12:29:15 From Vinay Kashyap to Everyone:
	https://www.aanda.org/articles/aa/full_html/2016/03/aa27395-15/aa27395-15.html
12:31:41 From Doug Burke to Everyone:
	Here's a paper I like for how astronomers look at things: https://ui.adsabs.harvard.edu/abs/2009ApJ...693..822H/abstract 
	
	χ2 and Poissonian Data: Biases Even in the High-Count Regime and How to Avoid Them
	
	(for Jeff, it includes a count-rate example as well as a spectral fit )
12:33:37 From Keith Arnaud to Everyone:
	This one count in every bin comes about in the case when there is background and you are using profile likelihood. There is no point in doing that binning in the case of no background.
12:45:55 From Herman Marshall to Everyone:
	Replying to "This one count in ev..."
	
	I’m not sure what you mean by a “profile likelihood”.  Also, I’m not sure why it might matter if there is background.
12:48:56 From Keith Arnaud to Everyone:
	Replying to "This one count in ev..."
	
	This is if you have a background and you add a model which has a free parameter for the background rate in each bin. You can then solve for these background rates to get a new statistic. It is not a true maximum likelihood estimator but is called a profile likelihood in the literature. See the statistics appendix in the xspec manual.
12:50:48 From Herman Marshall to Everyone:
	Replying to "This one count in ev..."
	
	So, this is really the case where there are many “uninteresting parameters”, which are the background rates in each bin.
12:51:29 From Keith Arnaud to Everyone:
	Replying to "This one count in ev..."
	
	Right.
12:52:44 From Herman Marshall to Everyone:
	Replying to "This one count in ev..."
	
	However, can’t there actually be zeros in the background bins *and* in the source bins?  So, binning to one count per bin would change the bins.
12:52:56 From Axel Donath to Everyone:
	Replying to "This one count in ev..."
	
	The problem with this is that the assumption is that the background rate would be uncorrelated, which for any reasonable physical model it is not…
12:54:13 From Jeff Scargle to Everyone:
	Glad to see your comment about simulations.  After all, a lot of astronomers — realizing that the statistical theory involves assumptions that may not hold, and that assumptions about the data yield other uncertainties anyway — turn to Monte Carlo studies
12:54:31 From Keith Arnaud to Everyone:
	Replying to "This one count in ev..."
	
	Hermann, people have observed that sometimes this profile likelihood fails badly for reasons I don’t understand however binning to at least one count per bin seems to solve it.
12:55:14 From Keith Arnaud to Everyone:
	Replying to "This one count in ev..."
	
	Axel, no the issue is whether the errors in the bins are correlated not whether the expected values in each bin are correlated.
12:56:17 From Jeff Scargle to Everyone:
	Replying to "This one count in ev..."
	
	Keith … yes, this is an incredibly important point that a lot of people get wrong!
12:57:08 From Herman Marshall to Everyone:
	Replying to "This one count in ev..."
	
	Hmmm, looks like we should try to understand why the profile likelihood fails if some bins are zero.  Theoretically, there should be no problem, right?
12:57:38 From Yang Chen  to Everyone:
	Thanks for the comments everyone! I just copied all of them. I need some time to process them 🙂
12:58:44 From Keith Arnaud to Everyone:
	Replying to "This one count in ev..."
	
	I yield to the statisticians on this one but my understanding is that profile likelihood does not behave like “true” likelihood. Perhaps we need to discuss this on another zoom.
12:59:06 From Jeff Scargle to Everyone:
	Replying to "This one count in ev..."
	
	I think so.  The code may not allow it.  A similar issue with analysis tools that do not cover negative flux estimates — which of course arise often in low flux situations, especially with a significanqt background.
13:04:20 From Xiao-Li Meng to Everyone:
	Replying to "This one count in ev..."
	
	Keith is right. Profile likelihood is a "quick and dirty" approximation to the Bayesian way of getting rid of nuisance parameter by maximizing over the nuisance parameter instead of integrating it over.  It is effective only when the  likelihood has a multivariate Gaussian-type of shape.
13:15:11 From Yang Chen  to Everyone:
	Would the following model make sense: y_i follows Poisson(u_i), u_i follows Gamma(a, b) and set a/b = s_i(theta)
13:15:30 From Yang Chen  to Everyone:
	The a/b there is the expectation of the Gamma distribution.
13:17:46 From Xiao-Li Meng to Everyone:
	that's very good model to try, and question is its physical interpretation, at least approximate one
13:17:57 From Justina Yang to Everyone:
	I have to leave a bit early, thank you both for the talks and thanks all for the discussion!
13:27:04 From Yang Chen  to Everyone:
	In the model that I wrote above, the likelihood from the Gamma part on the log scale is a sum of iid random variables, which is asymptotically normal, just the same as Max’s model.