Let yi 1 if ip i was heads and yi 0 otherwise let mh

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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 i=1 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.

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