Kevin Murphy discusses in this book (http://www.cs.ubc.ca/~murphyk/MLbook/index.html) the spike-and-slab model. I am struggling to understand the prior linked to this model. Why, if $\gamma$=0, and we expect w to be zero, is $\delta_0$(w) a reasonable prior? I have trouble making this link, please can someone share their intuition.
The sentence there might not be as clearly expressed as it could be (the use of "expect" in particular could be misleading).
If $\gamma_j=0$ it's telling us that we're in the case where $w_j=0$.
That is expressed by putting all the probability at $0$, and that is just what $\delta_0(w_j)$ says (it's a spike of height $1$ at $w_j=0$).
