Mathematics – Probability
Scientific paper
May 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aipc..568..132m&link_type=abstract
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 20th International Workshop. AIP Conference Proceedi
Mathematics
Probability
Probability Theory, Information Theory And Communication Theory
Scientific paper
This note deals with the entropy of a joint distribution IG=-∫∫h(x,y)ln h(x,y)dxdy (here a continuous law) and the well known decomposition IG=IX+IY-ImutXY (8) with the relative or mutual information ImutXY=K(h,fg) via Kullback K information, f and g the respective marginal densities, and IX and IY the marginal entropies for X and Y laws. But, as well, the densitiy factorizations h(x,y)=f(x)gY|X=x(x,y)=g(y)fX|Y=y(x,y) yield new formulas IG=IX+EX(IY|X)=IY+EY(IX|Y) or again IG=EX(IY|X)+EY(IX|Y)+ImutXY (7) when using conditional entropies expectations. Unlike (8), the last term in (7) is positive and therefore provides some analogies with variance decomposition. Moreover one gets also IX=EX(IY|X)+ImutXY (6) and this shows that entropy is an over additive function. .
No associations
LandOfFree
An entropy decomposition related to law's mixture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An entropy decomposition related to law's mixture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An entropy decomposition related to law's mixture will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-924014