Nevertheless recent advances in theory and

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Unformatted text preview: the whole theory would look nicer if it were built from the start without reference to Bayesianism and priors.” Nevertheless, recent advances in theory and particularly in computation have shown Bayesian statistics to be very useful for many applications. Machine learning is concerned mainly with prediction ability. A lot of the methods we discussed do not worry about exactly what the underlying distribution is - as long as we can predict, we are happy, regardless of whether we even have a meaningful estimate for p(y |θ). 2 Point estimates Rather than estimate the entire distribution p(θ|y ), sometimes it is sufficient to find a single ‘good’ value for θ. We call this a point estimate. For the sake of completeness, we will briefly discuss two widely used point estimates, the maximum likelihood (ML) estimate and the maximum a posteriori (MAP) estimate. 2.1 Maximum likelihood estimation ˆ The ML estimate for θ is denoted θML and is the value for θ under which the data are most likely: ˆ θML ∈ arg max p(y |θ)....
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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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