## Think Bayes

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The fundamental idea behind all Bayesian statistics is Bayes’s theorem, which is sur‐
prisingly easy to derive, provided that you understand conditional probability. So we’ll
start with probability, then conditional probability, then Bayes’s theorem, and on to
Bayesian statistics.

The fundamental idea behind all Bayesian statistics is Bayes’s theorem, which is sur‐prisingly easy to derive, provided that you understand conditional probability. So we’llstart with probability, then conditional probability, then Bayes’s theorem, and on toBayesian statistics.A probability is a number between 0 and 1 (including both) that represents a degree ofbelief in a fact or prediction. The value 1 represents certainty that a fact is true, or thata prediction will come true. The value 0 represents certainty that the fact is false.Intermediate values represent degrees of certainty. The value 0.5, often written as 50%,means that a predicted outcome is as likely to happen as not. For example, the probabilitythat a tossed coin lands face up is very close to 50%.A conditional probability is a probability based on some background information. Forexample, I want to know the probability that I will have a heart attack in the next year.According to the CDC, “Every year about 785,000 Americans have a first coronaryattack (http://www.cdc.gov/heartdisease/facts.htm).

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