In dajmcdon/ubc-stat406-labs: Tutorials and labs for UBC Stat 406 in the 2020-2021 online year

Recall "Maximum likelihood estimation". We're going to do this by hand. The Poisson Likelihood is given by [ L(\lambda ; y_1,\ldots,y_n) = \prod_{i=1}^n \frac{\lambda^{y_i}\exp(-\lambda)}{y_i!}. ]

1. Generate $n=100$ observations from a Poisson distribution with parameter $\lambda=3$.

2. Examine the slide from class. What key ingredient do I need to make this work?

3. Remember that if I use a monotone function like log, I don't change the minimizer. Use this trick!! Write a function which gives the key ingredient as a function of $\lambda$.

4. Suppose $\lambda=1$, $y_1=3$, $y_2=5$. What value should your function return? Check that it does.

5. Using your data and my sample code from class, maximize the loglikelihood and report the maximizer. Use gam=.01 and start at 23. Set tol=1e-5. Is this the value you would expect? What should the answer be?

dajmcdon/ubc-stat406-labs documentation built on Aug. 18, 2020, 1:23 p.m.