.

2022

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In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N. (C) 2012 Elsevier Ireland Ltd. All rights reserved.

Elsevier2012

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Quantum-based approach for laboratory risk assessment and decision-making

Ruoxing Liao

2022

Elsevier2012