Timeline for Is likelihood the y axis coordinate on the distribution curve?
Current License: CC BY-SA 4.0
17 events
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| Oct 29, 2023 at 6:55 | comment | added | Kirsten | Thanks Dave. I just wanted to confirm there wasn't something missing. I am glad you like it. | |
| Oct 24, 2023 at 21:40 | comment | added | Dave | @Kirsten I thought he explained it quite well and even mentioned in the beginning of the video that the explanation applies to continuous distributions. What do you find to be missing from his animation? | |
| Oct 24, 2023 at 21:38 | comment | added | Kirsten | Should that be a fresh question? | |
| Oct 24, 2023 at 21:22 | comment | added | Kirsten | Thanks Dave. Do you have a visual way of explaining this? Josh explains that the distributions can be moved. ~youtube.com/watch?v=pYxNSUDSFH4 | |
| Oct 23, 2023 at 20:46 | comment | added | Dave | @Kirsten There's also a philosophical diference in that the likelihood fixes a value and varies the parameters(s), while the PDF fixes the parameters and then varies the value. What this means, at least in the (absolutely) continuous case such as with a Gaussian distribution, is that the likelihood looks at the height of the PDF at, say, $x=0$ as the parameters change, such as seeing which parameter gives the highest value at $x=0$ (so $\mu=0$ for a Gaussian distribution). In contrast, the PDF would fix the parameter and then calculate how high the PDF is at $x=0$. | |
| Oct 23, 2023 at 20:38 | history | edited | Dave | CC BY-SA 4.0 |
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| Oct 23, 2023 at 20:24 | vote | accept | Kirsten | ||
| Oct 18, 2023 at 1:22 | comment | added | Dave | @Kirsten The two can coincide but do not have to. “These are sometimes the same” hardly seems like a legitimate mathematical definition. | |
| Oct 18, 2023 at 1:18 | comment | added | Kirsten | @whuber so likelihood is probability density? according to josh but not you? | |
| Oct 17, 2023 at 22:26 | comment | added | whuber♦ | @Kirsten That is correct: because probability densities can become infinite, so can likelihoods. It's virtually certain, though, that any likelihood (for any reasonable model) evaluated on data will be finite. As an example, consider a Gamma$(\theta)$ model for a single observation $x.$ When $\theta \lt 1,$ the likelihood for $x=0$ is infinite. However, the chance that $x=0$ is nil. That's the distinction between probability density and probability that the video is attempting to illustrate. | |
| Oct 17, 2023 at 21:56 | comment | added | Kirsten | The accepted one with the green tick | |
| Oct 17, 2023 at 21:37 | comment | added | Dave | @Kirsten Whose answer? | |
| Oct 17, 2023 at 21:30 | comment | added | Kirsten | Sorry. It is in the answer here ~stats.stackexchange.com/questions/4220/… | |
| Oct 17, 2023 at 21:10 | comment | added | Dave | @Kirsten What in that link makes you think that likelihood can be infinite? I did not read it in detail but did not see any such claim. | |
| Oct 17, 2023 at 21:08 | comment | added | Kirsten | I am understanding from this post that likelihood can be infinite ~stats.stackexchange.com/questions/140463/… | |
| Oct 17, 2023 at 20:45 | history | edited | Dave | CC BY-SA 4.0 |
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| Oct 17, 2023 at 0:22 | history | answered | Dave | CC BY-SA 4.0 |