Timeline for Jeffreys' prior for a discrete parameter space
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| yesterday | comment | added | Roger V. | Literature on bayesian feature selection might contain some recipes - since they are concerned with inherently discrete parameters, like the number of features in a model. | |
| 2 days ago | answer | added | Sextus Empiricus | timeline score: 1 | |
| 2 days ago | comment | added | Sextus Empiricus | @Glen_b but a prior is independent from the observation. I can see how the likelihood has the shape of a negative binomial distribution for a single observation, but for multiple observations I am not sure what it is and it deviates from a negative binomial (maybe the negative binomial isn't conjugate after all). | |
| 2 days ago | comment | added | Glen_b | If it is observed, you do know what it was. Or you can come at it from the relationship between the binomial and the negative binomial | |
| 2 days ago | comment | added | Sextus Empiricus | @Glen_b That might indeed be a conjugate prior. But the count of successes is not known, it is observed. So if we use the negative binomial as prior, then what count of successes to use? | |
| Dec 14 at 2:08 | comment | added | Glen_b | Number of trials to get a known count of successes (the observed data) would be negative binomial. | |
| Dec 13 at 16:38 | comment | added | Sextus Empiricus | Possibly another approach could be to have a multistage model with a continuous parameter that models a discrete distribution from which the parameter $n$ is obtained, and we let the variance of that distribution approach zero. Should different of such multistage models lead to the same result (same prior). | |
| Dec 13 at 16:33 | comment | added | kjetil b halvorsen♦ | Relevant: stats.stackexchange.com/questions/500781/…, stats.stackexchange.com/questions/275600/…, stats.stackexchange.com/questions/113851/…, stats.stackexchange.com/questions/588863/…, stats.stackexchange.com/questions/502124/… and search for more ... | |
| Dec 13 at 16:22 | comment | added | Sextus Empiricus | The binomial distribution has a relationship between variance and expectation like $Var[X] = (1-p) E[X]$. Are there known distributions that match that? Or otherwise we could maybe model it as a normal distribution $X \sim N(np,np(1-p))$ and for that case a Jeffreys prior should exist and might be computed. | |
| Dec 13 at 16:16 | comment | added | Sextus Empiricus | Possibly we could try some continuous analogue of a binomial distribution? That might lead to different options, but I am sure there are some more simple/desired cases among them. | |
| Dec 13 at 16:07 | history | asked | Sextus Empiricus | CC BY-SA 4.0 |