Application of Kähler manifold to signal processing and Bayesian inference

We review the information geometry of linear systems and Bayesian inference, and the simplification available in the K\"{a}hler manifold case. We find conditions for information geometry of linear systems to be K\"{a}hler, and the relation of the K\"{a}hler potential to information geometric quantities such as $\alpha $-divergence, information distance and the dual $\alpha $-connection structure. The K\"{a}hler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the $\alpha $-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the K\"{a}hler case. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the K\"{a}hler structure.