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Motivation: Epigenetic heterogeneity within a tumour can play an importantrole in tumour evolution and the emergence of resistance to treatment. It isincreasingly recognised that the study of DNA methylation (DNAm) patterns alongthe genome -- so-called `epialleles' -- offers greater insight into epigeneticdynamics than conventional analyses which examine DNAm marks individually.  Results: We have developed a Bayesian model to infer which epialleles arepresent in multiple regions of the same tumour. We apply our method to reducedrepresentation bisulfite sequencing (RRBS) data from multiple regions of onelung cancer tumour and a matched normal sample. The model borrows informationfrom all tumour regions to leverage greater statistical power. The total numberof epialleles, the epiallele DNAm patterns, and a noise hyperparameter are allautomatically inferred from the data. Uncertainty as to which epiallele anobserved sequencing read originated from is explicitly incorporated bymarginalising over the appropriate posterior densities. The degree to whichtumour samples are contaminated with normal tissue can be estimated andcorrected for. By tracing the distribution of epialleles throughout the tumourwe can infer the phylogenetic history of the tumour, identify epialleles thatdiffer between normal and cancer tissue, and define a measure of globalepigenetic disorder.

Quantification of tumour evolution and heterogeneity via Bayesian epiallele detection