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We develop Bayesian inference methods for a recently-emerging type ofepigenetic data to study the transmission fidelity of DNA methylation patternsover cell divisions. The data consist of parent-daughter double-stranded DNAmethylation patterns with each pattern coming from a single cell andrepresented as an unordered pair of binary strings. The data are technicallydifficult and time-consuming to collect, putting a premium on an efficientinference method. Our aim is to estimate rates for the maintenance and de novomethylation events that gave rise to the observed patterns, while accountingfor measurement error. We model data at multiple sites jointly, thus usingwhole-strand information, and considerably reduce confounding betweenparameters. We also adopt a hierarchical structure that allows for variation inrates across sites without an explosion in the effective number of parameters.Our context-specific priors capture the expected stationarity, ornear-stationarity, of the stochastic process that generated the data analyzedhere. This expected stationarity is shown to greatly increase the precision ofthe estimation. Applying our model to a data set collected at the human FMR1locus, we find that measurement errors, generally ignored in similar studies,occur at a nontrivial rate (inappropriate bisulfite conversion error: 1.6$%$with 80$%$ CI: 0.9--2.3$%$). Accounting for these errors has a substantialimpact on estimates of key biological parameters. The estimated average failureof maintenance rate and daughter de novo rate decline from 0.04 to 0.024 andfrom 0.14 to 0.07, respectively, when errors are accounted for. Our resultsalso provide evidence that de novo events may occur on both parent and daughterstrands: the median parent and daughter de novo rates are 0.08 (80$%$ CI:0.04--0.13) and 0.07 (80$%$ CI: 0.04--0.11), respectively.

Statistical inference of transmission fidelity of DNA methylation patterns over somatic cell divisions in mammals