Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective.

Area of Science:

• Signal Processing
• Statistical Inference
• Robust Estimation

Background:

• Introduced intrinsically Bayesian robust filter (IBRF) for optimal filtering relative to a prior over model uncertainty.
• Previous methods were limited to model-constrained Bayesian robust filters.
• Limited optimization to filters optimal for specific models within the uncertainty class.

Purpose of the Study:

• Extend IBRF theory to scenarios with both a prior distribution and sample data.
• Develop optimal Bayesian filtering (OBF) for improved robustness and optimality.
• Demonstrate advantages of Bayesian regression within OBF for linear Gaussian models.

Main Methods:

• Extension of intrinsically Bayesian robust filter (IBRF) theory.
• Incorporation of prior distributions and sample data.
• Application of Bayesian regression within the optimal Bayesian filtering (OBF) framework.

Main Results:

• Developed optimal Bayesian filtering (OBF), achieving optimality relative to the posterior distribution.
• Extended IBRF theories for effective characteristics and canonical expansions to the OBF setting.
• Demonstrated superior performance of Bayesian regression in OBF compared to classical Bayesian approaches for linear Gaussian models.

Conclusions:

• Optimal Bayesian filtering (OBF) provides a robust framework for filtering with prior uncertainty and data.
• The developed OBF framework offers significant advantages, particularly in linear Gaussian models.
• This work advances Bayesian filtering techniques for complex random process models.