Timeline for Bayesian Hypothesis Testing: Bayes Factor vs Comparing the Posterior Distribution
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2021 at 14:51 | comment | added | Tom Bennett | Thanks a lot! It makes a lot of sense. This also means that as readers of these reports, we need to make a call on how much stock to put into the priors. | |
| Oct 6, 2021 at 14:32 | comment | added | Christian Hennig | Reporting both is surely not wrong. From my point of view it depends on the strength of your prior. If you have a prior that is well informed by all kinds of background knowledge that I don't have, I'll tend to trust your posterior. If the prior is just "uniform because I don't know any better" or any other default choice, your posterior doesn't really tell me more than your BF. (A heretic may then say, why do a Bayesian analysis in the first place?) | |
| Oct 6, 2021 at 13:39 | comment | added | Tom Bennett | I may be wrong about this. I was thinking about what happens when the posterior probabilities and BF suggest conflicting things. For example, if the weight of animal ,$\theta$, has a prior that is uniformly distributed on $[0, 1000]$ and H0 is $[0, 1]$, H1 $(1, 1000]$. Then $P(H_0)/P(H_1)=\frac1{99}$. If posterior probability ratio is $P(H_0|D)/P(H_1|D)=\frac1{9}$, this gives a BF of 11 but $P(H_1|D)=0.9$. So if we look at BF, we are in favor of H0 but if we look at the posterior, we are in favor of H1. Maybe we should just report both so that people can apply their own priors if they want to | |
| Oct 6, 2021 at 0:12 | comment | added | Christian Hennig | @TomBennett I don't quite get this, it sounds like a competition between them, but I don't see it as a competition. | |
| Oct 5, 2021 at 23:51 | comment | added | Tom Bennett | Thanks for the great response. They all make sense. In addition, I am thinking of another justification. Since the Bayes factor can be written as $\frac{P(H_0|D)}{P(H_1|D)}/\frac{P(H_0)}{P(H_1)}$, it feels like I can interpret it as how much the posterior probability ratio "beats" the prior probability ratio. It is a bit like how much it can beat a baseline, where the prior ratio is the baseline. Let me know how you think of this. Thanks | |
| Oct 5, 2021 at 23:47 | vote | accept | Tom Bennett | ||
| Oct 5, 2021 at 21:06 | history | answered | Christian Hennig | CC BY-SA 4.0 |