Thanks Wayne. I won't claim to have grasped all of that in a first quick read.
However I will persevere... (Like Brian in his later post) I get now the
impression now that jiggling is really rather like the Monte Carlo sampling
approach. A braver person than I (thanks TJ!) persisted with the Google search
and in fact found mention of 'jiggling' fits (and a brief commentary on its
relative merit in an obscure location, i.e. the top hit with 'jiggling
statistical error':
http://books.google.co.uk/books?id=9h2AOyACvU4C&pg=PA109&lpg=PA109&dq=jiggling+statistical+error&source=bl&ots=7205B6jUi_&sig=C_LKeMyzGNla0HFs-TbONEmIWq4&hl=en&ei=EeMCS7OEAceztgf80ej2DQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAgQ6AEwAA#v=onepage&q=jiggling%20statistical%20error&f=false
The conclusion as far as I understand is, to paraphrase, 'better to bootstrap
than to jiggle'!
Cheers,
Paul
Quoting Wayne Boucher <[log in to unmask]>:
> Hello,
>
> A good question.
>
> 'covariance':
>
> A reference for this is Numerical Recipes, chapter 15.5 (Nonlinear models)
> in the second edition (I think).
>
> The standard Levenberg-Marquardt nonlinear fitting algorithm (which
> is what we use) provides an estimate of the so-called covariance matrix.
> This includes not only estimates of the variance (so also the standard
> deviation) of the parameters (along the diagonal) but also the
> cross-correlations. The covariance estimate we use completely ignores the
> latter (so sort of assumes the parameter estimates are independent) and
> just uses the diagonal values. Even if we didn't ignore the off-diagonal
> terms apparently this is only a valid estimate if the distributions are
> "normal" (gaussian).
>
> 'bootstrap':
>
> A reference for this is:
> Bootstrap Methods for Standard Errors, Confidence Intervals and Other
> Measures of Statistical Accuracy
> B. Efron and R. Tibshirani
> Statistical Science, 1986, Vol. 1, No. 1, 54-77
>
> What this does is repeatedly sample the data points (so, the (x,y) pairs)
> over and over again. But with repeats allowed. So if you have 4 data
> points, say, (x1, y1), (x2, y2), (x3, y3), (x4, y4) then the parameters
> themselves are estimated from fitting those. But then you repeatedly
> sample those 4 points but allowing some of the values to be repeated (and
> so some ignored) and you fit that. The standard deviation of the results
> of those fittings (for each parameter separately) is taken as an estimate
> of the error for that parameter. The authors of this paper swear it's the
> way it should be done. I don't know.
>
> 'jiggling':
>
> No reference here because we made it up and I suspect it might well be
> dubious. So here we repeatedly take samples of the data using normal
> distributions around x and around y (for each point) with standard
> deviation the estimates of the "noise" in x and y (respectively). So the
> first sample would fit (x1+delta_x1, y1+delta_y1), (x2+delta_x2,
> y2+delta_y2), etc., where the deltas are sampled as described. Then you
> do the next sampling, etc. The error estimate is the standard deviation
> of each parameter. I mean this just sounds dubious to me. And it's
> pretty sensitive, we found. So I'd ignore this definitely.
>
>
> Now there is (at least) one other subtlety here, for all three methods,
> namely that the parameters that we are fitting are (quite often) not the
> parameters you are (directly) intersted in. So you might be interested in
> some value v = f(p) where p are the parameters of the fit and f is some
> function. If you have an estimate p0 for p then I would say it's probably
> ok (but not totally obvious) that you can take v0 = f(p0) as an estimate
> of v. But with errors I don't really know whether there is an accepted
> way to go from an estimate of the error of p to the error of v. You can
> try a Taylor series expansion but it's just not clear to me how valid that
> is. (It might be ok, though.)
>
> I hope that helps (a bit!).
>
> Wayne
>
> On Tue, 17 Nov 2009, Paul Driscoll wrote:
>
> > Hi,
> >
> > In the data fitting area of Analysis we are offered error handling options
> of
> > 'covariance','bootstrap' and 'jiggling'. Is there any description anywhere
> of
> > the relative merits or de-merits of these different options? Is any of
> them
> > similar or identical to using 'Monte Carlo' generation of data sets within
> the
> > uncertainties of the measured values (such is often used in some other
> > implementations and is a method that I intrinsically understand)?
> >
> > Specifically, if I am trying to extract K_D for a ligand binding series
> what is
> > the best Analysis-based way of assessing the confidence limits on the
> fitted
> > values? (i.e. ideally I don't want to have to go to another program to sort
> this
> > out.)
> >
> > [BTW, if you Google 'jiggling' you quickly run into material that can get
> one
> > fired from one's job; even 'jiggling fitting' does not help and I decided
> not to
> > go further.]
> >
> > Thanks in advance,
> > Cheers,
> > Paul
> >
> >
> > --
> > Paul C. Driscoll
> > Honorary Professor of Structural Biology
> > Structural and Molecular Biology
> > University College London
> > Gower Street
> > London WC1E 6BT, UK
> > Tel.: 44-20 7679 7035
> > Mobile: 07876 777937
> >
> > -------------------------------------------------
> > This mail sent through UCL Biochemistry's Webmail:
> > http://webmail.biochem.ucl.ac.uk/ (unsecured)
> > https://webmail.biochem.ucl.ac.uk/ (secured)
> >
>
--
Paul C. Driscoll
Honorary Professor of Structural Biology
Structural and Molecular Biology
University College London
Gower Street
London WC1E 6BT, UK
Tel.: 44-20 7679 7035
Mobile: 07876 777937
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