24 Bayes 2

# 24 Bayes 2 - Bayesian Statistics II With some description...

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Bayesian Statistics II With some description of the Beta distribution…

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Concept by Example | Let us suppose we have 5 scientists each analyzing the same 100 observations. Let us suppose the purpose of the experiment is to determine the probability that a certain genetic effect will take place in the next generation of a given type of simple organism. If the effect occurs 50% of the time, we say it occurs at random. | Suppose the effect occurs 90 out of the 100 times it was observed.
Scientist #1 | Scientist #1 is a theorist. She thinks the successes are occurring at random because her theoretical understanding of the biochemical mechanism suggests that there should not be an effect. | The scientist has a very strong preconceived belief.

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Scientist #2 | Scientist #2 is an experimentalist. After observing the data he thinks p=0.9. | This scientist is ready to abandon theory in favor of strong belief in the data.
Scientist #3 | Scientist #3 is a well known skeptic. She decides there is something strange about the reported results since they violate her strongly held expectation that nothing, other than a random effect, should be observed. She tries the experiment again herself and the effect turns up 82 times. | Her estimate of the effect is (82+90)/200=0.86

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Scientist #4 | Scientist #4 is a thorough and careful experimentalist. He writes you for the data, and observes in it a run of 50 straight successes, which he decides to ignore and comes up with an estimate of p=40/50=0.8 | This scientist is weighting the observations according to their believability.
Scientist #5 | Scientist #5 is other-directed. She finds out the names of the other scientists working on the problem and contacts them to check their findings.

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