Timeline for How to fit a linear model in the Bayesian way in Mathematica?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 28, 2020 at 9:18 | vote | accept | Sjoerd Smit | ||
| Jul 14, 2019 at 22:37 | history | became hot network question | |||
| Jul 14, 2019 at 18:00 | history | tweeted | twitter.com/StackMma/status/1150465091277602816 | ||
| Jul 14, 2019 at 17:10 | comment | added | Sjoerd Smit | Fair enough. Just to be clear though: my model also has a prior over the variance and the prior/posterior distributions over the fit variables is not Gaussian but a conditional product of an inverse gamma and Gaussian distribution. | |
| Jul 14, 2019 at 16:53 | comment | added | chris |
For Gaussian noise with a Gaussian prior, the MAP solution is a description of the Gaussian posterior, which is an exhaustive description of the corresponding Distribution. In any case I think people reading your post would also be interested in knowing that Mathematica now has FitRegularization now built in. The rest is linguistics IMHO.
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| Jul 14, 2019 at 15:44 | comment | added | Sjoerd Smit | @chris It depends on what you call "the solution". I you ask me, the "solution" in a Bayesian setting is always a distribution, not a value or point estimate. A MAP estimate is a reduction of said distribution to a single value, which amounts to throwing away information. However, if you want to make a MAP estimate using my code, that's easy: all of the distributions are there. Just reduce them to numbers any way you want. Mean, median, mode: your choice. | |
| Jul 14, 2019 at 15:39 | comment | added | chris | OK I am not trying to lower the interest of what you did. I believe MAP falls within the Bayesian framework. If I use say a Gaussian prior, the MAP give an exact solution, not an approximation. I guess this is just semantics though. | |
| Jul 14, 2019 at 15:26 | comment | added | Sjoerd Smit |
@chris I'm aware of the new fit regularization options. In particular, fitting with L2 regularization can be considered as an approximation to a MAP estimate with the appropriate priors. BayesianLinearRegression is meant to implement the full Bayesian treatment, not an approximation.
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| Jul 14, 2019 at 15:18 | comment | added | chris | It might be of interest to look at the option FitRegularization in FindFit | |
| S Jul 14, 2019 at 14:34 | answer | added | Sjoerd Smit | timeline score: 52 | |
| S Jul 14, 2019 at 14:34 | history | asked | Sjoerd Smit | CC BY-SA 4.0 |