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REPRESENTING AND GENERATING
UNCERTAINTY EFFECTIVELY
Ph.D. Candidate Azdeen Najah1 Paper Review - Presenting and Generating Uncertainty
Effectively
W. David Kelton
Department of Quantitative Analysis and Operations Management
University of Cincinnati
Cincinnati, Ohio 45221-0130, U.S.A.
Web-Page:
Proceedings of the 2007 Winter Simulation Conference
S. G. Henderson, B. Biller, M.-H. Hsieh, J. Shortle, J. D. Tew, and R.
R. Barton, eds.
2
Paper Review - Presenting and Generating
Uncertainty Effectively
English definition of
“uncertainty”
Source: (Definition of uncertainty noun from the Cambridge Advanced
Learner's Dictionary & Thesaurus © Cambridge University Press)
a situation in which something is
not known, or something that is
not known or certain:
Nothing is ever decided, and all the uncertainty
is very bad for staff morale. Life is full of
uncertainties
3
Paper Review - Presenting and Generating Uncertainty Effectively
Ambiguity - The referents of terms in a sentence about the world are not clearly
specified and therefore it cannot be determined whether the sentence is satisfied.
Empirical - a sentence about a world (an event) is either satisfied or not satisfied in
each world, but it is not known in which worlds it is satisfied; this can be resolved by
obtaining additional information (e.g., an experiment).
Randomness - sentence is an instance of a class for which there is a statistical law
governing whether instances are satisfied.
Vagueness - there is not a precise correspondence between terms in the sentence
and referents in the world.
Inconsistency - there is no world that would satisfy the statement.
Incompleteness - information about the world is incomplete, some information is
missing.
4 Paper Review - Presenting and Generating Uncertainty
Effectively
Random Uncertainties: result from the randomness of measuring
instruments. They can be dealt with by making repeated
measurements and averaging. One can calculate the standard
deviation of the data to estimate the uncertainty.
Systematic Uncertainties: result from a flaw or limitation in the
instrument or measurement technique. Systematic uncertainties
will always have the same sign. For example, if a meter stick is too
short, it will always produce results that are too long.
5
Paper Review - Presenting and Generating Uncertainty Effectively
Sources of Uncertainty
6 Paper Review - Presenting and Generating Uncertainty
Effectively
Uncertainty Model
The specific mathematical theories for the
uncertainty types include, but are not limited to,
the following:
Probability.
Fuzzy Sets.
Belief Functions.
Random Sets.
Rough Sets.
Combination of Several Models (Hybrid), e.g.,
Fuzzy Sets and Probability.
7 Paper Review - Presenting and Generating Uncertainty
Effectively
8 Paper Review - Presenting and Generating Uncertainty
Effectively
“Risk vs. Uncertainty”
Risk: We don’t know what is going to happen next,
but we know what the distribution looks like.
Risk Uncertainty
Uncertainty: We don’t know what is going to
happen next, and we do not know what the
possible distribution looks like.
9
Paper Review - Presenting and Generating Uncertainty
Effectively
When we don’t know what any future outcome will be, but
we understand the probability distribution — think of dice
or a multiple choice exam — we have risk, but we do NOT
have uncertainty. We never know what the roll of the dice
will be, but we know its one of six choices.
Is that uncertainty? The answer is of course not — it is an
unknown outcome with well-defined possibilities. We
may not know precisely which outcome will occur in
advance, but we do know its either 1, 2,3, 4, 5 or 6. Call
that risk or an unknown future, but do not call that
uncertainty.
10
Paper Review - Presenting and Generating Uncertainty
Effectively
Total
Number of
combinations
Probability
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%
6 5 13.89%
7 6 16.67%
8 5 13.89%
9 4 11.11%
10 3 8.33%
11 2 5.56%
12 1 2.78%
Total 36 100%
11 Paper Review - Presenting and Generating Uncertainty
Effectively
Simulation Histogram showing the uncertainty
12
Paper Review - Presenting and Generating Uncertainty
Effectively
Prof. Frank H Knight (1921)
proposed that "risk" is
randomness with knowable
probabilities, and
"uncertainty" is randomness
with unknowable
probabilities. However, risk
and uncertainty both share
features with randomness.
The illustration here explains
the relationship of the
concepts better than words...
Source: Knight, F H (2002/1921), Risk, Uncertainty and Profit,
Washington, DC: Beard Books.13 Paper Review - Presenting and Generating Uncertainty
Effectively
All risks are uncertain, however, not all
uncertainties are risks.
