Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] Half-Life measurement

On 10/14/21 11:31 AM, Paul Nord wrote:
New question from a colleague:
What's the chi squared value for your model?

My quick answer was: We're not optimizing for chi squared. The model is
very non-linear.

That's 100% true as stated. So far so good.

Now let's take the next step down that road.

Teachers spend all day every day dealing with ill-posed
questions. When was the last time a student came up to
you and said "I'm confused in one of the following 4
possible ways; pick one."?????

In response to an ill-posed question, usually the best path
forward is to figure out where the questioner is coming from
and answer /the question that should have been asked/.

Sometimes this involves some guesswork and some iteration.

So let's try this: For Gaussian distributions, in particular
if the overall multi-dimensional distribution is the product
of a bunch of one-dimensional Gaussians, the χ² is essentially
the /limp/ i.e. the log improbability. It isn't usually defined
that way or explained that way, but it's more-or-less equivalent.

For the decay experiment, which revolves around Poisson statistics,
χ² is the wrong question and least-squares fitting is the wrong
method ... but the idea of /limp/ survives. Least-limp fitting.
You could tell your colleague that the limp per degree of freedom
is such-and-such.

I reckon that's the answer to
the question that should have been asked.