scholarly journals Replacing Input Probability Distributions with Mean Values can Bias Simulation Output: An Illustration Using the Core Diabetes Model

2016 ◽  
Vol 19 (7) ◽  
pp. A372
Author(s):  
P McEwan ◽  
V Foos ◽  
M Lamotte
Keyword(s):  
Probability Distributions ◽  
Mean Values ◽  
The Core ◽  
Diabetes Model ◽  
Simulation Output ◽  
Input Probability

Comparison of Monte Carlo and Fuzzy Math Simulation Methods for Quantitative Microbial Risk Assessment

2003 ◽  
Vol 66 (10) ◽  
pp. 1900-1910 ◽  
Author(s):  
VALERIE J. DAVIDSON ◽  
JOANNE RYKS
Keyword(s):  
Risk Assessment ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Interval Arithmetic ◽  
Food Systems ◽  
Probability Distributions ◽  
Economic Cost ◽  
Fuzzy Mathematics ◽  
Quantitative Microbial Risk Assessment ◽  
Mean Values

The objective of food safety risk assessment is to quantify levels of risk for consumers as well as to design improved processing, distribution, and preparation systems that reduce exposure to acceptable limits. Monte Carlo simulation tools have been used to deal with the inherent variability in food systems, but these tools require substantial data for estimates of probability distributions. The objective of this study was to evaluate the use of fuzzy values to represent uncertainty. Fuzzy mathematics and Monte Carlo simulations were compared to analyze the propagation of uncertainty through a number of sequential calculations in two different applications: estimation of biological impacts and economic cost in a general framework and survival of Campylobacter jejuni in a sequence of five poultry processing operations. Estimates of the proportion of a population requiring hospitalization were comparable, but using fuzzy values and interval arithmetic resulted in more conservative estimates of mortality and cost, in terms of the intervals of possible values and mean values, compared to Monte Carlo calculations. In the second application, the two approaches predicted the same reduction in mean concentration (−4 log CFU/ml of rinse), but the limits of the final concentration distribution were wider for the fuzzy estimate (−3.3 to 5.6 log CFU/ml of rinse) compared to the probability estimate (−2.2 to 4.3 log CFU/ml of rinse). Interval arithmetic with fuzzy values considered all possible combinations in calculations and maximum membership grade for each possible result. Consequently, fuzzy results fully included distributions estimated by Monte Carlo simulations but extended to broader limits. When limited data defines probability distributions for all inputs, fuzzy mathematics is a more conservative approach for risk assessment than Monte Carlo simulations.

scholarly journals Imprecise Imputation as a Tool for Solving Classification Problems with Mean Values of Unobserved Features

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lev V. Utkin ◽  
Yulia A. Zhuk
Keyword(s):  
Partial Information ◽  
Probability Distributions ◽  
Classification Problem ◽  
Support Vector ◽  
Classification Problems ◽  
Mean Values ◽  
Numerical Examples ◽  
The Standard Model ◽  
The Mean ◽  
Available Information

A method for solving a classification problem when there is only partial information about some features is proposed. This partial information comprises the mean values of features for every class and the bounds of the features. In order to maximally exploit the available information, a set of probability distributions is constructed such that two distributions are selected from the set which define the minimax and minimin strategies. Random values of features are generated in accordance with the selected distributions by using the Monte Carlo technique. As a result, the classification problem is reduced to the standard model which is solved by means of the support vector machine. Numerical examples illustrate the proposed method.

scholarly journals Analysis of a Discrete-Time Queueing Model with Disasters

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3283
Author(s):  
Mustafa Demircioglu ◽  
Herwig Bruneel ◽  
Sabine Wittevrongel
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Time Slot ◽  
Probability Distributions ◽  
Single Server ◽  
Bernoulli Process ◽  
Tail Probabilities ◽  
Mean Values ◽  
The Mean ◽  
The Impact

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

scholarly journals Evaluation of the Accuracy of Four Digital Methods by Linear and Volumetric Analysis of Dental Impressions

