Conditional Independence - Rules of Conditional Independence

Rules of Conditional Independence

A set of rules governing statements of conditional independence have been derived from the basic definition.

Note: since these implications hold for any probability space, they will still hold if considers a sub-universe by conditioning everything on another variable, say K. For example, would also mean that .

Note: below, the comma can be read as an "AND".

Read more about this topic:  Conditional Independence

Famous quotes containing the words rules of, rules, conditional and/or independence:

    There are ... two minimum conditions necessary and sufficient for the existence of a legal system. On the one hand those rules of behavior which are valid according to the system’s ultimate criteria of validity must be generally obeyed, and on the other hand, its rules of recognition specifying the criteria of legal validity and its rules of change and adjudication must be effectively accepted as common public standards of official behavior by its officials.
    —H.L.A. (Herbert Lionel Adolphus)

    One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.
    Paul Feyerabend (1924–1994)

    Conditional love is love that is turned off and on....Some parents only show their love after a child has done something that pleases them. “I love you, honey, for cleaning your room!” Children who think they need to earn love become people pleasers, or perfectionists. Those who are raised on conditional love never really feel loved.
    Louise Hart (20th century)

    Children are as destined biologically to break away as we are, emotionally, to hold on and protect. But thinking independently comes of acting independently. It begins with a two-year-old doggedly pulling on flannel pajamas during a July heat wave and with parents accepting that the impulse is a good one. When we let go of these small tasks without anger or sorrow but with pleasure and pride we give each act of independence our blessing.
    Cathy Rindner Tempelsman (20th century)