14 Paper Review - Presenting and Generating Uncertainty Effectively
Calculating the statistics using Excel
When dealing with repeated measurements, there are three important statistical
quantities: average (or mean), standard deviation, and standard error. These are
summarized in the table below:
Statistic What it is Statistical interpretation
Symb
ol
average
an estimate of
the "true" value
of the
measurement
the central value xave
standard
deviation
a measure of the
"spread" in the
data
You can be reasonably sure (about
70% sure) that if you repeat the same
measurement one more time, that next
measurement will be less than one
standard deviation away from the
average.
s
standard
an estimate in
the uncertainty in
the average of
You can be reasonably sure (about
70% sure) that if you do the entire
experiment again with the same
number of repetitions, the average SE
15 Paper Review - Presenting and Generating Uncertainty
Effectively
Calculating the statistics using Excel
Spreadsheet programs (like Microsoft Excel) can calculate statistics easily. Once you
have the data in Excel, you can use the built-in statistics package to calculate the
average and the standard deviation.
•To calculate the average of cells A2 through A6:Select the cell you want the average to
appear in (D1 in this example)
•Type "=average(a2:a6)"
•Press the Enter key
To calculate the standard deviation of the five numbers, use Excel's built-in STDEV
function.
Excel doesn't have a standard error function,
so you need to use the formula for standard error:
where N is the number of observation
16
Paper Review - Presenting and Generating Uncertainty
Effectively
Uncertainty in Calculations
What if you want to determine the uncertainty for a quantity that was calculated
from one or more measurements? There are complicated and less complicated
methods of doing this. we will use the simple one. The Upper-Lower Bounds
method of uncertainty in calculations is not as formally correct, but will do. The
basic idea of this method is to use the uncertainty ranges of each variable to
calculate the maximum and minimum values of the function. You can also think of
this procedure as examining the best and worst case scenarios.
For example, if you want to find the area of a square and measure one side as a length of
1.2 +/- 0.2 m and the other length as 1.3 +/- 0.3 meters, then the area would be:
A = l * w = 1.2 * 1.3 = 1.56 m^2
The minimum area would be using the "minimum" measurements so l = 1.2 - 0.2 = 1.0
and w = 1.3 - 0.3 = 1.0
So the "minimum' area is A-min = 1.0 * 1.0 = 1.0 m^2
Likewise for the maximum area, l = 1.2 + 0.2 = 1.4 and w = 1.3 + 0.3 = 1.6
So the Maximum area is A-max = 1.4 * 1.6 = 2.24 m^2
Thus, we can say the area is A = 1.5 +/- 0.6 m^2
17 Paper Review - Presenting and Generating Uncertainty
Effectively
Different kinds of simulation models and
inputs
18
Paper Review - Presenting and Generating Uncertainty
Effectively
Most simulation models, and indeed most operations research models,
might be viewed as having two aspects:
structural and quantitative.
The structural components include the logical elements and relationships
among them.
The quantitative components of a model are the values of numerical
inputs, or ranges or probability distributions that describe what values these
inputs might assume.
DETERMINISTIC VS. RANDOM INPUTS
In general, a deterministic model produces specific results given certain
inputs by the model user, contrasting with a stochastic model which
encapsulates randomness and probabilistic events.
19
Paper Review - Presenting and Generating Uncertainty
Effectively
20
Independent of distributed random inputs
All random inputs across a simulation model are
independent of each other, and independent and
stationary within themselves.
Paper Review - Presenting and Generating Uncertainty
Effectively
Accuracy vs. Precision
Low Accuracy
High Precision
High Accuracy
Low Precision
High Accuracy
High Precision
Accuracy: is how close a measured value is to the actual
(true) value.
Precision: is how close the measured values are to each
other.
Accurate: means correct. An accurate measurement
correctly reflects the size of the thing being measured.
Precise: repeatable, reliable, getting the same
measurement each time. A measurement can be precise but
not accurate.
21 Paper Review - Presenting and Generating Uncertainty Effectively
Software and uncertainty:
Successful software development involves
understanding uncertainty, and uncertainty only
comes from a few sources in a software project.
The uncertainties of a software project increase
with the size of the project and the inexperience
of the team with the domain and technologies.
