Geometric Shrinkage Priors for Kählerian Signal Filters

Abstract

We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In particular, the ansätze related to Kähler 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.

Keywords

• Kähler manifold
• information geometry
• Bayesian prediction
• superharmonic prior