  We construct geometric shrinkage priors for K\"ahlerian signal filters. Based
on the characteristics of K\"ahler manifolds, an efficient and robust algorithm
for finding superharmonic priors which outperform the Jeffreys prior is
introduced. Several ans\"atze for the Bayesian predictive priors are also
suggested. In particular, the ans\"atze related to K\"ahler potential are
geometrically intrinsic priors to the information manifold of which the
geometry is derived from the potential. The implication of the algorithm to
time series models is also provided.
