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From Computational Statistics (CSE383M and CS395T)
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To Calculate

(These problems will be the class activity on Monday, but you can get a head start on them if you want.)

I measured the temperature of my framitron manifold every minute for 1000 minutes, with the same accuracy for each measurement. The data is plotted on the right (with data points connected by straight lines), and is in the file Modelselection.txt.

1. From the data, estimate the measurement error <math>\sigma</math>. (You can make any reasonable assumptions that follow from looking at the data.)

2. Write down a few guesses for functional forms, with different (or adjustable) numbers of parameters that might be good models for the data. Order these by their model complexity (number of parameters) from least to most.

3. Fit each of your models to the data, obtaining the parameters and <math>\chi^2_{min}</math> for each. (Hint: write your code generally enough that you can change from model to model by changing only one or two lines.)

4. Which of your models "wins" the model selection contest if you use AIC? Which for BIC?