22
Paper Review - Presenting and Generating Uncertainty
Effectively
Generating Random Numbers using
Excel:
23
Paper Review - Presenting and Generating Uncertainty
Effectively
24
Paper Review - Presenting and Generating Uncertainty
Effectively
References:
25 Paper Review - Presenting and Generating Uncertainty Effectively

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Representing and generating uncertainty effectively presentatıon

  • 1. REPRESENTING AND GENERATING UNCERTAINTY EFFECTIVELY Ph.D. Candidate Azdeen Najah1 Paper Review - Presenting and Generating Uncertainty Effectively
  • 2. W. David Kelton Department of Quantitative Analysis and Operations Management University of Cincinnati Cincinnati, Ohio 45221-0130, U.S.A. Web-Page: Proceedings of the 2007 Winter Simulation Conference S. G. Henderson, B. Biller, M.-H. Hsieh, J. Shortle, J. D. Tew, and R. R. Barton, eds. 2 Paper Review - Presenting and Generating Uncertainty Effectively
  • 3. English definition of “uncertainty” Source: (Definition of uncertainty noun from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press) a situation in which something is not known, or something that is not known or certain: Nothing is ever decided, and all the uncertainty is very bad for staff morale. Life is full of uncertainties 3 Paper Review - Presenting and Generating Uncertainty Effectively
  • 4. Ambiguity - The referents of terms in a sentence about the world are not clearly specified and therefore it cannot be determined whether the sentence is satisfied. Empirical - a sentence about a world (an event) is either satisfied or not satisfied in each world, but it is not known in which worlds it is satisfied; this can be resolved by obtaining additional information (e.g., an experiment). Randomness - sentence is an instance of a class for which there is a statistical law governing whether instances are satisfied. Vagueness - there is not a precise correspondence between terms in the sentence and referents in the world. Inconsistency - there is no world that would satisfy the statement. Incompleteness - information about the world is incomplete, some information is missing. 4 Paper Review - Presenting and Generating Uncertainty Effectively
  • 5. Random Uncertainties: result from the randomness of measuring instruments. They can be dealt with by making repeated measurements and averaging. One can calculate the standard deviation of the data to estimate the uncertainty. Systematic Uncertainties: result from a flaw or limitation in the instrument or measurement technique. Systematic uncertainties will always have the same sign. For example, if a meter stick is too short, it will always produce results that are too long. 5 Paper Review - Presenting and Generating Uncertainty Effectively
  • 6. Sources of Uncertainty 6 Paper Review - Presenting and Generating Uncertainty Effectively
  • 7. Uncertainty Model The specific mathematical theories for the uncertainty types include, but are not limited to, the following: Probability. Fuzzy Sets. Belief Functions. Random Sets. Rough Sets. Combination of Several Models (Hybrid), e.g., Fuzzy Sets and Probability. 7 Paper Review - Presenting and Generating Uncertainty Effectively
  • 8. 8 Paper Review - Presenting and Generating Uncertainty Effectively
  • 9. “Risk vs. Uncertainty” Risk: We don’t know what is going to happen next, but we know what the distribution looks like. Risk Uncertainty Uncertainty: We don’t know what is going to happen next, and we do not know what the possible distribution looks like. 9 Paper Review - Presenting and Generating Uncertainty Effectively
  • 10. When we don’t know what any future outcome will be, but we understand the probability distribution — think of dice or a multiple choice exam — we have risk, but we do NOT have uncertainty. We never know what the roll of the dice will be, but we know its one of six choices. Is that uncertainty? The answer is of course not — it is an unknown outcome with well-defined possibilities. We may not know precisely which outcome will occur in advance, but we do know its either 1, 2,3, 4, 5 or 6. Call that risk or an unknown future, but do not call that uncertainty. 10 Paper Review - Presenting and Generating Uncertainty Effectively
  • 11. Total Number of combinations Probability 2 1 2.78% 3 2 5.56% 4 3 8.33% 5 4 11.11% 6 5 13.89% 7 6 16.67% 8 5 13.89% 9 4 11.11% 10 3 8.33% 11 2 5.56% 12 1 2.78% Total 36 100% 11 Paper Review - Presenting and Generating Uncertainty Effectively
  • 12. Simulation Histogram showing the uncertainty 12 Paper Review - Presenting and Generating Uncertainty Effectively
  • 13. Prof. Frank H Knight (1921) proposed that "risk" is randomness with knowable probabilities, and "uncertainty" is randomness with unknowable probabilities. However, risk and uncertainty both share features with randomness. The illustration here explains the relationship of the concepts better than words... Source: Knight, F H (2002/1921), Risk, Uncertainty and Profit, Washington, DC: Beard Books.13 Paper Review - Presenting and Generating Uncertainty Effectively
