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Pattern Recognition by Matthias Nagel, Matthias Richter, Jürgen Beyerer

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In conclusion, for infinitely many samples, the uncertainty of the estimation vanishes and the a posteriori distribution converges to a Dirac distribution at the empirical mean of the samples. This means that any resemblance to the a priori assumption vanishes and the result depends solely on the data and actually equals the ML estimator. An example of such a sequence of a posteriori distributions is depicted in Figure 4.2.

To conclude the example, we must still calculate the conditional feature distribution given the dataset p(m|D). As all densities are Gaussian, the calculation of Equation (4.42) needs little effort. Again, α denotes a universal normalizing constant in

p( m|D )= p( m|μ ) p( μ|D )dμ =α

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