Binary De Bruijn Processes

TL;DR

This paper introduces a binary de Bruijn process for modeling binary time series data that captures temporal correlation using de Bruijn Graphs, extending beyond independent Bernoulli models.

Contribution

It proposes a novel binary process based on de Bruijn Graphs to model correlated binary sequences, with inference methods and practical applications.

Findings

The model captures long-range dependencies in binary sequences.

Application to precipitation data demonstrates improved modeling.

Analysis of boat race data shows the model's effectiveness.

Abstract

Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome successes of past events. Presented here is a novel approach for modelling binary time series data called a binary de Bruijn process which takes into account temporal correlation. The structure is derived from de Bruijn Graphs - a directed graph, where given a set of symbols, V, and a 'word' length, m, the nodes of the graph consist of all possible sequences of V of length m. De Bruijn Graphs are equivalent to mth order Markov chains, where the 'word' length controls the number of states that each individual state is dependent on. This increases correlation over a wider area. To quantify how clustered a sequence generated from a de Bruijn process is, the run lengths of letters are observed along with run length properties. Inference is also presented along with two application examples: precipitation data and the Oxford and Cambridge boat race.