We consider the problem of parameter estimation for a stochastic kinetic computer model of mitochondrial DNA population dynamics. The model is an attempt to describe the hypothesised link between deletion accumulation and neuronal loss in the substantia nigra region of the human brain. As with many applications in the biological sciences, the data available to calibrate the model come from different sources and relate to two different aspects of the model; we have several independent sets of experimental data on both deletion mutation accumulation and neuron survival. Furthermore these data appear to provide somewhat conflicting information about the model parameters. We describe a modelling framework which allows us to synthesize this conflicting information and arrive at a consensus inference. In particular, random effects are incorporated into the model in order to account for between-individual heterogeneity which may be the source of the apparent conflict.