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bayes_theorem [2018/12/31 20:03] paul |
bayes_theorem [2019/03/31 14:49] (current) |
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| + | ====== Bayes Theorem ====== | ||
| Probability discovered by Thomas Bayes in the 18th century. | Probability discovered by Thomas Bayes in the 18th century. | ||
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| $P(Sally\ has\ the\ flu\ |\ the\ flu\ patient\ is\ a\ girl) = 0.20$\\ | $P(Sally\ has\ the\ flu\ |\ the\ flu\ patient\ is\ a\ girl) = 0.20$\\ | ||
| $P(Sally\ has\ the\ flu\ |\ the\ flu\ patient\ is\ a\ boy) = 0$ | $P(Sally\ has\ the\ flu\ |\ the\ flu\ patient\ is\ a\ boy) = 0$ | ||
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| + | **Sometimes you know that you might encounter some new evidence in the future, but you don't know how that evidence should effect the probability** | ||
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| + | ===== Bayes Theorem ===== | ||
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| + | Bayes Theorem gives you a way to figure out what your conditional probabilities should be. | ||
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| + | $P(H) =$ Prior probability, | ||
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| + | $P(H|E) =$ Probability of hypothesis H, given condition E. | ||
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| + | $P(E|H) =$ Probability of the condition E, given hypothesis E. | ||
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| + | $P(E) =$ Probability of the condition E. | ||
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| + | The probability of a hypothesis, $H$ conditional on a new piece of evidence, $E$ | ||
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| + | $P(H|E) = \frac{P(E|H)P(H)}{P(E)}$ | ||
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| + | To summarize, Bayes Theorem tells us how to calculate the probability of a hypothesis given a condition. This depends on three things: | ||
| + | - Conditional probability given H | ||
| + | - The prior probability of the hypothesis | ||
| + | - The prior probability of the evidence | ||
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