Growth of Random Trees by Leaf Attachment
This work addresses the growth modeling of distributed ledgers as random trees, but it appears incremental as it applies existing Bayesian methods to a specific domain without major breakthroughs.
The paper tackles the problem of modeling the growth of time-ordered rooted trees through probabilistic leaf attachment, using a Bayesian approach to sample attachment points from a posterior leaf distribution, with computational examples provided.
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.