Mathematical models in science usually have free parameters that should ideally be estimated from empirical data. Sometimes, however, model parameters cannot be estimated because pertinent empirical data are simply not available. A colleague and I are looking for examples of such models in the scientific literature (economics, biology, medicine, physics etc.), and we would be grateful for any pointers. Specifically, these would be models that had some heuristic value (e.g., through generating predictions for various plausible parameter combinations), despite the fact that the parameters could not directly be estimated.
The attached papers contain some examples where predictions are made without reliable parameter values, in some cases having heuristic value.
The most detail is in my 1979 MSc thesis, available from U Sydney. also Dorn's thesis (U Regensburg 1981)
Amended on 22 July 2018
I have recently reached to the conclusion that Normal distribution or Gauss distribution is not present in Nature, although it is surely present in Mathematics. Then, I have always used Non-parametric statistics in my research papers (please see file; Dr. Terentyeva Urine BIN). Biotin (vitamin H) concentrations in humans and foodstuffs are also distributed non-parametric manner (please see file; Wide Range of Biotin).
Further, median life-span of humans is estimated as c.a. 750 years by using linear regression and non-parametric statistics due to kind discussion with physicist Dr. Kenji Nishi (studied semi-conductor at MIT) (please see Fig. 4 of the file; J Chrom B rat BIN LIP Km).
Thus, notorious cosmological constant ( Einstein ) is not present in the Universe, since Dr. Einstein has hypothesized that Universe is symmetric and parametric.
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