byx2000.github.io
For example, suppose you measure the decay of a radioactive source at fixed times t = 0,1,2,... and fit y = A e^{-kt}. The only randomness is small measurement error with, say, SD = 0.5. The bootstrap sees the huge spread in the y-values that comes from the deterministic decay curve itself, not from noise. It interprets that structural variation as sampling variability and you end up with absurdly wide bootstrap confidence intervals that have nothing to do with the actual uncertainty in the experiment.
Maybe a residuals plot and IID tests of residuals (i.e. tests of some of the strong assumptions!) would be a better next step for the author than error estimates, but I stand by my original feedback. Right now even the simplest case of a straight line fit is reported with only exact slope & intercept (well, not exact, but to an almost surely meaningless 16 decimals!), though I guess he thought to truncate the goodness of fit measures at ~4 digits.
> That already makes strong modeling assumptions (usually including IID, Gaussian noise, etc.,) to get the parameter estimates in the first place
You lose me here - I don't agree with "usually". I guess you're thinking of examples where you are sampling from a population and estimating features of that population. There's nothing wrong with that, but that is a much smaller domain than curve fitting in general.
If you give me a set of x and y, I can fit a parametric curve that tries to minimises the average squared distance between fit and observed values of y without making any assumptions whatsoever. This is a purely mechanical, non-stochastic procedure.
For example, if you give me the points {(0,0), (1,1), (2,4), (3,9)} and the curve y = a x^b, then I'm going to fit a=1, b=2, and I certainly don't need to assume anything about the data generating process to do so. However there is no concept of a confidence interval in this example - the estimates are the estimates, the residual error is 0, and that is pretty much all that can be said.
If you go further and tell me that each of these pairs (x,y) is randomly sampled, or maybe the x is fixed and the y is sampled, then I can do more. But that is often not the case.
Suggestion: Most of the fits that you've done assume that the errors are normally distributed. It would be worthwhile adding some graphical or numerical checks on that, rather than having goodness of fit or visual inspection be the only indication if this is a faulty assumption.
It gave made for a good quick check testing some data I had.
I really like your tool and thought you might enjoy sharing it on NextGen Tools, a Product Hunt alternative: https://nxgntools.com
I’d appreciate any feedback and would love to hear your thoughts.