[R] Bivariate normal

[Rolf Turner]

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}}