Geometric shrinkage priors for K\"ahlerian signal filters

TL;DR

This paper introduces geometric shrinkage priors for K"ahlerian signal filters, leveraging K"ahler manifold properties to develop efficient algorithms that outperform traditional priors, with applications to time series models.

Contribution

It presents a novel method for constructing superharmonic priors based on K"ahler geometry, enhancing Bayesian predictive performance.

Findings

Superharmonic priors outperform Jeffreys prior.

Algorithms are efficient and robust.

Applications to time series models demonstrate effectiveness.

Abstract

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.