Generalized likelihood ratio test vs likelihood ratio test

1. What is generalized likelihood ratio test?
2. Are odds ratio and likelihood ratio the same?
3. Are likelihood ratio tests always the most powerful tests?
4. What is meant by the likelihood ratio?

What is generalized likelihood ratio test?

The generalized likelihood ratio test is a general procedure for composite testing problems. The basic idea is to compare the best model in class H1 to the best in H0, which is formalized as follows. We have two composite hypotheses of the form: Hi : X ∼ pi(x|θi) , θi ∈ Θi ,i = 0, 1 .

Are odds ratio and likelihood ratio the same?

The odds ratio is the effect of going from “knowing the test negative” to “knowing it's positive” whereas the likelihood ratio + is the effect of going from an unknown state to knowing the test is +.

Are likelihood ratio tests always the most powerful tests?

The simplest testing situation is that of testing a simple hypothesis against a simple alternative. Here the Neyman-Pearson Lemma completely vindicates the LR-test, which always provides the most powerful test.

What is meant by the likelihood ratio?

The Likelihood Ratio (LR) is the likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that that same result would be expected in a patient without the target disorder.