## A New Cauchy-Based Black-Box Technique for Uncertainty in Risk Analysis (2002)

Venue: | in Risk Analysis, Reliability Engineering and Systems Safety |

Citations: | 28 - 13 self |

### BibTeX

@INPROCEEDINGS{Kreinovich02anew,

author = {V. Kreinovich and S.A. Ferson},

title = {A New Cauchy-Based Black-Box Technique for Uncertainty in Risk Analysis},

booktitle = {in Risk Analysis, Reliability Engineering and Systems Safety},

year = {2002},

pages = {267--279}

}

### Years of Citing Articles

### OpenURL

### Abstract

Uncertainty is very important in risk analysis. A natural way to describe this uncertainty is to describe a set of possible values of each unknown quantity (this set is usually an interval), plus any additional information that we may have about the probability of different values within this set. Traditional statistical techniques deal with the situations in which we have a complete information about the probabilities; in real life, however, we often have only partial information about them. We therefore need to describe methods of handling such partial information in risk analysis. Several such techniques have been presented, often on a heuristic basis. The main goal of this paper is to provide a justification for a general formalism for handling different types of uncertainty, and to describe a new black-box technique for processing this type of uncertainty.

### Citations

793 | Statistical Reasoning with Imprecise Probabilities - Walley - 1991 |

352 |
Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation
- GRIEWANK
- 2000
(Show Context)
Citation Context ...e standard programming languages such as Fortran or C, we can let the compute perform an explicit differentiation; for that, we can use one of the existing automatic differentiation tools (see, e.g., =-=[1,10]). These t-=-ools analyze the code of the program for computing f(x 1 ; : : : ; x n ) and, as they perform their analysis, they produce the "differentiation code", i.e., a program that computes the parti... |

191 | Computational Complexity and Feasibility of Data Processing and Interval Computations
- Kreinovich, Lakeyev, et al.
- 1998
(Show Context)
Citation Context ...] and references therein). In this case, the problem of error estimation for indirect measurements becomes computationally difficult (NPhard) even when the function f(x 1 ; : : : ; x n ) is quadratic =-=[17,27]-=-. However, in most real-life situations, the possibility to ignore quadratic terms is a reasonable assumption, because, e.g., for an error of 1% its square is a negligible 0.01%. With the above restri... |

57 |
Measurement errors: Theory and practice
- Rabinovich
- 1993
(Show Context)
Citation Context ...we only know intervals will be one of the settings considered in this paper. Another setting which we will consider is a setting described in standard engineering textbooks on measurement (see, e.g., =-=[9,24]-=-; see also [3,11]). In this setting, the measurement error \Deltax i of each direct measurement is normally distributed with 0 average and known standard deviation oe i , and measurement errors of dif... |

30 | Error Estimations for Indirect Measurements: Randomized Vs. Deterministic Algorithms for 'Black-Box' Programs
- Trejo, Kreinovich
- 2001
(Show Context)
Citation Context ... interval and probabilistic uncertainty -- and can, therefore, be safely ignored in the basic risk analysis. Methods described in this paper can be used to cover model uncertainty as well; see, e.g., =-=[26]-=-. 2 What is a natural way of representing partial information about probabilities? Which representation of probability distribution should we choose? In probability theory, there are many different wa... |

24 |
Measurements Errors Models
- WA
- 1987
(Show Context)
Citation Context ...we only know intervals will be one of the settings considered in this paper. Another setting which we will consider is a setting described in standard engineering textbooks on measurement (see, e.g., =-=[9,24]-=-; see also [3,11]). In this setting, the measurement error \Deltax i of each direct measurement is normally distributed with 0 average and known standard deviation oe i , and measurement errors of dif... |

12 |
Parallel computers estimate errors caused by imprecise data
- Kreinovich, Bernat, et al.
- 1991
(Show Context)
Citation Context ... the box, and that is extended linearly for all other values (we will see, in the description of an algorithm, how this is done). As a result, we arrive at the following algorithm (first described in =-=[15,16,19,26]-=-): Algorithm. ffl Apply f to the results of direct measurements: e y := f(e x 1 ; : : : ; e x n ); ffl For k = 1; 2; : : : ; N , repeat the following: ffl use the standard random number generator to c... |

9 |
Error estimate of the result of indirect measurements by using a calculational experiment, Measurement Techniques
- Kreinovich, Pavlovich
- 1985
(Show Context)
Citation Context ... the box, and that is extended linearly for all other values (we will see, in the description of an algorithm, how this is done). As a result, we arrive at the following algorithm (first described in =-=[15,16,19,26]-=-): Algorithm. ffl Apply f to the results of direct measurements: e y := f(e x 1 ; : : : ; e x n ); ffl For k = 1; 2; : : : ; N , repeat the following: ffl use the standard random number generator to c... |

8 | From Interval Methods of Representing Uncertainty to 13 General Description
- Kreinovich, Ferson
- 1999
(Show Context)
Citation Context ... handling different types of uncertainty, and to describe a new black-box technique for processing this type of uncertainty. For a survey with a detailed description of our approach see [8]; see also =-=[4,6,7,21,18,25]-=-. Third component of uncertainty description: model uncertainty -- a comment. In the above description, we implicitly assume that once we know the values of all the parameters, we know the exact behav... |

5 |
Combining Probability Distributions From Experts in Risk Analysis. Risk Anal
- RT, RL
- 1999
(Show Context)
Citation Context ...on. In these cases, we can use standard statistical techniques to represent, elicit, and aggregate uncertainty. A survey of the corresponding techniques as applied to risk analysis is given, e.g., in =-=[2]-=-. 2 The need for techniques corresponding to partial information about probabilities. In many other real-life situations, however, we have only partialsinformation about the probabilities. To handle s... |

