# Lab 2

In Lab 2, ML parameter estimates are obtained by minimizing the negative log likelihood from the fit of a CDA to the data (fit is obtained using the Kalman filter). The uncertainty in the estimates is illustrated with likelihood profiling. The parameter being profiled is held constant at some value x while the ML CDA is fit to the data. The -log L for this x value is the profile value at x. So, the x-axis shows the value of the parameter being held, while the y-axis shows the negative log likelihood (normed by substracting the minimum neg log like). This normed -log L is approximately chi-square distributed with 1 degree of freedom (from statistical theory).

Panel 1: This shows the data with the CDA fit using the ML parameters.

Panel 2: This shows the likelihood profile for mu. mu is the parameter that defines the longterm trend. In Leslie matrix modeling, this would be lambda (more precisely mu = median exp(lambda) ). The profile shows your uncertainty given that you allow uncertainty in whether the variability in the data is due to process or non-process error.

Panel 3&4: These show the likelihood profiles for process and non-process error.

At the matlab prompt, type 'Lab2'.

You'll be asked to enter a data code. Type 0 and see the available data. Now, you'll pick an animal. The ML parameters will be estimated (this takes a moment) and the likelihood profiles will be plotted (this takes quite a few moments).

Panel 1: This shows the data with the CDA fit using the ML parameters.

Panel 2: This shows the likelihood profile for mu. mu is the parameter that defines the longterm trend. In Leslie matrix modeling, this would be lambda (more precisely mu = median exp(lambda) ). The profile shows your uncertainty given that you allow uncertainty in whether the variability in the data is due to process or non-process error.

Panel 3&4: These show the likelihood profiles for process and non-process error.

At the matlab prompt, type 'Lab2'.

You'll be asked to enter a data code. Type 0 and see the available data. Now, you'll pick an animal. The ML parameters will be estimated (this takes a moment) and the likelihood profiles will be plotted (this takes quite a few moments).

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