Conditional distribution

A conditional distribution is the probability law of one random quantity given information about another.

Table of contents
- Conditional density Conditional distribution
- Full conditional distribution Conditional distribution

Conditional density ( $f_{Y ∣ X = x} (y)$ )

Where the marginal density

f_{X} (x)

is positive, a joint probability density determines the conditional density

f_{Y ∣ X = x} (y) = \frac{f _{X, Y} ( x , y )}{f _{X} ( x )} .

It integrates to one in

y

, and supplies conditional expectations by integrating against it. Its values on a probability-zero set of conditioning points are not fixed by the joint probability distribution.

Full conditional distribution

A full conditional distribution is the conditional law of one component of a joint model given all the other components and the observed data. A Gibbs sampler updates components by drawing from these laws.

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