5 | Nonlinear Optimization: Complexity Issues - SA - 1991 |

4 |
Representation, elicitation, and aggregation of uncertainty in risk analysis – from traditional probabilistic techniques to more general, more realistic approaches: a survey
- Ferson, Kreinovich
(Show Context)
Citation Context ... formalism for handling different types of uncertainty, and to describe a new black-box technique for processing this type of uncertainty. For a survey with a detailed description of our approach see =-=[8]-=-; see also [4,6,7,21,18,25]. Third component of uncertainty description: model uncertainty -- a comment. In the above description, we implicitly assume that once we know the values of all the paramete... |

4 | Combining fuzzy and probabilistic knowledge using belief functions
- Kreinovich, Langrand, et al.
(Show Context)
Citation Context ... handling different types of uncertainty, and to describe a new black-box technique for processing this type of uncertainty. For a survey with a detailed description of our approach see [8]; see also =-=[4,6,7,21,18,25]-=-. Third component of uncertainty description: model uncertainty -- a comment. In the above description, we implicitly assume that once we know the values of all the parameters, we know the exact behav... |

4 |
The worse, the better: a survey of paradoxical computational complexity of interval computations
- Nesterov, Kreinovich
- 1996
(Show Context)
Citation Context ...osophical comment: sometimes, distortion of simulated phenomenon makes simulation more efficient. The use of Cauchy distribution in the above algorithm may seem somewhat counter-intuitive (see, e.g., =-=[14,22]-=-). Indeed, in the interval setting, we do not know the exact probability distribution of each error \Delta i , but we do know that each error \Delta i belongs to the corresponding interval [\Gamma\Del... |

3 |
Ginzburg L, Akcakaya R. Whereof one cannot speak: when input distributions are unknown. Risk Analysis
- Ferson
- 1996
(Show Context)
Citation Context ... handling different types of uncertainty, and to describe a new black-box technique for processing this type of uncertainty. For a survey with a detailed description of our approach see [8]; see also =-=[4,6,7,21,18,25]-=-. Third component of uncertainty description: model uncertainty -- a comment. In the above description, we implicitly assume that once we know the values of all the parameters, we know the exact behav... |

2 |
Griewank A. Computational differentiation: techniques, applications, and tools
- Berz, Bischof, et al.
- 1996
(Show Context)
Citation Context ...e standard programming languages such as Fortran or C, we can let the compute perform an explicit differentiation; for that, we can use one of the existing automatic differentiation tools (see, e.g., =-=[1,10]). These t-=-ools analyze the code of the program for computing f(x 1 ; : : : ; x n ) and, as they perform their analysis, they produce the "differentiation code", i.e., a program that computes the parti... |

2 |
simulation modeling, sometimes simulation with distortions is useful
- Kreinovich, In
- 1989
(Show Context)
Citation Context ...osophical comment: sometimes, distortion of simulated phenomenon makes simulation more efficient. The use of Cauchy distribution in the above algorithm may seem somewhat counter-intuitive (see, e.g., =-=[14,22]-=-). Indeed, in the interval setting, we do not know the exact probability distribution of each error \Delta i , but we do know that each error \Delta i belongs to the corresponding interval [\Gamma\Del... |

2 | Automatic differentiation or Monte-Carlo methods: which is better for error estimation - Kreinovich, Starks, et al. - 1998 |

1 |
Multivariate error analysis
- AA
- 1973
(Show Context)
Citation Context ...rvals will be one of the settings considered in this paper. Another setting which we will consider is a setting described in standard engineering textbooks on measurement (see, e.g., [9,24]; see also =-=[3,11]-=-). In this setting, the measurement error \Deltax i of each direct measurement is normally distributed with 0 average and known standard deviation oe i , and measurement errors of different direct mea... |

1 |
Ferson S, Ginzburg LR. Hybrid processing of stochastic and subjective uncertainty data. Risk Analysis 1996;16:785--791
- JA
- 1996
(Show Context)
Citation Context |

1 |
Ginzburg L, Kreinovich V, Schulte H. Interval computations as a particular case of a general scheme involving classes of probability distributions
- Ferson
(Show Context)
Citation Context |

1 |
Mathematics in chemistry. An introduction to modern methods
- HG
- 1990
(Show Context)
Citation Context ...rvals will be one of the settings considered in this paper. Another setting which we will consider is a setting described in standard engineering textbooks on measurement (see, e.g., [9,24]; see also =-=[3,11]-=-). In this setting, the measurement error \Deltax i of each direct measurement is normally distributed with 0 average and known standard deviation oe i , and measurement errors of different direct mea... |

1 |
Kreinovich V. Applications of interval computations
- RB
- 1996
(Show Context)
Citation Context ... of the concentration but we may know that this concentration is between, say, 10 \Gamma5 and 10 \Gamma3 . In this case, any value from the interval [10 \Gamma5 ; 10 \Gamma3 ] is possible; see, e.g., =-=[12,13]-=-. An important risk-related situation that leads to intervals is when a measurement does not detect any presence of a certain substance because its concentrationsx is below the detection limit D. In t... |

1 |
CA, Wojtkiewicz SF, Ferson S. Challenge problems: uncertainty in system response given uncertain parameters. Reliability Engineering and System Safety (this issue
- WL, JC, et al.
(Show Context)
Citation Context ...is bisection idea has been successfully used in interval computations; see, e.g., [13]. 7 Testing our method on a variant of a challenge problem The original challenge problem. The original challenge =-=[23]-=- included two problems: the simpler one, with only two variables, and a more sophisticated oscillator problem. In the oscillator problem, we are interested in the parameter y that is connected with th... |