Empirical Distributions of Beliefs Under Imperfect Observation

Let (xn)n be a process with values in a finite set X and law P , and let yn = f(xn) be a function of the process. At stage n, pn = P (xn | x1, . . . ,xn−1), element of Π = ∆(X), is the belief of a perfect observer of the process on its realization at stage n. A statistician observing y1, . . . ,yn’s holds a belief en = P (pn | x1, . . . ,xn) ∈ ∆(Π) on the… CONTINUE READING