Inference on the history of a randomly growing tree

• 成果类型: Article
• 署名作者: Crane, Harry; Xu, Min
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12428
• 发表日期: 2021
• 页码: 639-668
• 关键词: network

摘要

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modelled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains important information such as the source of the infection. We consider the problem of statistical inference on aspects of the latent history using only a single snapshot of the final tree. Our approach is to apply random labels to the observed unlabelled tree and analyse the resulting distribution of the growth process, conditional on the final outcome. We show that this conditional distribution is tractable under a shape exchangeability condition, which we introduce here, and that this condition is satisfied for many popular models for randomly growing trees such as uniform attachment, linear preferential attachment and uniform attachment on a D-regular tree. For inference of the root under shape exchangeability, we propose O(n log n) time algorithms for constructing confidence sets with valid frequentist coverage as well as bounds on the expected size of the confidence sets. We also provide efficient sampling algorithms which extend our methods to a wide class of inference problems.