world:coupling
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world:coupling [2024/06/15 11:07] rdouc |
world:coupling [2024/06/20 15:02] (current) rdouc ↷ Page moved from yazid:coupling to world:coupling |
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| - | * What is nice is that we are able to couple these random variables whereas their densities are known only up to a multiplicative constant. I wonder if it is better to couple in that way: $\pi(y) \propto Q(x,\rmd y) \alpha_{MH}(x,y)$ and $\tilde \pi(y) \propto Q(x',\rmd y) \alpha_{MH}(x',y)$. Up to some tricks, can we deduce a way of coupling two MH starting from different initial distributions, maybe with delayed coupling? Can we compare it to the coupling of Pierre Jacob et al.? | + | * What is nice is that we are able to couple these random variables whereas their densities are known only up to a multiplicative constant. I wonder if it is interesting to couple in that way: $\pi(y) \propto Q(x,\rmd y) \alpha_{MH}(x,y)$ and $\tilde \pi(y) \propto Q(x',\rmd y) \alpha_{MH}(x',y)$. Up to some tricks, can we deduce a way of coupling two MH starting from different initial distributions, maybe with delayed coupling? Can we compare it to the coupling of Pierre Jacob et al.? |
| * Moreover, if we look at the problem today, if $(\tilde X_0,X_0)=\tilde \pi \otimes \pi$ then, $(\tilde X_1,X_1)$ is a coupling of $(\tilde \pi,\pi)$, no? | * Moreover, if we look at the problem today, if $(\tilde X_0,X_0)=\tilde \pi \otimes \pi$ then, $(\tilde X_1,X_1)$ is a coupling of $(\tilde \pi,\pi)$, no? | ||
| </WRAP> | </WRAP> | ||
world/coupling.1718442471.txt.gz · Last modified: 2024/06/15 11:07 by rdouc
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