Materials ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 1958 ◽  
Author(s):  
Stefano Pagano ◽  
Michele Moretti ◽  
Roberto Marsili ◽  
Alessandro Ricci ◽  
Giancarlo Barraco ◽  
...  
Keyword(s):  
Probability Distributions ◽  
Three Dimensional ◽  
Point Clouds ◽  
Volumetric Analysis ◽  
Digital Impression ◽  
Dental Arch ◽  
Mean Values ◽  
Coordinate Measurement ◽  
Dental Clinics ◽  
Accuracy And Precision

The quality of dental arch impression has a substantial role in the precision of the intervention. It is traditionally acquired with resins that solidify when in contact with the air. Compared to that method, digital impression gives great advantages and, together with three-dimensional (3D) digitization devices, allows a simplification of the digital impression process. The growing adoption of such systems by a large number of dental clinics determines the need for an in-depth evaluation of the accuracy and the precision of the different systems. The aim of this work is to define a methodology for the evaluation of the accuracy and precision of 3D intraoral and desktop scanning systems, by using volumetric and linear methods. The replica of a tooth was realized with zirconium; afterward, high-accuracy point clouds of the master model were acquired by a coordinate measurement machine (CMM). In this way, the dimensions of the replica were accurately known. An intraoral scanner (I) and three desktops (D1, D2, D3) were then used to scan the replica. The geometry resulting from the CMM was compared with the ones derived from the scanners, using two different commercial programs (Geomagic and 3-Matic) and a custom-developed algorithm (MATLAB). Geomagic showed the mean values to be in a range from 0.0286 mm (D1) to 0.1654 mm (I), while 3-Matic showed mean values from −0.0396 mm (D1) to 0.1303 mm (I). MATLAB results ranged from 0.00014 mm (D1) to 0.00049 mm (D2). The probability distributions of the volumetric error of the measurements obtained with the different scanners allow a direct comparison of their performances. For the results given by our study, the volumetric approach that we adopted appears to be an excellent system of analysis.

scholarly journals Harnessing Expert Judgment to Support Clinical Decisions When the Evidence Base Is Weak

2018 ◽  
Vol 39 (1) ◽  
pp. 74-79 ◽  
Author(s):  
James G. Dolan ◽  
Peter J. Veazie
Keyword(s):  
Formal Method ◽  
Probability Distributions ◽  
Evidence Base ◽  
Outcome Data ◽  
Professional Judgment ◽  
Evidence Based ◽  
Clinical Decisions ◽  
Mean Values ◽  
Evidence Summary ◽  
Important Health

Purpose. In the process of developing an evidence-based decision dashboard to support treatment decisions for patients with newly diagnosed prostate cancer, we found that the clinical evidence base is insufficient to provide high-quality comparative outcome data. We therefore sought to determine if clinically acceptable outcome estimates could be created using a modified version of the Sheffield Elicitation Framework (SHELF), a formal method for eliciting judgments regarding probability distributions of expected decision outcomes. Methods. We asked a panel of 3 urologists, 4 radiation oncologists, and 2 medical oncologists to estimate the probabilities of 11 treatment outcomes based on their clinical experience and an annotated evidence summary. The estimates were elicited using a Microsoft Excel spreadsheet containing a self-guided, adapted version of the SHELF Roulette method distributed via email. We created combined outcome estimates by taking the mean values of the panel members’ upper and lower 95% bounds for each outcome. The combined estimates were then distributed via email to the panel for final approval. Results. Eight of the 9 responses were judged to be correct applications of the SHELF method and included in the combined outcome estimates. The final set of outcome estimates was unanimously accepted by the clinician panel members and used to create a decision dashboard suitable for clinical use and evaluation. Conclusions. Many important health care decisions need to be made in situations where the evidence base is inadequate. Use of a formal protocol for eliciting expert judgments is feasible and can be used to promote evidence-based practice by providing a powerful tool to facilitate the combination of professional judgment with research evidence and patient preferences to guide clinical decisions.

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