# How does a Bayes regularization works?

I'm trying to get grasp of Bayes regularization algorithm. List of symbols 1st:
$$F$$ - objective function
$$\gamma$$ - regularization parameter
$$M$$ - number od neural network weights
$$N$$ - number of data tuples
$$e$$ - modeling error
$$w$$ - net weight
$$D$$ - data set input-output pair
$$H$$ - Hess matrix of objective function computed based on Jacoby's matrix

I get it that minimalising an objective function: $$F = \gamma\sum\limits _{j=1} ^Mw_j^2 + (1-\gamma)\sum\limits_{i=1}^Ne_i^2$$ is equivalent to maximising likelihood $$P(w|D,\gamma)$$, which can be computed according to Bayes' theorem: $$P(w|D,\gamma) = \frac{P(D|w,\gamma)P(w|\gamma)}{P(D|\gamma)}$$ Likelihood $$P(w|\gamma)$$ is assumed to be a gaussian one and can be computed as: $$P(w|\gamma)=\left(\frac{\gamma}{2N}\right)^{\frac{M}{2}}\cdot e^{-\frac{\gamma}{2}w^Tw}$$ Likelihood $$P(D|\gamma)$$ can be computed too as: $$P(D|\gamma)=\left(\frac{\pi}{\gamma}\right)^{-\frac{N}{2}}\left(\frac{\pi}{1-\gamma}\right)^{-\frac{M}{2}}\frac{(2\pi)^\frac{M}{2}\cdot -e^{-F(w)}}{\sqrt{|H|}}$$ And now my questions are: how is $$P(D|w,\gamma)$$ computed? Or maybe is there any special assumptions about it? And should I minimalise or maximise $$P(w|D,\gamma)$$ to minimalise objective function $$F$$.
I base on those articles: Article1 Article2

If anyone is able to explain those thing to me, I'd be most grateful.
Thank you,
Max

If anyone needs it in future: all above likelihoods are assumed to be a gaussian distributions. Likelihood $$P(\gamma)$$ is assumed to be uniform. In the article it is shown how exactly are they defined and how to compute further is described in detail in article linked above.