Editing Bayesian Statistics (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
The core of Bayesian thinking is the '''Update'''.

'''Frequentist vs. Bayesian''':
* '''Frequentist''': If I flip a coin 10 times and get 7 heads, a frequentist might say the probability of heads is 70%.
* '''Bayesian''': I ''know'' coins are usually fair (My '''Prior'''). Even if I see 7 heads, I don't immediately believe the coin is broken. I update my belief slightly. Only if I see 1,000 heads do I abandon my prior and accept the coin is unfair.

'''Bayes' Theorem in Plain English''':
The probability that your hypothesis is true given the evidence depends on:
1. How likely the evidence is if the hypothesis is true ('''Likelihood''').
2. How likely the hypothesis was to begin with ('''Prior''').
3. Divided by how likely the evidence is overall ('''Normalization''').

'''The Base Rate Fallacy''': This is a common cognitive bias that Bayesian math corrects. If a rare disease affects 1 in 10,000 people, and a test is 99% accurate, a positive test result doesn't mean you have a 99% chance of being sick. Because the disease is so rare (Low Prior), you actually only have about a 1% chance. Most people ignore the "Base Rate" and panic; Bayesians do the math.
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