We will assume that the data were generated from a

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Unformatted text preview: ). We will assume that the data were generated from a probability distribution that is described by some parameters θ (not necessarily scalar). We treat θ as a random variable. We will use the shorthand notation p(y |θ) to represent the family of conditional density functions over y , parameterized by the ran­ dom variable θ. We call this family p(y |θ) a likelihood function or likelihood model for the data y , as it tells us how likely the data y are given the model specified by any value of θ. We specify a prior distribution over θ, denoted p(θ). This distribution rep­ resents any knowledge we have about how the data are generated prior to 1 observing them. Our end goal is the conditional density function over θ, given the observed data, which we denote as p(θ|y ). We call this the posterior distribution, and it informs us which parameters are likely given the observed data. We, the modeler, specify the likelihood function (as a function of y and θ) and the prior (we completely specify this) using our know...
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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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