Orthogonal Bayesian Updating, Parallel Testing and Asymptotic Convergence

In this chapter, we describe the process of Bayesian updating by means of performing sequential testing with different tests (orthogonal testing), in order to improve the performance of the screening process altogether. We provide a formal derivation for the equation for Bayesian updating with different tests, and an equivalent formulation of this equation by chaining the likelihood ratios of individual tests. We compare the properties of sequential vs. orthogonal testing, and graphically depict the positive and negative predictive value equations, demonstrating their intersectionality through domain partitions of the geometric space in S. More broadly, we demonstrate the properties of asymptotic convergence in Bayesian inference and discuss the properties and applications of parallel testing.