The pilgrim process
Walter Dempsey, Peter McCullagh

TL;DR
The paper introduces the pilgrim process, a probabilistic model for time-to-event data with connections to survival analysis, exchangeable partitions, and well-known stochastic processes, revealing new links between these concepts.
Contribution
It presents the pilgrim process as a novel, simple, and analytically tractable model linking survival analysis, exchangeable partitions, and classical stochastic processes.
Findings
Close connection with Kaplan-Meier estimator
Analytical results on the distribution of blocks
Links to Chinese restaurant and Indian buffet processes
Abstract
Pilgrim's monopoly is a probabilistic process giving rise to a non-negative sequence that is infinitely exchangeable, a natural model for time-to-event data. The one-dimensional marginal distributions are exponential. The rules are simple, the process is easy to generate sequentially, and a simple expression is available for both the joint density and the multivariate survivor function. There is a close connection with the Kaplan-Meier estimator of the survival distribution. Embedded within the process is an infinitely exchangeable ordered partition processes connected to Markov branching processes in neutral evolutionary theory. Some aspects of the process, such as the distribution of the number of blocks, can be investigated analytically and confirmed by simulation. By ignoring the order, the embedded process can be considered as an infinitely exchangeable partition…
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Taxonomy
TopicsBayesian Methods and Mixture Models · Stochastic processes and statistical mechanics · Complex Systems and Time Series Analysis
