That’s something that Charles Margossian said in a work meeting today, referring to the idea that if a certain software feature (embedded Laplace in Stan) were made more flexible, that would complicate the API.

That was a good point, and I like the pithy phrase. It belongs in some compendium of quotations, right next to “Freedom is seldom found / by beating someone to the ground.” For now I’ll put it in the lexicon.

I guess this is related to the well-known tension between freedom and security in politics, or the tension between freedom and regularization in statistical inference. As is always the case, much depends on how you define freedom. For example, in the 8 schools, if you estimate each school separately (the no-pooling model), you’ll overfit and get bad estimates. But if you embed it into a hierarchical model (either explicitly in a Bayesian setting or implicitly by considering the complete-pooling and no-pooling models as two alternatives), then you get more reasonable estimates of the effect in each school. In some sense, the no-pooling model has the most “freedom” and the least constraint of all these options. In another sense, the hierarchical model gives you more freedom because it regularizes away the worst excesses of the fit. By analogy, a trapeze artist working with a net or safety cord has more freedom than if she is fully untethered, as the security gives her the freedom to do maneuvers more smoothly.

Ultimately, for statistical software the most user friendly thing is for it to enable users to do useful analyses. So, in that sense, embedded Laplace will make Stan more user friendly by allowing users to fit bigger and more realistic models. But there’s a price to pay in the meantime.