  • 14. All risks are uncertain, however, not all uncertainties are risks. 14 Paper Review - Presenting and Generating Uncertainty Effectively
  • 15. Calculating the statistics using Excel When dealing with repeated measurements, there are three important statistical quantities: average (or mean), standard deviation, and standard error. These are summarized in the table below: Statistic What it is Statistical interpretation Symb ol average an estimate of the "true" value of the measurement the central value xave standard deviation a measure of the "spread" in the data You can be reasonably sure (about 70% sure) that if you repeat the same measurement one more time, that next measurement will be less than one standard deviation away from the average. s standard an estimate in the uncertainty in the average of You can be reasonably sure (about 70% sure) that if you do the entire experiment again with the same number of repetitions, the average SE 15 Paper Review - Presenting and Generating Uncertainty Effectively
  • 16. Calculating the statistics using Excel Spreadsheet programs (like Microsoft Excel) can calculate statistics easily. Once you have the data in Excel, you can use the built-in statistics package to calculate the average and the standard deviation. •To calculate the average of cells A2 through A6:Select the cell you want the average to appear in (D1 in this example) •Type "=average(a2:a6)" •Press the Enter key To calculate the standard deviation of the five numbers, use Excel's built-in STDEV function. Excel doesn't have a standard error function, so you need to use the formula for standard error: where N is the number of observation 16 Paper Review - Presenting and Generating Uncertainty Effectively
  • 17. Uncertainty in Calculations What if you want to determine the uncertainty for a quantity that was calculated from one or more measurements? There are complicated and less complicated methods of doing this. we will use the simple one. The Upper-Lower Bounds method of uncertainty in calculations is not as formally correct, but will do. The basic idea of this method is to use the uncertainty ranges of each variable to calculate the maximum and minimum values of the function. You can also think of this procedure as examining the best and worst case scenarios. For example, if you want to find the area of a square and measure one side as a length of 1.2 +/- 0.2 m and the other length as 1.3 +/- 0.3 meters, then the area would be: A = l * w = 1.2 * 1.3 = 1.56 m^2 The minimum area would be using the "minimum" measurements so l = 1.2 - 0.2 = 1.0 and w = 1.3 - 0.3 = 1.0 So the "minimum' area is A-min = 1.0 * 1.0 = 1.0 m^2 Likewise for the maximum area, l = 1.2 + 0.2 = 1.4 and w = 1.3 + 0.3 = 1.6 So the Maximum area is A-max = 1.4 * 1.6 = 2.24 m^2 Thus, we can say the area is A = 1.5 +/- 0.6 m^2 17 Paper Review - Presenting and Generating Uncertainty Effectively
  • 18. Different kinds of simulation models and inputs 18 Paper Review - Presenting and Generating Uncertainty Effectively
  • 19. Most simulation models, and indeed most operations research models, might be viewed as having two aspects: structural and quantitative. The structural components include the logical elements and relationships among them. The quantitative components of a model are the values of numerical inputs, or ranges or probability distributions that describe what values these inputs might assume. DETERMINISTIC VS. RANDOM INPUTS In general, a deterministic model produces specific results given certain inputs by the model user, contrasting with a stochastic model which encapsulates randomness and probabilistic events. 19 Paper Review - Presenting and Generating Uncertainty Effectively
  • 20. 20 Independent of distributed random inputs All random inputs across a simulation model are independent of each other, and independent and stationary within themselves. Paper Review - Presenting and Generating Uncertainty Effectively
  • 21. Accuracy vs. Precision Low Accuracy High Precision High Accuracy Low Precision High Accuracy High Precision Accuracy: is how close a measured value is to the actual (true) value. Precision: is how close the measured values are to each other. Accurate: means correct. An accurate measurement correctly reflects the size of the thing being measured. Precise: repeatable, reliable, getting the same measurement each time. A measurement can be precise but not accurate. 21 Paper Review - Presenting and Generating Uncertainty Effectively
  • 22. Software and uncertainty: Successful software development involves understanding uncertainty, and uncertainty only comes from a few sources in a software project. The uncertainties of a software project increase with the size of the project and the inexperience of the team with the domain and technologies. 22 Paper Review - Presenting and Generating Uncertainty Effectively
  • 23. Generating Random Numbers using Excel: 23 Paper Review - Presenting and Generating Uncertainty Effectively
  • 24. 24 Paper Review - Presenting and Generating Uncertainty Effectively References:
  • 25. 25 Paper Review - Presenting and Generating Uncertainty Effectively