A Bayesian Hierarchical Approach to Quasi-Replicate Dataset Modelling

It is very common for multiple experiments to be conducted under non-identical but similar conditions, perhaps because of implementation errors, natural variability in experimental material, or gradual drifting of experimental conditions. In the extremes of modelling, each dataset could be analysed independently or the differences ignored entirely and the datasets treated as replicates. In this paper, an alternative approach is proposed in which a common parametric family is assumed across all datasets, but which then links parameters in the separate datasets through prior models. It is assumed that knowledge exists about the relationship between the model parameters. For example, there may be some parameters which are expected to be equal, some which can be ordered, and others which follow more complex relationships. The proposed modelling approach is motivated by and illustrated using a collection of 18 autoradiography line-source experiments, which are then used to determine details of a blur function used in the analysis of electron microscope autoradiography images. Appropriate prior models are considered which contain prior parameters controlling the level of agreement with the assumption; at one extreme the analyses are independent, while at the other they are treated as replicates. The results show how the parameter estimates and goodness-of-fit depend on the level of agreement; in addition, a hyper-prior is placed on these parameters to for allow automatic analysis. Parameter estimation is performed using Markov chain Monte Carlo methods. As well as presenting a novel analysis of autoradiography data, the proposed method also provides a general framework for dealing with a wide variety of practical data analysis problems, showing potential for widespread use across the experimental sciences.