SDS321Lec25Slides-1 - Lecture 25 Decision Making Launch...

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Lecture 25 Decision Making Launch: When I was purchasing light bulbs, I had two choices. I bought several but the packing was taking up space so I took the bulbs out of the packages and have been storing them individually. I forgot which type I bought so I have decided to develop a hypothesis test. The lifetime, X, of the light bulbs is exponential with unknown parameter which I know is either 5 or 10 depending on the type I bought. The prior probability I give to buying the bulbs with =5 is 1/3 and to =10 is 2/3. What is the Maximum Likelihood Decision Rule for this if I observe lifetimes of n bulbs? What is the MAP Decision Rule if I observe lifetimes of n bulbs?
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What will we cover? Decision Rules for simple hypothesis testing using Maximum Likelihood (Likelihood Ratio Test) and MAP Decision Rules. Why should we care? Used in data mining, supervised learning, and other fields. This is the basis for the theory of the hypothesis testing methods. Learning Outcomes Lecture 25 Upon completion of this lesson, you should be  able to Develop Decision Rules for simple hypothesis testing using Maximum Likelihood and MAP. From the text: 8.2, 9.3
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There is more than one way to make a decision. Often frequentists use hypothesis testing involving likelihoods to make decisions. Bayesians use posterior distributions. There are different types of hypothesis testing situations. They could be: i. one-sided ii. two-sided iii. simple-simple Blast from the Past: Decision Making adapted from Russell and Norvig.
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