ANSWER TWO QUESTIONS. Where questions have more than one part, the percentage for
each part is given in brackets.
You have TWO hours to complete your answers.
Guideline word limits: a full answer should be between 600 and 1000 words
QUESTION ONE
EITHER
0
Show how you could use a differential equation to model population growth/decay in a closed
system. You should define any terms. show your steps and make clear any assumptions made
30%7
1
How could this approach be extended to include interactions between two populations of
dependent organisis i.e. a predator-prey system
40%]
11
Using figures, show how the population of such a system might vary over time (you may use
examples from the literature).
30%7
OR
Describe how a simple differential equation describing population dynamics can exhibit
complex non-linear (chaotic behaviour). You should define what is meant by ‘chaos’in this
system and explain what is meant by the attractor (or phase diagram) of such a system. Usc
figures in your answer to show how the phase diagram of this system might evolve over
time and with different choices of model parameter values.
[100%7
OUESTION TWO
Briefly describe the importance of Bayes Theorem in scientific analysis, and why it is (or
has been) considered controversial
20%]
11
You are a jury member in a court case where a suspect is on trial for theft of a valuable
obiect from a busy museum gallery in London. DNA evidence found at the scene matches
the suspect’s (with perhaps a 1 in 1 million match by chance) and video evidence puts
them in the museum at some point in the 2 days during which the theft was committed
How could you use Bayes Theorem to combine what you know (and don’t know) to
arive at a verdict (innocent or guilty ) Your answer does not have to be definitive so you
should discuss how to combine any information that may be relevant, any assumptions
you make or prior information that might be relevant, and how the resulting posterior
probability should be interpreted
80%]
OUESTION THREE
Briefly outline the difference between analytical and numerical modelling approaches to model
1nvers1on.
20%7
ii)What is a linear model Using specific examples, describe the benefits and drawbacks of using
a linear modelling approach
[60%]
[10%]
[10%]
ii) Explain the difference between constrained and unconstrained model inversion.
iv) How can we quantify whether a linear model is any good or not
QUESTION FOUR
Show how you could use Monte Carlo sampling to estimate the value of . Explain how the
error in this estimate would decrease with increasing samples
30%7
Outline the method of Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC
11
sampling. Explain why this approach is useful, using examples where possible.
[70%]
