fips.Posterior.averaging_kernel#

Posterior.averaging_kernel(W=None)[source]#

Return the averaging kernel, of the state or of aggregates of it.

Without W, \(A = K H\), state by state (dense, n x n; formed once, the same object each time). With an aggregation \(W\), \(W A W^*\), where \(W^* = W^T (W W^T)^{-1}\) is the pseudo-inverse of \(W\): it spreads a change of the aggregates back over the state elements (for a sum, evenly over the elements summed), so \(W A W^*\) is how the aggregated estimate responds to the aggregated truth. This is the form IMI uses; \(W A W^T\) is not an averaging kernel. It is computed without the n x n kernel.

Parameters:: W (Operator | None) – An aggregation, as cov() takes it. Its rows must be linearly independent.
Returns:: n x n on the state’s space, or k x k on the aggregation’s rows.
Return type:: Operator
Raises:: ValueError – If the columns of W do not have exactly the state’s labels, or its rows are linearly dependent.