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Unformatted text preview: eads. We will
see shortly that this is a principled Bayesian approach. Let yi = 1 if ﬂip i
was Heads, and yi = 0 otherwise. Let mH = m yi be the number of heads
in m tosses. Then the likelihood model is
p(y |θ) = θmH (1 − θ)m−mH .
1.1 (2) A note on the Bayesian approach The problem formulation we have just described has historically been a source
of much controversy in statistics. There are generally two subﬁelds of statis
2 tics: frequentist (or classical) statistics, and Bayesian statistics. Although
many of the techniques overlap, there is a fundamental diﬀerence in phi
losophy. In the frequentist approach, θ is an unknown, but deterministic
quantity. The goal in frequentist statistics might then be to determine the
range of values for θ that is supported by the data (called a conﬁdence in
terval). When θ is viewed as a deterministic quantity, it is nonsensical to
talk about its probability distribution. One of the greatest statisticians of
our time, Fisher, wrote that Bayesian statistics “is founded upon an error,
and must be wholly rejected.” Another of the great frequentists, Neyman,
wrote that, “...
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This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.
- Spring '12