Statistical Glossary

Local Independence:

The local independence postulate plays a central role in latent variable models . Local independence means that all the manifest variable s are independent random variables if the latent variable s are controlled (fixed).

Technically, the local independence may be described by formula

P(y1, ... ,yL | x) = L Õ l=1  Pl(yl | x)

where (y₁, ... ,y_L) is the vector of all the manifest variables, x is the latent variable , P(·|x) is the conditional probability for y=(y₁,...,y_L) given x ; P_l(·|x) are conditional probabilities for each manifest variable y_l separately. If the manifest variables {y_l} are continuous, then P(·|x) and P_l( ·| X ) are probability densities, not probabilities.

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