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It's a bit of a philosophical thing. The data arose because of results of some large set of processes, all unobserved. Assuming a deterministic world—just for c
by tel 10y ago
It's a bit of a philosophical thing. The data arose because of results of some large set of processes, all unobserved. Assuming a deterministic world—just for convenience of argument here—there's no actual underlying distribution which caused the data. Just a big equation with too many unknowns.
In practice, though, these systems are often well-described by distributions. In common parlance for statistics, people thus sometimes like to talk about that large set of unknowns as though it really were just some arbitrarily complex distribution which we don't know: the true model.
From a frequentist perspective, the idea of the true model is very important. Many arguments arise by considering it and trying to understand how to reduce the distance between your estimators and the unknown truth.
Bayesian foundations avoid this entirely, refusing to posit an unknown and instead talking about refinements of what we know.
- obastani 10y agoIt's not just philosophical -- there are examples of practical situations where there is a true model (especially in more traditional applications of statistics): - Polling for presidential election: The "true model" is the voting preferences of all 300 million Americans. A (uniformly) random sample of N Americans can be used to estimate the true model roughly with standard error 1/sqrt(N). - Particle physics: The "true model" is the decay probabilities of various particles as computed by quantum mechanics. Different models (and parameters) yield different decay probabilities, and experiments can be used to choose between models and/or estimate model parameters. Of course, oftentimes the true model is philosophical as you describe.
- tel 10y agoThat's reasonably fair, but it's worth noting that even in these situations the true circumstance might be a little more nuanced than the idea of a "true model" suggests. - In polling, it's a bit of an ideal world idea to think that the true voting preferences of all Americans are (1) fixed, (2) consistently measurable, or (3) even relevant given a lot of people won't vote. These are all sources of unknowns and variances which make me pretty unhappy with the idea of the idea of a true model even here. - In physics there's definitely a notion of a true model taken under the assumption that one set of equations and models is "correct" (which is its own philosophical problem!) but even then experiments don't measure this true model perfectly. They're also based on correction for variance in measurement and tooling which is assumed to be eventually ignorable. In any case, this has a much more definite notion of a true model, but I still find it difficult to swallow all together.
- dllthomas 10y ago> (3) even relevant given a lot of people won't vote This bit seems trivially resolved by interpreting "voting preferences" to include likelihood of voting.