  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.
