Timeline for Gibbs sampler with linear constraints
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2016 at 10:32 | answer | added | Davor Josipovic | timeline score: 3 | |
| Jun 11, 2014 at 20:37 | comment | added | user41037 | Very interesting, but i was wondering what happened with more random variables and more constraints ? For example : Consider the random variables : $X_1 \sim \mathcal{N_1}(m_1,\sigma_1^{2})$ $X_2 \sim \mathcal{N_2}(m_2,\sigma_2^{2})$ $X_3 \sim \mathcal{N_3}(m_3,\sigma_3^{2})$ $X_4 \sim \mathcal{N_4}(m_4,\sigma_4^{2})$ with the constraints $X_1 = X_2+X_3$ and $X_3=X_4$. | |
| Jun 11, 2014 at 18:57 | answer | added | R Hahn | timeline score: 1 | |
| Jun 11, 2014 at 18:23 | comment | added | Noah Stein | When you say sample over a polyhedron you mean condition on the sample being in that polyhedron? When you say constrain $X_1 = X_2$ you mean further condition on that event? Off-the-shelf Gibbs sampling will not handle such hard constraints and will perform very poorly (mix slowly) for softened versions of these. But given that you are working with just two univariate normals, it should be possible to work things out analytically. Am I correct in understanding that (unconditionally on the polyhedron and desired equality) $X_1$ and $X_2$ are independent? | |
| Jun 11, 2014 at 16:23 | comment | added | user41037 | I want to sample multivariate normal distributions over a polyhedra, for example over a rectangle. This problem is handle with the Gibbs sampler and gives truncated multivariate normal distributions. Hower, i don't know how to sample these distributions when are added general constraints bewteen the random variables. (like in the example.) | |
| Jun 11, 2014 at 16:21 | history | edited | user41037 | CC BY-SA 3.0 |
added 15 characters in body
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| Jun 11, 2014 at 16:16 | comment | added | Noah Stein | What do you mean by estimation over a polyhedron? | |
| Jun 11, 2014 at 15:55 | history | edited | user41037 | CC BY-SA 3.0 |
edited title
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| Jun 11, 2014 at 15:36 | history | asked | user41037 | CC BY-SA 3.0 |