Timeline for How to multiply a likelihood by a prior?
Current License: CC BY-SA 4.0
11 events
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| Jun 26, 2020 at 17:44 | comment | added | jbuddy_13 | @BruceET, thank you for this informative answer! I feel a little bit sheepish...I hadn't realized that Bayesian statistics was a completely different ballgame from the frequentist approach, which I'm more familiar with. I'll need to read through this several times to absorb it all, but this is a very useful resource for getting my bearings. | |
| Jun 25, 2020 at 23:26 | comment | added | Neil G | Yeah, but I thought it fit here? After all, in your answer you talk about the beta distribution (which is over probabilities in [0, 1]). If instead, you had arbitrarily chosen the beta prime distribution (which is over odds ratios in [0, $\infty$)), then you would have run into this problem of double counting. It seems to me to be sheer luck that we live in a world that prefers probabilities to odds ratios. | |
| Jun 25, 2020 at 23:22 | comment | added | BruceET | Might be worthwhile to post your own Q&A where the difficulty you mention and how it leads to a wrong answer are are on optimal display. | |
| Jun 25, 2020 at 23:13 | comment | added | Neil G | Yeah, fair enough. I remember being very confused when I first tried to do this pointwise product of densities with the general form of exponential families. "But why isn't the product in the same exponential family anymore?" Hopefully, I've drawn the right conclusion. If not someone will correct me soon enough :) | |
| Jun 25, 2020 at 23:11 | comment | added | BruceET | @ NeilG: I'm aware of some (wouldn't ever claim all!) of the difficulties with Bayesian inference. Tried to keep the example as simple and clean as possible. (No peeking at preliminary polling results before stating the prior.) | |
| Jun 25, 2020 at 22:21 | comment | added | Neil G | This is a great answer, but you have to be careful when there's overlapping information between the prior and the likelihood, which happens when you make certain distributional assumptions for example. | |
| Jun 25, 2020 at 22:13 | history | edited | BruceET | CC BY-SA 4.0 |
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| Jun 25, 2020 at 22:04 | history | edited | BruceET | CC BY-SA 4.0 |
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| Jun 25, 2020 at 21:54 | history | edited | BruceET | CC BY-SA 4.0 |
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| Jun 25, 2020 at 21:53 | vote | accept | jbuddy_13 | ||
| Jun 25, 2020 at 21:42 | history | answered | BruceET | CC BY-SA 4.0 |