Conditional independence, conditional mixing and conditional association

Conditional independence, conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law...

Conditional independence and natural conditional functions

The concept of conditional independence (CI) within the framework of natural conditional functions (NCFs) is studied. An NCF is a function ascribing natural numbers to possible states of the world; it is the central concept of Spohn's theory of deterministic epistemology. Basic properties of CI within this framework are recalled, and further results analogous to the results concerning probabili...

Conditional Independence

Propositional Independence Conditional independence

Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and proper...

Testing Conditional Independence using Conditional Martingale Transforms

This paper investigates testing conditional independence between Y and Z given λθ(X) for some θ ∈ Θ ⊂ R, for a function λθ(·) known upto a parameter θ ∈ Θ. First, the paper proposes a new method of conditional martingale transforms under which tests are asymptotically pivotal and asymptotically unbiased against √ n-converging Pitman local alternatives. Second, the paper performs an analysis of ...