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

$\begin{array}{l}p\left(m|\mathcal{D}\right)={\displaystyle \int p\left(m|\mu \right)}p\left(\mu |\mathcal{D}\right)\text{\hspace{0.17em}}d\mu \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\alpha {\displaystyle}\end{array}$

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