Timeline for A metric stronger than total variation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 2, 2018 at 19:03 | vote | accept | Aryeh Kontorovich | ||
| Jul 2, 2018 at 15:38 | comment | added | Henry.L | They consider one sample case so only one observation $x\in\mathbb{X}$, if you want a finite sequence of observations then $\mathbb{X}^n$ or even countably many observations $\mathbb{X}^\infty$. Then sample space can be chosen as you wish and the metric can be generalized easily. Or am I missing sth more subtle? | |
| Jul 2, 2018 at 15:35 | comment | added | Aryeh Kontorovich | But where is the maximum over subsets? I only see maximum over points. | |
| Jul 2, 2018 at 15:35 | comment | added | Henry.L | If we take the definition here: en.wikipedia.org/wiki/Posterior_predictive_distribution Then $Y=\mathbb{R}$ in that paper is the parameter space and $\mathbb{X}$ is the sample space on which you usually draw samples. | |
| Jul 2, 2018 at 15:31 | comment | added | Henry.L | Yes. $P,Q$ in OP are measure corresponding to posterior predictive densities in my mind, in that paper they only defined posteriors so in order to yield them to be defined on the same (finite) $\mathbb{X}$ you only have to yield the corresponding posterior predictive measure. The conditioned set $A$ is the observation. Of course you are right that $\mathbb{X}\neq \mathbb{R}$ for posteriors in Bayesian literature mostly. | |
| Jul 2, 2018 at 15:14 | comment | added | Aryeh Kontorovich | It seems that their metric is defined on distributions over a product space. I don't see how their definition yields mine, would you be able to elaborate? | |
| Jul 2, 2018 at 15:00 | history | answered | Henry.L | CC BY-SA 4.0 |