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Local Independence

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
Pl(yl | x)

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

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