It seems useful that confidence intervals can tell us *something* about how our estimates may be imprecise with asymmetric distributions. Take something Poisson, or Gamma, or what have you. There's lots of longer tails out there and giving some kind of confidence interval points at the directions of imprecision (and where you might be able to tell less vs more) than a p-value and an effect size, no?
In my experience, I only see Poisson or Gammas in signal processing papers. In this case, people will report an expected error of their estimator. Expected error is capturing something like variance (depending on the context).
Do you have any examples of papers which claim a 95% confidence interval when the distribution is modeled as Poisson or Gaussian?
When I was at a microbiome company, we included the Poisson-like (more complex b/c proportions, but close enough) CIs on our microbiome sequencing experiments. Ended up giving some useful intuition about various strengths of signal across experiments.
atomic physicists count photons to determine if an atom is “bright” or not, i.e. to distinguish a fluorescing atom from background noise. that’s Poissonian in some limit. in that case the error bars are usually drawn as 1-sigma CIs.
Yes, this is what I mean. If it's easy and off the top of your head, could you could share a paper that uses 1-sigma CIs? I'm looking for some good examples.
It seems useful that confidence intervals can tell us *something* about how our estimates may be imprecise with asymmetric distributions. Take something Poisson, or Gamma, or what have you. There's lots of longer tails out there and giving some kind of confidence interval points at the directions of imprecision (and where you might be able to tell less vs more) than a p-value and an effect size, no?
In my experience, I only see Poisson or Gammas in signal processing papers. In this case, people will report an expected error of their estimator. Expected error is capturing something like variance (depending on the context).
Do you have any examples of papers which claim a 95% confidence interval when the distribution is modeled as Poisson or Gaussian?
When I was at a microbiome company, we included the Poisson-like (more complex b/c proportions, but close enough) CIs on our microbiome sequencing experiments. Ended up giving some useful intuition about various strengths of signal across experiments.
Do you recall which you used? And is there a public reference you can link to? I'm hoping to follow-up with a post of more CI examples.
atomic physicists count photons to determine if an atom is “bright” or not, i.e. to distinguish a fluorescing atom from background noise. that’s Poissonian in some limit. in that case the error bars are usually drawn as 1-sigma CIs.
Yes, this is what I mean. If it's easy and off the top of your head, could you could share a paper that uses 1-sigma CIs? I'm looking for some good examples.
Here's a couple papers on determining whether a single ion qubit is bright or dark:
https://arxiv.org/pdf/2112.06341.pdf . This one has a nice appendix on the error model actually
Also this one
https://arxiv.org/abs/2008.00065
Thank you!