Solution Manual Bayesian Choice
Bayesian Statistics and Marketing describes the basic advantages of the Bayesian approach, detailing the nature of the computational revolution. Minergate gpu mining. Examples contained include household and consumer panel data on product purchases and survey data, demand models based on micro-economic theory and random effect models used to pool data among respondents. Solutions tosome exercises from Bayesian Data Analysis, second edition, by Gelman, Carlin, Stern,and Rubin 4 Mar 2012 These solutions are in progress.
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Suppose there are two factories of trick coins. One factory creates tail-biased coins, such that the probability of T (an outcome we’ll call “negative”) is 95%. We’ll call this the “healthy” factory. The second factory creates head-biased coins, such that the probability of H (an outcome we’ll call “positive”) is 95%. We’ll call this the “disease” factory. (Just like real diagnostic tests, “positive” suggests having the disease.) Now, suppose you grab a coin at random from a sack of coins. You flip the coin and it comes up “positive.” Our goal is to think about the probability that the coin came from the healthy factory or the disease factory.A. Suppose that thesack of coins has 50% healthy coins. (This is your initial, prior allocation ofcredibility across the two types of coins.) Given the “positive” outcome of thesingle flip, should your re-allocation of credibility end up with morecredibility on the healthy factory or the disease factory? Why?
B. Suppose that thesack of coins has 99% healthy coins. (This is your initial, prior allocation ofcredibility across the two types of coins, similar to real life.) Given the “positive”outcome of the single flip, should your re-allocation of credibility end upwith more credibility on the healthy factory or the disease factory? To answerthis question, do the following steps:
* Suppose the sack has10,000 coins. How many of them would you expect to be healthy? (Hint: Of 10,000coins, we expect 99% of them to be healthy. Compute the actual number.) Howmany would you expect to be diseased?
* If you tested every healthy coin, how many would you expectto come up positive? (Hint: For the number computed in the previous part, weexpect 5% to come up positive. Compute the actual number.)
* If you tested every diseased coin in the sack, how manywould you expect to come up positive?
* Out of all the coinsin the sack that you would expect to come up positive, what proportion of themare diseased? (Hint: Compute the total number of coins that you would expect tocome up positive. Of that total, what proportion is from diseased coins? Youranswer should be 16.1%; show your work. By the way, this exercise is similar toExercise 5.2 of DBDA2E.)