Eli is on vacation, a little surfing now and again. Back eventually, till then there is this to ponder
Statistical mathterbation has broken out everywhere, Beenstock is back, Force X is out there, and Eli was reading Andrew Gelman who posted a useful comment from George Box on models
It is widely recognized that the advancement of learning does not proceed by conjecture alone, nor by observation alone, but by an iteration involving both. Certainly, scientific investigation proceeds by such iteration. Examination of empirical data inspires a tentative explanation which, when further exposed to reality, may lead to its modification. . . .
Now, since scientific advance, to which all statisticians must accommodate, takes place by the alternation of two different kinds of reasoning, we would expect also that two different kinds of inferential process would be re- quired to put it into effect.In the comments, Corey refers to a paper which purports to show that Kepler's model was a worse fit to the data than the Ptolemaic model, however that paper had some problems
The first, used in estimating parameters from data conditional on the truth of some tentative model, is appropriately called Estimation. The second, used in checking whether, in the light of the data, any model of the kind proposed is plausible, has been aptly named by Cuthbert Daniel Criticism.
In brief, Spanos shows that the residuals of the Keplerian model fit to Kepler’s original n = 28 data set are indistinguishable from white noise, while the residuals of the Ptolemaic model fit to a data set of one Martian year (~2 Earth years) of *daily observations from the US Navy Observatory* (n = 687) show unmistakable autocorrelation. I don’t mind telling you that my jaw literally dropped when I realized that Spanos was checking the statistical adequacy of the two models on *two different data sets*.This, however, to Eli was unimportant, because physics, chemistry and increasingly biology are built upon the principle of parsimony, and this is something that need be made much more explicit in teaching science at all levels. Realizing this, the epicycles were roadkill. Kuhn, Popper and the rest never really came to terms with the two bedrocks of science, parsimony and consistency to understand the world.
The developments of the last thirty years have provided such models for biology and climate science, but the stamp collectors have not caught up. Cladistics is useful when simplicity is lacking. Pattern recognition can be powerful, but it also masks understanding. Neural nets have no sense of guilt.