Epigenetics is coming to the fore as a key process which underpins health. In particular emerging experimental evidence has associated alterations to DNA methylation status with healthspan and aging. Mammalian DNA methylation status is maintained by an intricate array of biochemical and molecular processes. It can be argued changes to these fundamental cellular processes ultimately drive the formation of aberrant DNA methylation patterns, which are a hallmark of diseases, such as cancer, Alzheimer’s disease and cardiovascular disease. In recent years mathematical models have been used as effective tools to help advance our understanding of the dynamics which underpin DNA methylation. In this paper we present linear and nonlinear models which encapsulate the dynamics of the molecular mechanisms which define DNA methylation. Applying a recently developed Bayesian algorithm for parameter estimation and model selection, we are able to estimate distributions of parameters which include nominal parameter values. Using limited noisy observations, the method also identified which methylation model the observations originated from, signaling that our method has practical applications in identifying what models best match the biological data for DNA methylation.