Timeline for Bayesian updating with conjugate priors using the closed form expressions
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2022 at 20:29 | comment | added | Eric Johnson | I actually did open one stats.stackexchange.com/questions/567648/…. Though the likelihood and prior are different. | |
| Mar 13, 2022 at 20:08 | comment | added | Tim | @EricJohnson Check other questions tagged as prior we already have a few questions like this. If they don't answer your question, you can always ask a new one. | |
| Mar 13, 2022 at 19:11 | comment | added | Eric Johnson | @Tim, Let's say you have calibration data set: $ \{ y_1, y_2, \ldots, y_k \} $ to infer the correct prior from. How would you do it? | |
| Mar 13, 2022 at 19:01 | comment | added | Tim | @EricJohnson priors are not set based on the data. | |
| Mar 13, 2022 at 18:28 | comment | added | Eric Johnson | @Tim, How could one set a reasonable values for $ \mu_{0}, \nu, \alpha, \beta $ from data? | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
|
|
| Jan 25, 2017 at 13:29 | comment | added | Tim | @DanielChorzelski as stated in the answer, this is formula when the value is known in advance. Second formula shows how to calculate mean and sd from the data. | |
| Jan 25, 2017 at 12:54 | comment | added | Daniel C | Thanks for the great answer, Tim! Sorry to keep asking, but I have one follow up question. You write: "this is formula for estimating μ when σ2 is known." Is this the posterior σ2 or the historically observed σ2 that we could use as a proxy of the variance of μ? Thanks! | |
| Jan 13, 2017 at 11:34 | history | edited | Tim | CC BY-SA 3.0 |
added 122 characters in body
|
| Sep 28, 2016 at 14:08 | vote | accept | Vasek | ||
| Sep 27, 2016 at 19:10 | history | edited | Tim | CC BY-SA 3.0 |
added 96 characters in body
|
| Sep 27, 2016 at 14:15 | history | edited | Tim | CC BY-SA 3.0 |
added 1189 characters in body
|
| Sep 2, 2016 at 6:59 | comment | added | Vasek | Let us continue this discussion in chat. | |
| Sep 1, 2016 at 16:18 | comment | added | Vasek | Well, here we want to "simulate" an outcome (posterior). Apriori, we do not know any of its parameters such that the closed form expressions could be operationalized (as you explained previously). Unless one assumes some asymptotical cases when one of the posterior parameters is exactly equal to the related parameter in the observed data sets (and the remaining parameter could be then computed). So it's not really obvious how they come up with the results without using some samplers. But this is perhaps a question to the authors of methodology that I mentioned earlier. | |
| Sep 1, 2016 at 15:17 | comment | added | Vasek | Thanks for explaining. I'll then have to find some "textbook" (meaning something practical) explanation on how to proceed such more complicated approach for the application in interest. It's sort surprising conclusion; I'm basically replicating the methodology of some authors who (in multiple papers) used this conjugate priors closed-form expressions, explicitly mentioning that this way they might overcome the need of employing MCMC samplers. | |
| Sep 1, 2016 at 15:02 | comment | added | Tim | @Vasek If it is not known then you should not use this approach... Basically, this is just a simple "textbook" example of usage of conjugate priors and most real-life application would require more complicated models (e.g. estimated using MAP or MCMC). | |
| Sep 1, 2016 at 14:59 | comment | added | Vasek | Thank you. This is useful!! My follow-up question is, how should one decide on σ2 value? In my application where I'm "updating" the large data set with the properties of the small data set, the posterior (resulting) variance is not known. | |
| Sep 1, 2016 at 14:12 | history | answered | Tim | CC BY-SA 3.0 |