On 2/10/2008, at 11:02 AM, Ravi Varadhan wrote:


I think it is meaningful to ask for a non-trivial Pr (X < x, Y=y) when you are writing down the likelihood for parameter estimation. This is commonly the case in likelihood estimation in bivariate failure time models. If one
interprets Pr(Y=y) as the density evaluated y then:

Pr(X<x,Y=y) = Pr(X<x | Y=y) * f(y)

In R:

Pr(X<x,Y=y) = pnorm(x, mu=mu[1] + Sigma[1,2]*(y-mu[2])/Sigma[2,2],
sd=sqrt(Sigma[1,1] - (Sigma[1,2]^2)/Sigma[2,2])) * dnorm(y, mu=mu[2],
sd=sqrt(sigma[2,2]))

Fair enough; don't know if this was what Sasha is after, but I guess it
could be.

One should be careful with one's terminology however. Loose lips sink ships.

Likelihoods are not in general probabilities which, as I am given to
understand, is why Fisher coined the usage ``likelihood'' in this context.

        cheers,

                Rolf

######################################################################
Attention:\ This e-mail message is privileged and confid...{{dropped:9}}

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Reply via email to