Lecture 5 : Likelihood ratio tests , Neyman - Pearson detectors , ROC curves , and sufficient statistics
نویسنده
چکیده
In the last lecture we saw that the likelihood ratio statistic was optimal for testing between two simple hypotheses. The test simply compares the likelihood ratio to a threshold. The “optimal” threshold is a function of the prior probabilities and the costs assigned to different errors. The choice of costs is subjective and depends on the nature of the problem, but the prior probabilities must be known. In practice, we face several questions:
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Mathematical Statistics
This material is designed to introduces basic concepts and fundamental theory of mathematical statistics. A review of basic concepts will include likelihood functions, sufficient statistics, and exponential family of distributions. Then point estimation will be discussed, including minimum variance unbiased estimates, Cramér-Rao inequality, maximum likelihood estimates and asymptotic theory. To...
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