We consider the problem of understanding how DNA methylation fidelity, i.e. the preservation of methylated sites in the genome, varies across the genome and across different cell types. Our approach uses a stochastic model of DNA methylation across generations and trains it using data obtained through next generation sequencing. By training the model locally, i.e. learning its parameters based on observations in a specific genomic region, we can compare how DNA methylation fidelity varies genome-wide. In the paper, we focus on the computational challenges to scale parameter estimation to the whole-genome level, and present two methods to achieve this goal, one based on moment-based approximation and one based on simulation. We extensively tested our methods on synthetic data and on a first batch of experimental data.