G-test - Relation To Mutual Information

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:

    Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.
    Ralph Waldo Emerson (1803–1882)

    There is a certain standard of grace and beauty which consists in a certain relation between our nature, such as it is, weak or strong, and the thing which pleases us. Whatever is formed according to this standard pleases us, be it house, song, discourse, verse, prose, woman, birds, rivers, trees, room, dress, and so on. Whatever is not made according to this standard displeases those who have good taste.
    Blaise Pascal (1623–1662)

    Then, anger
    was a crease in the brow
    and silence
    a catastrophe.
    Then, making up
    was a mutual smile
    and a glance
    a gift.
    Now, just look at this mess
    that you’ve made of that love.
    You grovel at my feet
    and I berate you
    and can’t let my anger go.
    Amaru (c. seventh century A.D.)

    We hear a great deal of lamentation these days about writers having all taken themselves to the colleges and universities where they live decorously instead of going out and getting firsthand information about life. The fact is that anybody who has survived his childhood has enough information about life to last him the rest of his days.
    Flannery O’Connor (1925–1964)