I ordered two math books from amazon so that I don’t have to enter into a recall war at the library with the other person who seems to want them so badly. I’m really digging the one I’m reading now though — Differential Geometry and Statistics. It’s got a gentle introduction to geometric concepts when dealing with things like fitting statistical models to data and will hopefully will give me a more sophisticated view on modeling. It’s way easier to read than Amari’s monograph on the same subject, which has a whole chapter devoted to a complex theoretical apparatus with no examples. Saying things like “the curvature looks like this function, which we call the Fisher information” is not nearly as helpful as “remember the Fisher information? It looks like this. This turns out to be a special case of the a general concept called the curvature.”
I need to read the material bottom-up. Or sideways, depending on where you think Statistics is relative to Differential Geometry. Actually, since it’s geometry, we’re trying to free ourselves from the tyranny of coordinates, so “up” and “sideways” are pretty meaningless altogether.