The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class of joint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present study is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context of linear Gaussian models.

中文翻译：

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具有网络先验的贝叶斯回归：最佳贝叶斯过滤视角

最近引入的固有贝叶斯鲁棒滤波器 (IBRF) 相对于不确定性类别的联合随机过程模型的先验分布提供完全最优的滤波，而以前该理论仅限于模型约束的贝叶斯鲁棒滤波器，其优化仅限于对于不确定性类别中的模型来说是最佳的过滤器。本文将 IBRF 理论扩展到不确定性类和样本数据都有先验的情况。结果是最优贝叶斯过滤 (OBF)，其中最优性与从先验和数据导出的后验分布有关。IBRF 的有效特征和规范扩展理论扩展到 OBF 设置。