Lecture 14—Monday, February 12, 2007

What was covered?

Terminology Defined

Fitting regression models when the data generating mechanism is not normal

Constructing the Likelihood

or what is called a joint probability, the probability of simultaneously observing all m events. Another way of writing this is

where I use product notation in the last step.

Maximum likelihood estimation

The likelihood

This is the probability of our data. If we knew λ we could calculate the probability of obtaining any set of values x1, x2, ... , xm. Furthermore, for fixed λ if we summed this expression over all possible values of x1, x2, ... , xm we would get 1.

Viewed this way it's no longer a probability. (For fixed data if we sum over all possible values of λ we will not get 1.) So instead we call this function the likelihood function. Keep in mind that it is still the joint probability function for our data under the assumed probability model only by another name.

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Jack Weiss
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E-Mail: jack_weiss@unc.edu
Address: Curriculum in Ecology, Box 3275, University of North Carolina, Chapel Hill, 27516
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Last Revised--Feb 18, 2007
URL: http://www.unc.edu/courses/2007spring/enst/562/001/docs/lectures/lecture14.htm