Gelman Against Parsimony
In two posts, Bayesian stats guru Andrew Gelman argues against parsimony, though it seems to be favored ’round these parts, in particular Solomonoff Induction and BIC as imperfect formalizations of Occam’s Razor.
I’ve never seen any good general justification for parsimony...
Maybe it’s because I work in social science, but my feeling is: if you can approximate reality with just a few parameters, fine. If you can use more parameters to fold in more information, that’s even better.
In practice, I often use simple models–because they are less effort to fit and, especially, to understand. But I don’t kid myself that they’re better than more complicated efforts!
My favorite quote on this comes from Radford Neal‘s book, Bayesian Learning for Neural Networks, pp. 103-104: “Sometimes a simple model will outperform a more complex model . . . Nevertheless, I believe that deliberately limiting the complexity of the model is not fruitful when the problem is evidently complex. Instead, if a simple model is found that outperforms some particular complex model, the appropriate response is to define a different complex model that captures whatever aspect of the problem led to the simple model performing well.”
...ideas like minimum-description-length, parsimony, and Akaike’s information criterion, are particularly relevant when models are estimated using least squares, maximum likelihood, or some other similar optimization method.
When using hierarchical models, we can avoid overfitting and get good descriptions without using parsimony–the idea is that the many parameters of the model are themselves modeled. See here for some discussion of Radford Neal’s ideas in favor of complex models, and see here for an example from my own applied research.