# Exercise 2

Exercise 2: Separating process and non-process error is not easy

Type 'Lab2' at matlab prompt.

When asked for data code, type 2 (Trumpeter swans).

When the figure comes up, type Lab2 again, and type in data code 3 (White-capped albatross).

Do it one more time, and type in the data code 1 (Grey-headed albatross).

Questions for Exercise 2:

1. In these 3 examples, we see that the maximum likelihood fit assigns all the variability in the data to non-process error (e.g. measurement error). Why is that? If the CDA really had high process error, how likely is a beeline exponential decline with relatively equal deviations on both sides of the decline? Type in 'SimCDA' at the matlab prompt to plot out 9 realizations of a CDA (you choose the parameters) and see how likely it is.

2. That pattern is unlikely, which suggests that process error is low, but is it 0? Why is the ML fit assigning 0 to the process error? That's biologically unreasonable; process error cannot be zero. By the way, this really is the maximum likelihood estimate. Recall the definition of likelihood; we have competing models (hypotheses) for how the data were produced and some of models produce the data more easily than others.

3. However, we don't know if it matters if process error is around 1e-5 (for example) and the ML fit assigns 1e-18 to

it. How might you try to understand that? It depends on what you're trying to do with the CDA (i.e. what PVA risk

metric you're trying to estimate). How might you try to understand risk metric sensitivity?

Type 'Lab2' at matlab prompt.

When asked for data code, type 2 (Trumpeter swans).

When the figure comes up, type Lab2 again, and type in data code 3 (White-capped albatross).

Do it one more time, and type in the data code 1 (Grey-headed albatross).

Questions for Exercise 2:

1. In these 3 examples, we see that the maximum likelihood fit assigns all the variability in the data to non-process error (e.g. measurement error). Why is that? If the CDA really had high process error, how likely is a beeline exponential decline with relatively equal deviations on both sides of the decline? Type in 'SimCDA' at the matlab prompt to plot out 9 realizations of a CDA (you choose the parameters) and see how likely it is.

2. That pattern is unlikely, which suggests that process error is low, but is it 0? Why is the ML fit assigning 0 to the process error? That's biologically unreasonable; process error cannot be zero. By the way, this really is the maximum likelihood estimate. Recall the definition of likelihood; we have competing models (hypotheses) for how the data were produced and some of models produce the data more easily than others.

3. However, we don't know if it matters if process error is around 1e-5 (for example) and the ML fit assigns 1e-18 to

it. How might you try to understand that? It depends on what you're trying to do with the CDA (i.e. what PVA risk

metric you're trying to estimate). How might you try to understand risk metric sensitivity?

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