Analysis of measurement data subject to additive and multiplicative effects - Jagan, Kavya; Forbes, Alistair (Journal of physics. Conference series, 2018)
Many calibration problems in metrology involve fitting a model to measurement data representing the response of a system. The standard assumption about the measurement system is that the random effects associated with the measurements are drawn from the same distribution. In practice however, the uncertainty associated with the measurements may depend on the magnitude of the response being measured. For example, the measurement of displacement using laser interferometry follows such a model in which the uncertainty has a dependence on length due to the uncertainty associated with the refractive index of the air. For such systems, the model is inherently nonlinear for which standard approaches such linear least-squares estimation provide only approximate solutions. This paper describes a Bayesian approach for analysing such data. The data is modelled as a linear or non-linear response subject to additive and multiplicative noise components. We assume that prior, possibly vague, information about the variances associated with additive and multiplicative noise components is given in terms of Gamma distributions. The Bayesian posterior distribution for such models cannot be expressed analytically in closed form and a Metropolis-Hastings Markov chain Monte Carlo algorithm is used to sample from the posterior distribution. This method is illustrated on data relating to the radioactive decay of Pb211.