Timeline for Can the likelihood take values outside of the range [0, 1]?
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| Oct 14, 2022 at 16:42 | comment | added | Glen_b | I don't think it needs to be mentioned there at all; I think it's covered by the connection to density and the difference between density and probability (addressed in many questions elsewhere on site). If you have a question to ask about answers to another question that can be covered by clarifying one of the answers, you can comment (asking a question you need clarification on); otherwise post a new question (with a link to the old one for context is of value). | |
| Oct 13, 2022 at 20:38 | comment | added | Kirsten | How should I ask how likelihood > 1 fits with the discussion at stats.stackexchange.com/questions/2641/… Surely it should be mentioned there? | |
| Oct 10, 2022 at 16:25 | comment | added | User1865345 | Thanks @Glen_b; +1 from me too. | |
| Oct 10, 2022 at 15:40 | comment | added | Glen_b | I've done as requested by including clarifications from the discussion. | |
| Oct 10, 2022 at 15:40 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Oct 10, 2022 at 5:57 | comment | added | User1865345 | Please make an edit, @Glen_b, to your post: anything trivial, if you may, so that the downvote could be removed. For context, see the comment. | |
| Oct 9, 2022 at 10:57 | comment | added | Kirsten | Let us continue this discussion in chat. | |
| Oct 9, 2022 at 10:50 | comment | added | Glen_b | Certainly density can exceed 1, just as I state in my answer. Again, density is not probability: (i) Consider a uniform distribution on (0, 0.1). ... what's the height of the density at x=0.05? (ii) consider a normal, mean 0, s.d. 0.1. What's the height of the density at 0? | |
| Oct 9, 2022 at 10:28 | comment | added | Kirsten | greater than zero yes. but not exceeding 1? | |
| Oct 9, 2022 at 9:55 | comment | added | Glen_b | For a continuous random variable, the probability of the data given the parameters is indeed $0$, but in that case the likelihood is not the probability. Rather for continuous variables it's defined in terms of density. Many posts on site discuss the fact that density and probability are not the same thing. The page you link certainly shows likelihoods greater than 0. | |
| Oct 9, 2022 at 9:42 | comment | added | Kirsten | Thanks Glen. Yes it was me and I may be out of my depth. However in my course I am understanding that similar to probability, likelihood of the data given the parameters can not be greater than zero. I found khakieconomics.github.io/2018/07/14/… seeming to support this. | |
| Oct 9, 2022 at 4:36 | comment | added | Glen_b | @Kirsten Sure (as is indicated by the link in my answer) ... I'm responding to the direct question "Can the likelihood take values outside of the range [0,1]?" to which the short version of my answer is "it cannot be below 0 but it can exceed 1". If the downvote was yours, could you clarify the problem you perceive? | |
| Oct 9, 2022 at 1:38 | comment | added | Kirsten | Are we talking about likelihood of data given parameters here? | |
| Sep 4, 2019 at 0:27 | comment | added | Glen_b | In response to your first comment, Fisher defined likelihood in such a way that $\mathcal{L}(\theta;\underline{x})=c\cdot \prod_i f_{X;\theta}(x_i)$ for any $c>0$ is a likelihood function (as long as any likelihood comparisons were performed with the same $c$, naturally). | |
| Sep 4, 2019 at 0:24 | comment | added | Homero Esmeraldo | And the current wikipedia article explains it better why the likelihood can be calculated with the probability density rather than the probability itself. en.wikipedia.org/wiki/… | |
| Sep 4, 2019 at 0:11 | comment | added | Homero Esmeraldo | what do you mean that it is defined up to a multiplicative constant? The wikipedia article doesn't explain it well either. | |
| Jul 25, 2017 at 15:18 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Mar 13, 2017 at 21:14 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Mar 5, 2015 at 17:07 | history | edited | Hong Ooi | CC BY-SA 3.0 |
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| Mar 5, 2015 at 13:51 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Mar 5, 2015 at 13:46 | history | answered | Glen_b | CC BY-SA 3.0 |