Timeline for Generating Bernoulli Correlated Random Variables with Space Decaying Correlations
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2011 at 19:18 | vote | accept | alandalusi | ||
| Apr 27, 2011 at 18:26 | comment | added | Anthony Quas | I guess this would work as long as the covariance matrix you get stays positive definite. I don't see any reason that it should in general, whereas the previous covariance matrix for the $Y$'s is always positive definite. | |
| Apr 27, 2011 at 16:33 | comment | added | alandalusi | It works!, but I noticed that the Correlation (or Conditional Probabilities) $Pr(X{_i}=1|X{_k}=1)$ between any fixed pair (i and k) slightly change as we add more objects into the physical space. So, I changed $Cov(Y{_i},Y{_k})$ to be $w(||x{_i}-x{_k}||)$ and it worked with fixed conditional probabilities, even if I add more objects. I am still testing it, but does this make sense to you? For your information, my distance functions is $e^{(-\frac{eucaliandistance}{dcorr})}$ | |
| Apr 26, 2011 at 23:32 | comment | added | alandalusi | OK, I think I understand your suggestion now. I will test it right away. | |
| Apr 26, 2011 at 23:03 | comment | added | alandalusi | Acually, It is positive definite, but does not have a dichotomized Gaussian distribution for the correlation matrix. | |
| Apr 26, 2011 at 22:59 | comment | added | Anthony Quas | No you didn't understand me correctly. Here is my concrete suggestion. (1) Compute $t_i=\Phi^{-1}(p_i)$; (2) Compute the matrix $Cov(Y_i,Y_k)$ as above (3) Use a multivariate normal generator to build some $Y_i$'s. (4) Set $X_i=1$ if $Y_i<t_i$ and 0 otherwise. You could compute the covariance of the Bernoulli's (using the nasty integral formula I wrote down), but if your purpose is to just generate the random #s, then the procedure I described will work just as well. | |
| Apr 26, 2011 at 21:44 | comment | added | alandalusi | If i understood you correctly, what you are saying is to simply use the Cov(Yi,Yk) above as the covariance matrix and plug it in the bernoulli generator. If so, then Unfortunately, I tried that but I keep getting an Unacceptable correlation matrix, which seams to be not positive definite. | |
| Apr 20, 2011 at 18:25 | history | edited | Anthony Quas | CC BY-SA 3.0 |
added 21 characters in body; deleted 8 characters in body
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| Apr 20, 2011 at 18:17 | history | answered | Anthony Quas | CC BY-SA 3.0 |