Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis

Abstract

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.

Aging Renewal Point Processes and Exchangeability of Event Times

“…In this section we will validate our analysis against synthetic samples of events generated by some archetypal mixed renewal processes. There are different methods to generate exchangeable random variables [53,54]. We will use the procedure where one chooses randomly the parameter of a family of distributions and then select a random sequence from the distribution with the chosen parameter.…”

Aging Renewal Point Processes and Exchangeability of Event Times

“…In this section,we will validate our analysis against synthetic samples of events generated by some archetypal mixed renewal processes. There are different methods to generate exchangeable random variables [59,60]. We will use the procedure where one chooses randomly the parameter of a family of distributions and then select a random sequence from the distribution with the chosen parameter.…”