pfjax.mvn_bridge

Multivariate normal bridge proposals.

Suppose we have the multivariate normal model

       W ~ N(mu_W, Sigma_W)
   X | W ~ N(W + mu_XW, Sigma_XW)
Y | X, W ~ N(AX, Omega).

We are interested in calculating the mean and variance of p(W|Y).

Module Contents

Functions

mvn_bridge_pars(mu_W, Sigma_W, mu_XW, Sigma_XW, A, Omega)	Calculate the unconditional mean of Y, the variance of Y and the covariance between W and Y.
mvn_bridge_mv(mu_W, Sigma_W, mu_Y, AS_W, Sigma_Y, Y)	Calculate the mean and variance of p(W|Y).

pfjax.mvn_bridge.mvn_bridge_pars(mu_W, Sigma_W, mu_XW, Sigma_XW, A, Omega)

Calculate the unconditional mean of Y, the variance of Y and the covariance between W and Y.

Parameters

• mu_W – Mean of W.

• Sigma_W – Variance of W.

• mu_XW – Mean fo X|W.

• Sigma_XW – Variance of X|W.

• A – Matrix to obtain mean of Y given X,W.

• Omega – Variance of Y|X,W.

Returns

• mu_Y - Unconditional mean of Y.

• AS_W - Covariance of W, Y.

• Sigma_Y - Unconditional variance of Y.

Return type

Tuple

pfjax.mvn_bridge.mvn_bridge_mv(mu_W, Sigma_W, mu_Y, AS_W, Sigma_Y, Y)

Calculate the mean and variance of p(W|Y).

Parameters

• mu_W – Mean of W.

• Sigma_W – Variance of W.

• mu_Y – Unconditional mean of Y.

• AS_W – Covariance of Y, W.

• Sigma_Y – Unconditional variance of Y.

• Y – Observed Y.

Returns

• mu_WY - Mean of W|Y.

• Sigma_WY - Variance of W|Y.

Return type

Tuple