Growth of Random Trees by Leaf Attachment

TL;DR

This paper introduces a Bayesian framework for modeling the growth of random trees through probabilistic leaf attachment, with applications to distributed ledgers and other time-ordered structures.

Contribution

It develops a likelihood-based Bayesian method for simulating tree growth by leaf attachment, incorporating connectivity and prior distributions.

Findings

Successful computational examples of Bayesian tree growth.

Framework applicable to distributed ledger structures.

Provides a probabilistic model for tree evolution.

Abstract

We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the merging of directed ordered paths from leaves to the root. Combining the likelihood with an assigned prior distribution leads to a posterior leaf distribution from which we sample attachment points for new vertices. We present computational examples of such Bayesian tree growth. Although the discussion is generic, the initial motivation for the paper is the concept of a distributed ledger, which may be regarded as a time-ordered random tree that grows by probabilistic leaf attachment.