The effect of normalisation and error model choice on the distribution of the maximum likelihood estimator for a biochemical reaction

Sparse and noisy measurements make parameter estimation for biochemical reaction networks difficult and might lead to ill-posed optimisation problems. This is potentiated if the data has to be normalised, and only fold changes rather than absolute amounts are available. Here, the authors consider the propagation of measurement noise to the distribution of the maximum likelihood (ML) estimator in an in silico study. Therefore, a model of a reversible reaction is considered, for which reaction rate constants using fold changes is estimated. Noise propagation is analysed for different normalisation strategies and different error models. In particular, accuracy, precision, and asymptotic properties of the ML estimator is investigated. Results show that normalisation by the mean of a time series outperforms normalisation by a single time point in the example provided by the authors. Moreover, the error model with a heavy-tail distribution is slightly more robust to large measurement noise, but, beyond this, the choice of the error model did not have a significant impact on the estimation results provided by the authors.