Timeline for Bayesian evidence with Sequential Monte Carlo and an unnormalized likelihood function: a contradiction?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2023 at 9:01 | vote | accept | Luke Gorrie | ||
| Mar 31, 2023 at 7:37 | answer | added | Xi'an | timeline score: 1 | |
| Mar 31, 2023 at 6:46 | comment | added | Luke Gorrie | On reflection I think that I took an unfortunate leap from "the likelihood function is not normalized" to "the likelihood function is a purely relative measure used only for calculating ratios." Maybe that's true for finding the posterior in SMC but not for estimating the marginal likelihood. I think the fix is to consider the marginal likelihood to be a genuine probability density for the data conditional on the model and the parameters (which sounds kind of obvious.) Then the marginal likelihood has a sensible scale between simulations. Right? :-) | |
| Mar 30, 2023 at 17:02 | comment | added | Taylor | You'll need to be specific about what your problem is and what algorithm you're using. I suspect that the confusion arises from the different uses for SMC. One is state space models and the other is not. In the first case, "marginal" refers to integrating out latent/hidden states. If you are not using state space models, the "marginal" in marginal likelihood refers to integrating out parameters. | |
| Mar 30, 2023 at 8:02 | history | asked | Luke Gorrie | CC BY-SA 4.0 |