Secondly, the key result of the work is a variation on the ECM algorithm. A previously coded implementation of the ECM algorithm is employed in the current project. The dissection and analysis of this article has afforded invaluable insight into the theory and practice of the application of EMlike algorithms. The deliverables of the current project depend on a thorough understanding of the inne...

The purpose of this note is to take a few steps toward a first order logic of incomplete information, based on the idea that such a logic may be obtained by importing an essential ingredient of probability theory, conditional expectation, into the logic. The reason that we focus on conditional expectation is that it is often used to model a kind of incomplete knowledge that is of interest in it...

We introduce the notion of a Cartan envelope for regular inclusion ( C , D ) . When exists, it is unique, minimal pair into which regularly embeds. prove exists if and only has unique faithful pseudo-expectation property also give characterization using ideal intersection property. For any covering inclusion, we construct Hausdorff twisted groupoid appropriate linear functionals description in ...

In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expecta...