If you have strong machine-learning experience and a few good publications in the current market, getting a postdoc at a top institution is nowhere near NBA odds. I don't know what the odds are specifically for Stanford, but if you apply to whoever has openings among top schools, there are many each year. If you know something about biology and a lot about machine learning, labs might even recruit you rather than vice versa.
This has certainly been my experience as a recent PhD in computational biology. I pretty much have my pick of Post Doc positions - I was getting offers before I even graduated. I was also able to negotiate 50k without much trouble, but I'm definitely worried about the opportunity cost. Giving up 100+ k for more than a year or two seems like a poor decision.
Also a Post Doc from a top lab directly correlates with how much $$ you can make in industry.
