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bayes_theorem [2019/01/01 02:23] paul [Bayes Theorem] |
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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| $P(H) =$ Prior probability, | $P(H) =$ Prior probability, | ||
| - | $P(H|E) =$ Probability of hypothesis H, given condition E | + | $P(H|E) =$ 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. | ||
| The probability of a hypothesis, $H$ conditional on a new piece of evidence, $E$ | The probability of a hypothesis, $H$ conditional on a new piece of evidence, $E$ | ||
| $P(H|E) = \frac{P(E|H)P(H)}{P(E)}$ | $P(H|E) = \frac{P(E|H)P(H)}{P(E)}$ | ||
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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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