In the book Gaussian Processes for Machine Learning in Chapter 2 p. 11 (see http://www.gaussianprocess.org/gpml/chapters/RW2.pdf), eq. 2.9 states:
$p(f_* | X, y) = \int p(f_* | x_*,w) p(w|X, y)dw$
the posterior predictive function.
I have huge difficulties trying to understand what $p(f_* | x_*, w)$ should look like. Since $f_* = f(x_*) = x_*^T w$ is uniquely determined, should I imagine this PDF as $0$ everywhere except at $x_*^T w$? How would it this PDF be written explicetly? How does one go about solving this integral?
Any help would be much appreciated!!