Relation To Mutual Information
For analysis of contingency tables the value of G can also be expressed in terms of mutual information.
Let
- , and
Then G can be expressed in several alternative forms:
where the entropy of a discrete random variable is defined as
and where
is the mutual information between the row vector and the column vector of the contingency table.
It can also be shown that the inverse document frequency weighting commonly used for text retrieval is an approximation of G applicable when the row sum for the query is much smaller than the row sum for the remainder of the corpus. Similarly, the result of Bayesian inference applied to a choice of single multinomial distribution for all rows of the contingency table taken together versus the more general alternative of a separate multinomial per row produces results very similar to the G statistic.
Read more about this topic: G-test
Famous quotes containing the words relation to, relation, mutual and/or information:
“Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
—Honoré De Balzac (1799–1850)
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)
“For do but note a wild and wanton herd
Or race of youthful and unhandled colts
Fetching mad bounds, bellowing and neighing loud,
Which is the hot condition of their blood;
If they but hear perchance a trumpet sound,
Or any air of music touch their ears,
You shall perceive them make a mutual stand,
Their savage eyes turned to a modest gaze
By the sweet power of music.”
—William Shake{peare (1564–1616)
“As information technology restructures the work situation, it abstracts thought from action.”
—Shoshana Zuboff (b. 1951)