scholarly journals Eliciting opinions of experts using uncertainty

2015 ◽  
Vol 56 ◽  
Author(s):  
Valentinas Podvezko ◽  
Askoldas Podviezko
Keyword(s):  
Decision Making ◽  
Probability Distribution ◽  
Decision Aid ◽  
Probability Distributions ◽  
Multiple Criteria Decision Making ◽  
Simulation Method ◽  
Statistical Simulation ◽  
Expert Evaluation ◽  
Absolute Level ◽  
Level Of Importance

Multiple criteria decision-making (MCDM) methods designed for evaluation of attractiveness of available alternatives, whenever used in decision-aid systems, imply active participation of experts. They participate in all stages of evaluation: casting a set of criteria, which should describe an evaluated process or an alternative; estimating level of importance of each criterion; estimating values of some criteria and sub-criteria. Social and economic processes are prone to laws of statistics,which are described and could be forecasted using the theory of probability. Weights of criteria, which reveal levels of their importance, could rarely be estimated with the absolute level of precision. Uncertainty of evaluation is characterised by a probability distribution. Aiming to elicit evaluation from experts we have to find either a distribution or a density function. Statistical simulation method can be used for estimation of evaluation of weights and/or values of criteria by experts. Alternatively, character of related uncertainty can be estimated by an expert himself during the survey process. The aim of this paper is to describe algorithms of expert evaluation with estimation of opinion uncertainty, which were applied in practice. In particular, a new algorithm was proposed, where an expert evaluates criteria by probability distributions.

scholarly journals A Discussion on Simple Support Functions

2014 ◽  
Vol 10 ◽  
pp. 13-21
Author(s):  
D.N. Kandekar
Keyword(s):  
Decision Making ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Support Function ◽  
Daily Life ◽  
Probability Distributions ◽  
Support Functions ◽  
Statistical Probability ◽  
Helpful Tool ◽  
Simple Support

Prediction about each and every incident happening in our daily life is impossible. But we can predict about some incidents. Probability is most helpful tool in predicting about outcomes or conclusions of such incidents. Such incidents happened in our life, always follow some known or unknown statistical probability distribution which may consist of simple or complicated probability density function. Therefore with help of probability distributions, we get some blurred idea about the functioning of incidents happening in our life. Using some commonly used probability distributions, we obtain conclusions which are helpful in decision making. Support functions viz. simple support functions are very useful in decision making. In this paper, we quote some results and applications regarding simple support function based on probability transformations.

scholarly journals Sensitivity Analysis of the TOPSIS Method in Respect of Initial Data Distributions

2016 ◽  
Vol 55 (1) ◽  
pp. 45-51
Author(s):  
Rūta Simanavičienė ◽  
Vaida Petraitytė
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Statistical Analysis ◽  
Initial Data ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Data Distribution ◽  
Multiple Criteria Decision Making ◽  
Topsis Method ◽  
Log Normal

The present article investigates the sensitivity of the multiple criteria decision-making method TOPSIS in respectof attribute probability distributions. To carry out research, initial data – attribute values – were generated according to anormal, log-normal, uniform, and beta distributions. Decision matrixes were constructed from the generated data. Byapplying the TOPSIS method to the matrixes generated, result samples were received. A statistical analysis was conductedfor the results obtained, which revealed that the distributions of the initial data comply with the distributions of the resultsreceived by the TOPSIS method. According to the most common alternative rank value, it was ascertained that the TOPSISmethod is the most sensitive for data distribution according to beta distribution, and the least sensitive for data distributionaccording to lognormal distribution.

Statistical Simulation of the Probability Distribution Kernel and Its Application to Solve the Quantile Optimization Problem with the Bilinear Loss Function

2020 ◽  
Vol 10 (3) ◽  
pp. 69-84
Author(s):  
P.A. Ardabyevskiy ◽  
D.A. Gonchar ◽  
Yu.S. Kan
Keyword(s):  
Probability Distribution ◽  
Loss Function ◽  
Software Package ◽  
Optimization Problem ◽  
Probability Distributions ◽  
Statistical Simulation ◽  
Random Parameters ◽  
Polyhedral Model ◽  
Distribution Kernel ◽  
Kernel Model

The article considers a plane quantile optimization problem with a bilinear loss function, which, using suffi cient optimality conditions, is reduced to a linear programming problem. The reduction is based on the use of a polyhedral model of the kernel of the probability distribution of the vector of random parameters. To build this model, an algorithm based on the method of statistical modeling is proposed. A description of the software package for constructing a kernel model for a number of probability distributions of random parameters is given.

scholarly journals Multi-Attribute Decision-Making Methods as a Part of Mathematical Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 915 ◽  
Author(s):  
Vinogradova
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Optimal Solution ◽  
Simulation Method ◽  
Statistical Simulation ◽  
Assessment Method ◽  
Research Literature ◽  
Preference Ranking ◽  
Multi Attribute Decision Making

