Abstract The spread of infectious disease in a human community or the proliferation fake news on social media can be modelled as randomly growing tree-shaped graph. history random growth process is often unobserved but contains important information such source infection. We consider problem statistical inference aspects latent using only single snapshot final tree. Our approach to apply labels...

For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a cor...

In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. An integrable random vector ξ in R is called swap-invariant if E ∣∣∑ j ujξj ∣∣ is invariant under all permutations of the components of ξ for each u ∈ R. Further a random sequence is swap-invariant if its finite-dimensional distributions are swap-invariant. Two characterizations of large classe...

In 1986 the International Journal of Epidemiology published "Identifiability, Exchangeability and Epidemiological Confounding". We review the article from the perspective of a quarter century after it was first drafted and relate it to subsequent developments on confounding, ignorability, and collapsibility.

We investigate the notion of a signature in Polyadic Inductive Logic and study the probability functions satisfying the Principle of Signature Exchangeability. In the binary case, we prove a representation theorem for such functions and show that they satisfy a binary version of the Principle of Instantial Relevance. We discuss polyadic versions of the Principle of Instantial Relevance and John...