Radiological experiments, designed to study absorbed dose in irradiated microscopic biological tissues, play a central role in microdosimetry. They yield data that cannot directly reveal the distribution of charge per event, but indirectly, through appropriate models, can lead to estimates of desired quantities. In particular, the measurements can be considered as independent random variables whose distribution is a mixture of Gamma densities with unknown but related parameters. The main data processing tasks is to estimate the weights of the components from the experimentally obtained measurements, which are subsequently used for quantifying the physically meaningful distribution of ion pairs per particle crossing the irradiated tissue volume. In the paper, the processing of the mixtures is addressed, and a procedure for estimating all the unknown model parameters proposed. A Bayesian approach to the problem is adopted based on the reversible jump Markov chain Monte Carlo sampling scheme. Samples from the unknown parameters are obtained from their posterior distributions either by Gibbs sampling or by implementing the Metropolis- Hastings scheme. After convergence, the so obtained samples are used to find the estimate of all the unknowns.