Optimization problems are relevant to various areas of human activity. In different cases, the problems are solved by applying appropriate optimization methods. A range of optimization problems has resulted in a number of different methods and algorithms for reaching solutions. One of the problems deals with the decision-making area, which is an optimal option selected from several options of comparison. Multi-Attribute Decision-Making (MADM) methods are widely applied for making the optimal solution, selecting a single option or ranking choices from the most to the least appropriate. This paper is aimed at providing MADM methods as a component of mathematics-based optimization. The theoretical part of the paper presents evaluation criteria of methods as the objective functions. To illustrate the idea, some of the most frequently used methods in practice—Simple Additive Weighting (SAW), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Complex Proportional Assessment Method (COPRAS), Multi-Objective Optimization by Ratio Analysis (MOORA) and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE)—were chosen. These methods use a finite number of explicitly given alternatives. The research literature does not propose the best or most appropriate MADM method for dealing with a specific task. Thus, several techniques are frequently applied in parallel to make the right decision. Each method differs in the data processing, and therefore the results of MADM methods are obtained on different scales. The practical part of this paper demonstrates how to combine the results of several applied methods into a single value. This paper proposes a new approach for evaluating that involves merging the results of all applied MADM methods into a single value, taking into account the suitability of the methods for the task to be solved. Taken as a basis is the fact that if a method is more stable to a minor data change, the greater importance (weight) it has for the merged result. This paper proposes an algorithm for determining the stability of MADM methods by applying the statistical simulation method using a sequence of random numbers from the given distribution. This paper shows the different approaches to normalizing the results of MADM methods. For arranging negative values and making the scales of the results of the methods equal, Weitendorf’s linear normalization and classical and author-proposed transformation techniques have been illustrated in this paper.

scholarly journals Confidence Analysis of DEER Data and its Structural Interpretation with Ensemble-Biased Metadynamics

2018 ◽  
Author(s):  
Eric J. Hustedt ◽  
Fabrizio Marinelli ◽  
Richard A. Stein ◽  
José D. Faraldo-Gómez ◽  
Hassane S. Mchaourab
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Statistical Error ◽  
Simulation Method ◽  
Confidence Band ◽  
Confidence Bands ◽  
Resonance Spectroscopy ◽  
Structural Interpretation ◽  
Distance Distributions ◽  
Double Electron Electron Resonance

ABSTRACTGiven its ability to measure multicomponent distance distributions between electron-spin probes, Double Electron-Electron Resonance spectroscopy (DEER) has become a leading technique to assess the structural dynamics of biomolecules. However, methodologies to evaluate the statistical error of these distributions are not standard, often hampering a rigorous interpretation of the experimental results. Distance distributions are often determined from the experimental DEER data through a mathematical method known as Tikhonov regularization, but this approach makes rigorous error estimates difficult. Here, we build upon an alternative model-based approach in which the distance probability distribution is represented as a sum of Gaussian components and use propagation of errors to calculate an associated confidence band. Our approach considers all sources of uncertainty, including the experimental noise, the uncertainty in the fitted background signal, and the limited time-span of the data collection. The resulting confidence band reveals the most and least reliable features of the probability distribution, thereby informing the structural interpretation of DEER experiments. To facilitate this interpretation, we also generalize the molecular-simulation method known as Ensemble-Biased Metadynamics. This method, originally designed to generate maximum-entropy structural ensembles consistent with one or more probability distributions, now also accounts for the uncertainty in those target distributions, exactly as dictated by their confidence bands. After careful benchmarks, we demonstrate the proposed techniques using DEER results from spin-labeled T4 lysozyme.

Use of an Atrial Fibrillation Medication Decision Aid Improves Knowledge and Process for Decision Making (Preprint)

2018 ◽  
Author(s):  
Molly Beinfeld ◽  
Suzanne Brodney ◽  
Michael Barry ◽  
Erika Poole ◽  
Adam Kunin
Keyword(s):  
Atrial Fibrillation ◽  
Decision Making ◽  
Shared Decision Making ◽  
Anticoagulant Therapy ◽  
Decision Aid ◽  
Response Rate ◽  
Intervention Group ◽  
Shared Decision ◽  
Community Based ◽  
Baseline Group

BACKGROUND A rural community-based Cardiology practice implemented shared decision making supported by an evidence-based decision aid booklet to improve the quality of anticoagulant therapy decisions in patients with atrial fibrillation. OBJECTIVE To develop a practical workflow for implementation of an anticoagulant therapy decision aid and to assess the impact on patients’ knowledge and process for anticoagulant medication decision making. METHODS The organization surveyed all patients with atrial fibrillation being seen at Copley Hospital to establish a baseline level of knowledge, certainty about the decision and process for decision making. The intervention surveys included the same knowledge, certainty, process and demographic questions as the baseline surveys, but also included questions asking for feedback on the decision aid booklet. Stroke risk scores (CHA2DS2-VASc score) were calculated by Copley staff for both groups using EMR data. RESULTS We received 46 completed surveys in the baseline group (64% response rate) and 50 surveys in the intervention group (72% response rate). The intervention group had higher knowledge score than the baseline group (3.6 out of 4 correct answers vs 3.1, p=0.036) and Decision Process Score (2.89 out of 4 vs 2.09, p=0.0023) but similar scores on the SURE scale (3.12 out of 4 vs 3.17, p=0.79). Knowledge and Process score differences were sustained even after adjusting for co-variates in stepwise linear regression analyses. Patients with high school or lower education appeared to benefit the most from shared decision making, as demonstrated by their knowledge scores. CONCLUSIONS It is feasible and practical to implement shared decision making supported by decision aids in a community-based Cardiology practice. Shared decision making can improve knowledge and process for decision making for patients with atrial fibrillation. CLINICALTRIAL None

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