Lecture 23/24

Question 1

aleatory uncertainty

Answer 1

natural randomness in the phenomena we are dealing with

Question 2

epistemic uncertainty

Answer 2

inaccuracy in our understanding and our models for predicting reality

Question 3

Three basic options

Answer 3

• ignore the uncertainty
• can allow for uncertainty using intuition
• can adopt a scientific approach, use mathematical laws of probability and base decisions on internal estimates

Question 4

politics of uncertainty

Answer 4

conceding uncertainty might be perceived as being inconsistent with being an expert

Question 5

Type I error

Answer 5

false positive

Question 6

Type II error

Answer 6

false negative

Question 7

reduce type I errors

Answer 7

increase level of confidence

Question 8

reduce type II errors

Answer 8

descriptive testing

Question 9

s.o.n.

Answer 9

state of nature

- true value of an uncertain variable - cannot be determined with absolute confidence

Question 10

A decision is sensitive if

Answer 10

• one test is done and the decision is different for different test results
• more than one test is done and the decision changes as new test results come to hand and the probability distribution for the state of nature will be updated

Question 11

theta

Answer 11

represents the state of nature

Question 12

z

Answer 12

represents the result of a test to obtain more information about the state of nature

Question 13

P(theta)

Answer 13

prior probability distribution (contains prior knowledge about state of nature)

Question 14

P(z|theta)

Answer 14

the likelihood of test result z, given the state of nature theta

Question 15

P(theta | z)

Answer 15

posterior probability distribution (contains updated information about state of nature theta)

Question 16

posterior analysis

Answer 16

involves calculating posterior probabilities for the state of nature, given an experiment has been done and the result is known, and then deciding what action to take

Question 17

preposterior analysis

Answer 17

involves deciding whether an experiment should be done and which exeriment

Question 18

four stages of preposterior analysis

Answer 18

• the test
• result
• action
• state of nature

Question 19

Allais’ Paradox

Answer 19

lottery ticket case studies

- phenomenon is not “irrational”,but is simply the result of the way people value the possible outcomes

Question 20

Requirements for a robust numerical measure of preference

Answer 20

• reflects the decision makers subjective preferences

- provides a scale preserving the order of expected values

Question 21

Daniel Bernoulli

Answer 21

• assumed utility of extra wealth inversely proportional to total assets
• proposed a scale based on the logarithm of total assets

Question 22

Buffon

Answer 22

• proposed a scale based on the reciprocal of total assets

Question 23

Cramer

Answer 23

• used a scale based on the square root of total assets

Question 24

von Neumann and Morgenstern

Answer 24

standard gamble

Question 25

standard gamble

Answer 25

- enabled subjectivity to be taken into account, while fulfilling the requirement for preserving the ordering of expected values - based on a particular form of a decision tree, with one action leading to a certain outcome and the other to a gamble or lottery

Question 26

'risk neutral' person

Answer 26

bases all decisions on expected utility

Question 27

'risk averse' person

Answer 27

will be uncomfortable with a small p* (i.e. large probability of big loss)

Question 28

'not risk averse' person

Answer 28

will be comfortable with a small p* (i.e. small probability of a big win)

Question 29

Criteria for Making Decisions

Answer 29

1. Criterion of Pure Pessimism 2. Criterion of Pure Optimism 3. Criterion of Regret

Question 30

Criterion of Pure Pessimism

Answer 30

(or maxi-min criterion) - identify for each action the minimum utility - choose the action with the largest minimum utility

Question 31

Criterion of Pure Optimism

Answer 31

(or maxi-max criterion) - identify for each action the maximum utility - choose the action with the largest maximum utility

Question 32

Criterion of Regret

Answer 32

- identify the regret for each action and state of nature - identify for each action the maximum regret - choose the action with the smallest maximum regret

Question 33

reliability

Answer 33

the probability that a component (or system) will function properly

Question 34

two basic types of systems

Answer 34

series and parallel

Question 35

P[S ^ s]

Answer 35

= 1 - P[S ^ f]

Question 36

Series system

Answer 36

P[S ^ s] = P[C1 ^ s] * P[C2 ^ s] * ... * P[Cn ^ s]

Question 37

Parallel systems

Answer 37

- level of redundancy = (n-k) where k is minimum number of properly functioning components for the system to function properly - system fails if more than (n-k) fail

Question 38

Birnbaum

Answer 38

suggested that to maximise the improvement in network reliability (R) one should improve the link a with the highest Reliability Importance (RI)

Question 39

RI

Answer 39

Reliability Importance | RI = dR / dr(a)

Question 40

RI for series

Answer 40

RI(1) = r(2) RI(2) = r(1) hence if link 1 is more reliable than link 2, RI(2) > RI(1) and should improve link 2

Question 41

RI for parallel

Answer 41

RI(1) = 1 - r(2) RI(2) = 1 - r(1) hence if link 1 is more reliable than link 2, RI(1) > RI(2) and should improve length 1 - counter intuitive

Question 42

Henley and Kuamoto

Answer 42

suggested that to maximise improvement in network reliabilty, one should improve link a with highest Criticality Importance (CI)

Question 43

CI

Answer 43

Criticality Importance | CI = RI * (r / R)

Question 44

CI for two links in series

Answer 44

``` CI(1) = r(2) * ( r(1) / R) CI(2) = r(1) * ( r(2) / R) since R = r1 * r2 CI(1) = CI(2) = 1 CI provides no help in deciding which length to strengthen ```

Question 45

CI for two links in parallel

Answer 45

CI(1) - C(2) = ( r(1) - r(2) ) / ( r(1) + r(2) - r(1)r(2) ) | suggsts one should improve the more reliable or stronger link