Timeline for Find the variance-covariance matrix for a linear combination of multiple bivariate normal distribution?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2021 at 0:56 | comment | added | jld | @CJR looks like you’ve got it but I’m happy to add any extra details if there’s any extra points that you’d like clarification on! | |
| Jul 8, 2021 at 23:32 | vote | accept | CJR | ||
| Jul 8, 2021 at 21:59 | comment | added | CJR | Thanks for expanding. I am still not quite sure how to calculate this expected value given the information I have (the weights $c_i$, the mean vector $\mu_{mix}$, the mean vector for each bi-var normal $\mu_i$, and the var-cov matrix for each bi-var normal $\Sigma_i$) . With that information, how do I calculate this expected value? Thank you! @jld | |
| Jul 8, 2021 at 21:45 | comment | added | jld | @CJR yeah sure. I'm using the result that for a random vector $S$ with mean vector $\mu$ the variance is $\text{Var}[S] = \text E[SS^T] - \mu\mu^T$. We know $\mu$ so the only remaining thing is the first term of $\text E[SS^T]$ and that's just the expected value of the 2x2 matrices $ss^T$ weighted by the mixture density | |
| Jul 8, 2021 at 21:01 | comment | added | CJR | Thanks for updating the post. I am still but unclear how the last line produces the variance-covariance matrix for the resulting mixture bivariate normal? If you could clarify that a bit more I'd really appreciate it. @jld | |
| Jul 8, 2021 at 20:16 | comment | added | jld | @CJR i just updated for the mixture case since it seems like maybe that's what you meant? | |
| Jul 8, 2021 at 20:16 | history | edited | jld | CC BY-SA 4.0 |
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| Jul 8, 2021 at 19:30 | comment | added | jld | @CJR for sure! glad this helped | |
| Jul 8, 2021 at 19:30 | history | edited | jld | CC BY-SA 4.0 |
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| Jul 8, 2021 at 19:24 | comment | added | CJR | Thanks! This was my intuition & I appreciate the quick response. | |
| Jul 8, 2021 at 19:08 | history | answered | jld | CC BY-SA 4.0 |