Transcript 07. Avila Uncertainty Management_Bali_2013

Analysis and Management of
Uncertainties
Rodolfo Avila
Bali, Indonesia, 9 – 13 September 2013
Outline
• Part 1. Basic concepts: Hazard, impact, probability,
risk
• Part 2. Types of uncertainties
• Part 3. Management of uncertainties
2
PART 1. BASIC CONCEPTS
SADRWMS Methodology Report
3
Hazard
• A hazard is a situation or agent that poses a threat
to humans, biota or the environment.
The higher the potential to cause harm or damage,
the higher is the hazard.
Hazards cannot be avoided, but they can be
controlled to avoid or reduce exposures and
impacts
4
Types of hazards
• Chemical, radiological, biological, physical, …
5
Hazard – exposure – effect - impact
• Exposures to a hazard resulting in adverse effects
is called “a negative impact”
• Low hazards can sometimes lead to very high
negative impacts, whereas high hazards may not
lead to impacts at all or to very low impacts
6
Hazards – impacts - risk
Hazards may or may
not lead to impacts, or
lead to high or low
impacts depending on
the exposure and effects
Something is missing !
7
Definition of Risk
The word risk derives from the early
Italian “risicare” , which means to dare
Risk is the "possibility of loss or injury:
peril.” (Webster Dictionary, 1999)
Antoine Arnauld 1662
Fear of harm ought to be proportional not
merely to the gravity of harm, but also to the
probability of the event
(”La logique, ou l´art de penser” a bestseller
at the time)
The concept of risk has (two) elements: the
likelihood of something happening and the
consequences if it happens
Representation of risk
Risk  Consequences  Pr obability
10
What is probability?
 The ancient Greek word  meant
plausible or probable. Socrates defined it
as ”likeness to truth”
 Probability is a measure of our
confidence that something is going to
happen. Probable means to be expected
with some degree of certainty
11
Conditional probabilities

Any probability P(E) of an event E is
conditional to some stipulated model or
assumption (A1), it should strictly be
written P(E|A1), i.e. the probability of E,
given A1.

There may be other assumptions (A2, A3,
A4, … Ai) in addition to the assumption A1
believed to be the most likely.
How can this fact be taken into account?
12
Example 1
Will a person survive the next twelve months?
 From the age and sex we might get an answer from vital
statistics, that will apply to the average person.
 We may know the habits and conditions, which will make us to
believe that the a higher or lower probability is more likely.
 Someone with better insight could always assess a better value.
As uncertainties are eradicated the value would approach zero
or unity
All estimates of probabilities are subjective and
depend of knowledge and experience
13
”A priori” and ”a posteriori”


A priori probability- estimated before the
fact. Can be reliable ”only for the most
part”
A posteriori probability- estimated after the
fact. By taking a sufficient large sample,
you can increase your confidence in the
estimated probability to whatever degree
you wish.
But, how reliable this probability is for
predicting future events?
14
Example 2




A person undergoes a medical test for a
relatively rare cancer. The cancer has an
incidence of 1 % among the general population.
Extensive trials have shown that the test does
not fail to detect the cancer when it is present.
The test gives a positive result in 21 % of the
cases in which no cancer is present.
When she was tested, the test produced a
positive result.
15
Example 2 (cont)
What is the probability that the person
actually has the cancer?



1%
4,6 %
79 %
What happens if she repeats the test
several times?
16
Sources of uncertainty
17
Future (System) Uncertainty
• Uncertainty due to our inability to make exact
predictions of the future evolution of the
system, the environment and of future
human actions
18
Model Uncertainty
• Uncertainty in conceptual, mathematical and
computer models used to simulate the
system behavior and evolution
19
Data/Parameter Uncertainty
• Uncertainty/variability in data and
parameters used as inputs in modeling and
dose calculations
• Can be represented using probability
distributions
20
Management of uncertainties
• Uncertainty always exists in modelling any
physical system
• Not possible to remove such uncertainties
totally
• Instead need to manage them and reduce
their effects
21
Approaches for Uncertainty Management
• Awareness – be aware of all major locations of
uncertainty
• Importance – determine relative importance of various
sources of uncertainty using sensitivity analysis
• Reduction – reduce uncertainties, e.g. through further
data collation
• Quantification – quantify effects of uncertainties on
model output using sensitivity analysis
22
Management of system uncertainty
• System uncertainty is usually managed by
performing analysis for a set of scenarios of
future evolution of the system
23
Management of Model Uncertainty
• Conceptual model: consider alternative
conceptual models and collect further data
• Mathematical/computer model: use model
verification, calibration and validation, and
range of models
24
Management of Data/Parameter Uncertainty
• Five approaches can be used:
• conservative/worse case approach
• best estimate and what if
• sensitivity analysis
• Probabilistic
• Can also be used to address model
uncertainties
25
Conservative/worse case approach
• Use pessimistic parameter values to overestimate
impact
• Danger of being so pessimistic as to be worthless and
misleading
• Difficult to define the worst value, and prove that this is
the worst one.
• Not always obvious what is conservative for a
particular combination of parameters, exposure
pathways and radionuclides
26
Magnification of errors
RQ
Percentile
Pessimistic
15
From 99
to +infinity
Probabilistic
6
95
Probabilistic
with
correlation
1
95
RQ=X1*X2 / X3
X1,X2
Lognormal(5,5)
X3
Uniform (10,20)
27
Probabilistic methods - Random variables



Random variables are used to describe
aleatory events (from the Latin word
aleatorius, which means games of
chance), i.e. events whose outcome is
uncertain
A discrete random variable can only take
specific values from a set of values
A continuous variable can take any value
within a defined range of values
28
Probability Density Function
3
2,5
2
1,5
1
0,5
0
0
0,625
1,25
1,875
2,5
29
Propagation of Uncertainties
Input
Parameter
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0.05
0.1625
0.275
0.3875
0.5
85
90
95
100 105 110
Endpoint = F(Input, Parameter)
7
6
5
4
3
2
1
0
Endpoint
0
125
250
375
500
30
Main problems of the probabilistic approach
1. Getting the probability distributions
2. Avoiding impossible combinations
31
Maximum entropy distribution selection
Constraint
PDF
Upper bound, lower
bound
Uniform
Min, Max, Mode
Triangular
(Beta)
Normal
H=∑pi*ln(pi)
Mean, SD
Range, Mean
Beta
Mean occurrence
rate
Poisson
32
Bayesian updating
Based on the
Bayes´theorem
Posterior
≈Prior*Likelihood
Observations
Prior
Posterior
Binomial
Beta
Beta
Poisson
Gamma
Gamma
Negative
binomial
Normal
Normal
Normal
Normal
Normal
Normal
Gamma
Gamma
33
Sensitivity analysis
“Sensitivity analysis is the study of how the
variation in the output of a model
(numerical or otherwise) can be
apportioned, qualitatively or quantitatively,
to different sources of variation, and how
the given model depends upon the
information fed into it.”
(Andrea Saltelli, 2000)
34
Input – Output dependencies
35
Tornado Plots
36