Timeline for Is the invariance property of the ML estimator nonsensical from a Bayesian perspective?
Current License: CC BY-SA 3.0
14 events
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| Mar 28, 2018 at 13:58 | vote | accept | user56834 | ||
| Mar 28, 2018 at 12:33 | answer | added | pglpm | timeline score: 16 | |
| Nov 16, 2017 at 21:08 | comment | added | Sextus Empiricus | The difference (which I believe should be made more salient, and possibly even delete the part on invariance) is then more like a question that is closer to, 'what is likelihood?', than 'what is it with this invariance propety?'. The problem in the expressions here is that while likelihood is equated to a probability, it is not the same as a probability. For instance $\int p(x|a) \text{d} a \neq 1$ and you can not add two likelihoods together like you add two associated probabilities (where $P(x|a_1 \lor a_2)$ has even it's problems in non frquentists logic as well) . | |
| Nov 16, 2017 at 21:04 | comment | added | Sextus Empiricus | I can detect a difference between the questions, but maybe it requires the question to be repositioned to make this more clear. The invariance of likelihood is not broken if you use injective mappings (and this issue was in the other question), or if you use a different type of likelihood that might behave in some occasions and applied as if it is a likelihood. What this question does in addition is defining a likelihood as a probability of multiple configurations, which makes it a bit difference. a likelihood of more configurations does not make sense, and seems to be the underlying Q. | |
| Nov 16, 2017 at 19:26 | comment | added | gung - Reinstate Monica | Thank you. It is best to assume people are responding in good faith. There are (relatively few, IMHO) occasions where people here aren't, but even then, sometimes they can be coaxed to come around. | |
| Nov 16, 2017 at 19:20 | comment | added | user56834 | @gung, You are completely right. And I regret reacting with that tone. I will stop doing it from now on. Sorry for this. Regarding the conversation, I am interested in pursuing productive ones, but felt that people's reactions in a couple of questions I asked were mostly counterproductive. Nevertheless, next time, I will respond differently. | |
| Nov 16, 2017 at 18:34 | comment | added | gung - Reinstate Monica | I understand your frustration, Programmer2134 (& @MartijnWeterings). However, please be careful of your tone in your comments. Productive conversations are only possible when our be nice policy is followed. If you aren't interested in pursuing productive conversations, you need to post these questions elsewhere. | |
| Nov 15, 2017 at 22:54 | comment | added | Sextus Empiricus | The formal part after "If I apply basic rules of probability theory to the simple case wheter $\eta=\tau(\theta)=\theta^2$" does not change the question. The matter is fully covered in the excellent answer from Samuel Benidt. The likelihood values (and as a consequence the maximum) do not change due to the mapping. Yes you need to take special care if the mapping is not one-to-one. But that is a whole different issue than the changes occuring due to probability distributions when you apply a transform. | |
| Nov 15, 2017 at 21:35 | review | Close votes | |||
| Nov 27, 2017 at 13:17 | |||||
| Nov 15, 2017 at 21:15 | comment | added | Sextus Empiricus | Possible duplicate of Invariance property of maximum likelihood estimator? | |
| Nov 14, 2017 at 12:32 | history | edited | user56834 |
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| Nov 14, 2017 at 12:14 | answer | added | Xi'an | timeline score: 8 | |
| Nov 14, 2017 at 12:09 | history | edited | Xi'an | CC BY-SA 3.0 |
added 38 characters in body; edited tags
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| Nov 14, 2017 at 8:35 | history | asked | user56834 | CC BY-SA 3.0 |