Skip to Main Content
Statistical Computing in Nuclear Imaging
book

Statistical Computing in Nuclear Imaging

by Arkadiusz Sitek
December 2014
Intermediate to advanced content levelIntermediate to advanced
275 pages
9h 12m
English
CRC Press
Content preview from Statistical Computing in Nuclear Imaging
26 Statistical Computing in Nuclear Imaging
1.8.1 CHAIN RULE AND MARGINALIZATION
T
he chain rule allows expressing the joint probability (e.g., probability distri-
bution of vector QoI) and is the generalization of Eq uation (1.6),
p( f
1
|{z}
, f
2
, f
3
, . . . , f
I
|
{z }
) = p(f
1
|f
2
, f
3
, . . . , f
I
)p(f
2
, f
3
, . . . , f
I
) (1.12)
where underbraces indicate two probability distributio ns: probability distri-
bution of f
1
and joint probability distribution f
2
, . . . , f
I
. Applying the above
I 1 additional times the original joint distribution p(f
1
, . . . , f
I
) can be ex-
pressed as a product:
p(f
1
, f
2
, f
3
, . . . , f
I
) = p(f
1
|f
2
, f
3
, . . . , f
I
)p(f
2
|f
3
, . . .
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,
and much more.
Start your free trial

You might also like

Industrial Statistics with Minitab

Industrial Statistics with Minitab

Pere Grima Cintas, Lluis Marco Almagro, Xavier Tort-Martorell Llabres
Learning Bayesian Models with R

Learning Bayesian Models with R

Hari Manassery Koduvely

Publisher Resources

ISBN: 9781439849347