examples: add binding lifetime analysis

[aafkevandenberg]

Typical DPI workflow: how to fit one or multiple exponentials to a distribution of binding lifetimes and check which model is optimal.

Docs can be found here: https://lumicks-pylake.readthedocs.io/en/binding-lifetime-example/examples/binding_lifetime/binding_lifetime.html

[JoepVanlier]

I went over it quickly once. I really like it! I like that it's a little bit more messy and requires to look at it from a practical point of view.

I will look in a bit more detail tomorrow.

[JoepVanlier]

It doesn't really test the quality of the fit itself. Even if the fits were all bad, it would still give a result that might look decent. Consider what would happen if you just fit a mean. The resulting bootstrap would probably show a pretty tight distribution even though the fit is bad.

Suggested change

	Bootstrapping is typically used in combination with maximum likelihood fitting to determine the uncertainty intervals for the fitted parameter and further test the quality of the fit.
	Bootstrapping is typically used in combination with maximum likelihood fitting to determine the uncertainty intervals for the fitted parameter. Informally, it tries to answer the question of "what if I reran this experiment many times, how would the parameter estimates scatter if I had more datasets like this one and fit them?".

[JoepVanlier]

I was wondering whether you had noticed this one.

[aafkevandenberg]

yeah, I feel this sentence is very similar to the brief intro to bootstrapping mentioned above the figure.

[JoepVanlier]

Great work!

I went through it again in more detail this time. I left a few more comments. I hope they are useful. I think one thing that would be good to separate a little bit is what we get from the method, and what is more like a decision on our part.

Second thing is that it might be worth tuning the phrasing here and there a tiny bit to make more clear which analyses are more about goodness of fit, and which about precision.

I do agree with your final conclusion that the advice here is either more data (preferred if possible) or the small model as a second option.

[JoepVanlier]

Please fix the small syntax error in the new section.

I also have one last small suggestion, but other than that, looks good to me!