STAT231 Lecture 2: Week 2-Lecture2--Likelihood examples.pdf

• School: University of Waterloo
• Department: Statistics
• Course: STAT231
• Professor: Matthias Schonlau

Document Summary

In general: we have a model and data, goal: estimate parameter(s) of the model, the likelihood method is a general method that solves this problem, likelihood inference has very good theoretical properties. Those will be covered in stat330 and stat 450. the data for specific parameter values ( ) pr( (cid:84) Likelihood function: the likelihood is the probability that you observe. (cid:591) is the set of all possible parameter values. And d are realizations from those random variables. Likelihood method: in search of parameter values: define the likelihood function l((cid:637)) (cid:637)(cid:3)(cid:349)(cid:400)(cid:3)(cid:410)(cid:346)(cid:286)(cid:3)(cid:448)(cid:286)(cid:272)(cid:410)(cid:381)(cid:396)(cid:3)(cid:381)(cid:296)(cid:3)(cid:393)(cid:258)(cid:396)(cid:258)(cid:373)(cid:286)(cid:410)(cid:286)(cid:396)(cid:400: find the value for the parameter that maximizes l((cid:637)) In practice we always maximize the log likelihood: the value that maximizes the likelihood, the estimate of (cid:637), is called the maximum likelihood estimate. Example: binomial distribution: take a random sample of homeless people in. Random is difficult for homeless: y :number of homeless infected with hiv, we assume independence, distribution is binomial y.