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Project Storm Fury
ReviewReview
A stochastic variable has the following probability distribution:A stochastic variable has the following probability distribution:
Values of XProbability distribution
of X
x P(X=x)
$1 P(X=1) = 1/3
$2 P(X=2) = 1/3
$3 P(X=3) = 1/3
ReviewReview
• What is X’s cumulative probability distribution?
• What is its expected value (X=?)
• What is the Variance of X?
• What is its standard deviation?
• What is X’s cumulative probability distribution?
• What is its expected value (X=?)
• What is the Variance of X?
• What is its standard deviation?
ReviewReview
What is the Variance of X?VarX = xi
2 P(X=xi) - 2
= [1(1/3) + 22(1/3) + 32(1/3)] - 22
= (1/3 + 4/3 + 3) - 4
= 2/3
What is its standard deviation ()?X = SqrRoot(VarX) = (2/3)1/2
= .8165
What is the Variance of X?VarX = xi
2 P(X=xi) - 2
= [1(1/3) + 22(1/3) + 32(1/3)] - 22
= (1/3 + 4/3 + 3) - 4
= 2/3
What is its standard deviation ()?X = SqrRoot(VarX) = (2/3)1/2
= .8165
Total Property Damage ($ of 1969)
Total Property Damage ($ of 1969)
Maximum sustained winds over timeMaximum sustained winds over time
Alternative HypothesesAlternative Hypotheses
• H1, the “beneficial” hypothesis. The average effect of seeding is to reduce maximum sustained wind speed.
• H2, the “null” hypothesis. Seeding has no effect on hurricanes. No change is induced in maximum sustained wind speed.
• H3, the “detrimental” hypothesis. The average effect of seeding is to increase the maximum sustained wind speed.
• H1, the “beneficial” hypothesis. The average effect of seeding is to reduce maximum sustained wind speed.
• H2, the “null” hypothesis. Seeding has no effect on hurricanes. No change is induced in maximum sustained wind speed.
• H3, the “detrimental” hypothesis. The average effect of seeding is to increase the maximum sustained wind speed.
Mathematical expressionsMathematical expressions
• P(w' | H2) = P(w) = fN(100, 15.6)
• P(w' | H1) = ƒN(85, 18.6)
• P(w' | H3 ) = ƒN(110, 18.6)
• P(w' | H2) = P(w) = fN(100, 15.6)
• P(w' | H1) = ƒN(85, 18.6)
• P(w' | H3 ) = ƒN(110, 18.6)
Probability density function for Debbie resultsProbability density function for Debbie results
• P(69, 85 | H1) = 1.50 x 2.14 =3.21
• P(69, 85 | H2) = 0.372 x 1.64 = 0.61
• P(69, 85 | H3) = 0.195 X 0.886 = 0.173
P(H1 | 69, 85) = (3.21 x 1/3)/(3.21 x 1/3 + 0.61 x 1/3 + 0.173 x 1/3)
= .81
P(H2 | 69, 85) = .15
P(H3 | 69, 85) = .04
• P(69, 85 | H1) = 1.50 x 2.14 =3.21
• P(69, 85 | H2) = 0.372 x 1.64 = 0.61
• P(69, 85 | H3) = 0.195 X 0.886 = 0.173
P(H1 | 69, 85) = (3.21 x 1/3)/(3.21 x 1/3 + 0.61 x 1/3 + 0.173 x 1/3)
= .81
P(H2 | 69, 85) = .15
P(H3 | 69, 85) = .04
Prior probabilities - pre and post DebbiePrior probabilities - pre and post Debbie
• P(H1) = .15
• P(H2) = .75
• P(H3) = .10
• P(H1) = .15
• P(H2) = .75
• P(H3) = .10
• P(H1) = .49
• P(H2) = .49
• P(H3) = .02
• P(H1) = .49
• P(H2) = .49
• P(H3) = .02
.81(.15)/ [.81(.15) +.15(.75) + .04(.1)] = .51 .15(.75)/ [.81(.15) +.15(.75) + .04(.1)] = .47.04(.1)/ [.81(.15) +.15(.75) + .04(.1)] = .02
The Seeding DecisionThe Seeding Decision
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall
Cumulative probability functions
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall
Cumulative probability functions
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall.
Discrete approximation for five outcomes.
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall.
Discrete approximation for five outcomes.
Interval of changes in maximum sustained wind
Representative value in discrete approximation
(%) If seeded If not seeded
Increase of 25% or more 32 0.038 0.054
Increase of 10 to 25% 16 0.143 0.206
Little change, +10 to -10% 0 0.392 0.480
Reduction of 10 to 25% -16 0.255 0.206
Reduction of 25% or more -34 0.172 0.054
Probability that windchange will bewithin interval
The seeding decision for the nominal hurricaneThe seeding decision for the nominal hurricane
$21.7M
The expected value of perfect informationThe expected value of perfect information
The value of further testsThe value of further tests
ReviewReview
1. Decide whose benefits and costs count, and how much. This is typically referred to as determining standing.
2. Select the portfolio of alternative initiatives. 3. Catalog potential consequences and select measurement
indicators. 4. Predict quantitative consequences over the life of the project
for those who have standing.5. Monetize (attach cash values to) all the predicted
consequences. 6. Discount for time to find present values.7. Sum up benefits and Costs for each initiative and Perform
sensitivity analysis underlying key assumptions
1. Decide whose benefits and costs count, and how much. This is typically referred to as determining standing.
2. Select the portfolio of alternative initiatives. 3. Catalog potential consequences and select measurement
indicators. 4. Predict quantitative consequences over the life of the project
for those who have standing.5. Monetize (attach cash values to) all the predicted
consequences. 6. Discount for time to find present values.7. Sum up benefits and Costs for each initiative and Perform
sensitivity analysis underlying key assumptions
Adapting to Climate Change 1Adapting to Climate Change 1
Adapting to Climate Change 2Adapting to Climate Change 2
Adapting to Climate Change 3Adapting to Climate Change 3
Adapting to Climate Change 4Adapting to Climate Change 4
Adapting to Climate Change 5Adapting to Climate Change 5
Source: Oregon Environmental Quality Commission, Oregon Climate Change Adaptation Framework. December 10, 2010, Salem OR