# bayesian logistic regression - gaussian distribution on parameters?

In general, to classify instances, they use: $p(y=+1 |\beta) = \sigma(\beta^TX)$ (where $\sigma$ is obviously the sigmoid function). Now they need to find the values of $\beta$.

They then say that to avoid overfitting, they'll use a prior distribution on $\beta$ specifying that each value of $\beta$ is likely to be near 0. They then impose a univariate Gaussian prior with mean =0 and variance >0 on each parameter $\beta$. (Section 3).

What I don't understand is:

1. How does specifying $\beta$ to be near 0 help avoid overfitting?

2. How could one assume a Gaussian distribution on a set of parameters that they're supposed to estimate?

Any kind of help would be greatly appreciated...

1) The overfitting will come if a huge number of parameters $\beta$ is significantly different from zero. Putting a prior distribution on each $\beta$ centered on zero is, in some sense, as forcing all the parameters to be non significantly and then only the ones that are strongly significant can have a posterior distribution non close to the zero.