Modelling Correlated Bernoulli Data Part II: Inference

TL;DR

This paper develops a Bayesian inference method for the de Bruijn process, a correlated Bernoulli model, and demonstrates its application to real-world binary data such as boat race outcomes.

Contribution

It introduces a Bayesian inference approach for the de Bruijn process, extending Markov chain models to account for known correlations in binary data.

Findings

Effective inference method using Bayes' factors

Application to Oxford and Cambridge boat race data

Demonstrates modeling of correlated binary sequences

Abstract

Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the probability of a success can be dependent on the outcome successes of past events. The de Bruijn process (DBP) was introduced in Kimpton et al. [2022]. This is a correlated Bernoulli process which can be used to model binary data with known correlation. The correlation structures are included through the use of de Bruijn graphs, giving an extension to Markov chains. Given the DBP and an observed sequence of binary data, we present a method of inference using Bayes' factors. Results are applied to the Oxford and Cambridge annual boat race.