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...

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.
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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
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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.
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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.
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6. Sources of Uncertainty
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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.
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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.
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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.
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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%
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12. Simulation Histogram showing the uncertainty
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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
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14. All risks are uncertain, however, not all
uncertainties are risks.
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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
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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
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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
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18. Different kinds of simulation models and
inputs
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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.
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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.
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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.
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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.
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23. Generating Random Numbers using
Excel:
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References:

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