Question 1. (maximum 300 words)
A consulting company is assessing the impact of a proposed new dam on streamflow within the downstream catchment. The consultants have historical data for rainfall, evapotranspiration and streamflow. They have developed a hydrological model of the catchment and have used Monte Carlo simulation to estimate future streamflow.
Some results of the Monte Carlo simulation are shown in the figure below. Based on these results, the consultants claim the risk of extinction to sensitive species in the riverine ecosystems is ‘low' to ‘moderate'. They say that allocating some water to environmental flows will ameliorate this risk.
(a) Do you think the consultants' conclusions are reasonable? Why or why not?
(b) When modelling using Monte Carlo simulation, what are the four key types of uncertainty that need to be considered? Briefly describe each one.
(c) Write two questions, specifically relating to this dam modelling example, asking the consultants to explain how they accounted for uncertainty in the modelling.
(d) Outline two ways in which the consultant could improve their use of Monte Carlo simulation in this risk assessment.
Question 2. (maximum 250 words)
Governments increasingly emphasise the desirability of making science socially robust in the context of risk assessment and decision-making under uncertainty. What recommendations do you have to make science more socially robust?
Question 3.
A forestry company has three strategic options in the face of uncertainty posed by a fungal disease that may or may not be harmful to timber. The options are to do nothing, improve genetic resistance of the host trees, or expand the business by increasing the forest estate. The table below summarises the judgments of senior managers regarding the profit anticipated under each option and state.
| |
|
Disease |
|
Action
|
|
benign
|
harmful
|
|
Do nothing
|
|
$150,000
|
$50,000
|
|
Improve host resistance
|
|
$120,000
|
$80,000
|
|
Increase estate
|
|
$180,000
|
$60,000
|
(a) What attitude to risk underpins the maximin decision criterion? What is the best option using maximin?
(b) What attitude to risk underpins the maximax decision criterion? What is the best option using maximax?
(c) The subjective beliefs of senior managers is that there is a 75% chance the disease will be benign and a 25% chance it will be harmful. Calculate subjective expected utility (SEU) for each of the three options.
(d) What is the best option according to the SEU decision criterion?
Question 4. (maximum 200 words)
The figure below shows a cognitive map capturing understanding of the drivers of algal blooms in an inland river. The system could also be described using a Bayesian Belief Network (BBN).
What are the strengths and weaknesses of cognitive maps and BBNs in this context?
Question 5.
(a) How does the ‘law of small numbers' affect the interpretation of data? (maximum 100 words)
(b) Two alternatives to buffer against psychological frailties in the interpretation of data are
- use of a specified p-value for the Type I error rate (typically 0.05), or
- routine use of confidence intervals.
Which of these two alternatives is better in your opinion? Why? (twelve marks, maximum 250 words)
(c) A p-value is the probability of observing a particular data set given a hypothesis, Pr (data | hypothesis). Bayesian statisticians use Bayes' theorem and prior information to calculate a different quantity. Describe the quantity Bayesian statisticians use, in one sentence.
Question 6.
Demographic stochasticity poses a substantial risk to the viability of a small population of a critically endangered snail.
(a) Define ‘demographic stochasticity.
(b) Why is demographic stochasticity important in small populations?
The per annum fecundity (f) of each individual in the population is estimated to be 0.4. The per annum survivorship (s) of each individual is estimated to be 0.7. The current population size (Nt) is 10 individuals.
(c) Using the formula below, calculate the mean expectation for the population size next year.
Nt+1 = (f+s)Nt.
(d) A computer simulates demographic stochasticity by drawing random numbers from a uniform distribution bounded by zero and one. A single iteration of the simulation draws the random numbers shown in the table below. Assuming again that Nt = 10, calculate the population size next year for this iteration.
|
Individual
|
Fecundity
|
Survivorship
|
|
1
|
0.31
|
0.46
|
|
2
|
0.29
|
0.73
|
|
3
|
0.49
|
0.85
|
|
4
|
0.05
|
0.07
|
|
5
|
0.02
|
0.40
|
|
6
|
0.41
|
0.20
|
|
7
|
0.38
|
0.23
|
|
8
|
0.20
|
0.33
|
|
9
|
0.38
|
0.59
|
|
10
|
0.44
|
0.93
|
Question 7. (maximum 300 words)
Managers of Wilson's Promontory National Park have identified three alternatives for improving the condition of Coastal Grassy Woodlands. In good condition these woodlands comprise (native) Banksia trees and a ground layer of native grasses. Some of the alternatives involve controversial actions that may spark public outrage. Objectives for the managers include:
- Maximise Banksia cover
- Maximise native grass cover
- Minimise costs of implementation
- Minimise public outrage
The performance matrix below describes the merit of each alternative against each objective. The managers of the park ask you to facilitate discussion with stakeholders.
In your role as the facilitator, how would you go about progressing decision-making?
|
Objective
|
Preference
|
Alternative A
|
Alternative B
|
Alternative C
|
|
Banksia cover (%)
|
More is better
|
60
|
70
|
70
|
|
Grass cover (%)
|
More is better
|
30
|
20
|
20
|
|
Cost
|
Less is better
|
$5M
|
$5M
|
$5M
|
|
Public outrage
|
Less is better
|
High
|
medium
|
Low
|