Timeline for Understanding likelihood vs conditional joint pdf
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2022 at 18:20 | comment | added | Xi'an | The density of the ordered sample is $n!$ times the density of the unordered one. | |
| Dec 7, 2022 at 17:13 | comment | added | mjc | @Xi'an I'm afraid I don't understand. How does the ordering of the data affect the equality of the joint pdf to the product of the individual pdfs? | |
| Dec 7, 2022 at 17:10 | comment | added | mjc | @AdamO Thanks, that's a relief to have confirmed. The proportionality you mention is actually added as a further step in the notes, which I omitted from my quote, but the notes do as quoted use the $\propto$ sign for the first step, between $f$ and the product with the proportionality constant. | |
| Dec 7, 2022 at 17:06 | comment | added | AdamO | I would agree calling $f$ a likelihood is an abuse of terminology. It's also bizarre, most obviously it's a density function, but then the "propto" symbol is there, but they have included the normalizing constant. Much easier to write $f(x|\theta) \propto \exp(c (x_i - \theta) ^2) $ | |
| Dec 7, 2022 at 17:02 | comment | added | Xi'an | Still, the density of the data could be proportional to the rhs if, e.g., the data is produced in an ordered way, with $x_1<x_2<\cdots$. | |
| Dec 7, 2022 at 16:43 | history | edited | mjc | CC BY-SA 4.0 |
added 405 characters in body
|
| Dec 7, 2022 at 16:35 | history | asked | mjc | CC BY-SA 4.0 |