Timeline for Baysian Inference with beta-binomial model with different number of trials
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2023 at 14:03 | vote | accept | Anton Kerel | ||
| Aug 4, 2023 at 11:10 | comment | added | Doctor Milt | Hi @AntonKerel, the fact that your original experiment had 101 trials is already encoded in your posterior distribution for $\mu$. The number of trials in the new experiment ($N=40$) is just a fixed parameter. You know that the conditional distribution for the outcome you care about is $X|\mu \sim \mathrm{Bin}(40, \mu)$, but you want the marginal distribution. To get this, you need to integrate out $\mu$, i.e. average over all possible values of $\mu$ according to your posterior distribution. | |
| Aug 4, 2023 at 10:18 | comment | added | Anton Kerel | (you can ignore $D$ in the formula's above) | |
| Aug 4, 2023 at 10:00 | comment | added | Anton Kerel | For Binomial case, I am not sure how to write it down nicely $$ p(x=3|D, 40) = \int_{0}^{1} p(x=3|\mu, 40) p(\mu|D, 101) d\mu $$. This does not feel right since I have the posterior that has a parameter $N$=101 (2success + 99 failures) and the probability that I am trying to estimate is for $N$=40. | |
| Aug 4, 2023 at 9:51 | comment | added | Anton Kerel | Thank you @Doctor Milt. Indeed, I am interested in doing Bayesian inference and I do not want to use point estimates (Maximum a posteriori estimates aka MAP). I found a similart formula (and I understand the logic behind it) to the last one you posted. It is for Bernnoulli case $$ p(x=1|D) = \int_{0}^{1} p(x=1|\mu) p(\mu|D) d\mu = \int_{0}^{1} \mu p( \mu | D) $$. | |
| Aug 3, 2023 at 15:32 | history | answered | Doctor Milt | CC BY-SA 4.0 |