September 2012
Intermediate to advanced
486 pages
10h 41m
English
Content preview from Bayesian Statistics: An Introduction, 4th Edition
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
Start your free trial
A.23 Bivariate normal distribution
The ordered pair (X, Y)T of observations has a bivariate normal distribution, denoted
if it has joint density
where
The means and variances are
and X and Y have correlation coefficient and covariance
Most properties follow from those of the ordinary, univariate and normal distribution. One point worth noting (which is clear from the form of the joint density function) is that if X and Y have a bivariate normal distribution, then they are independent if they are uncorrelated (a result which is not true in general).