A Bayesian framework for comparing the structure of spontaneous correlated activity recorded under different conditions

Distant-dependent correlations in spontaneous retinal activity are thought to be instructive in the development of the retinotopic map and eye-specific segregation maps. Many studies which seek to investigate these correlations and their role in map formation record spontaneous retinal activity from different pheno-types or experimental conditions and compare the distance-dependence of the correlations between different conditions. They seek to demonstrate that these correlations differ significantly, and this analysis is often key to the study’s conclusions. In this work, we assess the methods of inference which have been previously used to investigate this problem and conclude that they are inadequate. We propose a hierarchical Bayesian framework to model distant-dependent correlations in spontaneous retinal activity data and specify a method which uses the data to specify the form of the model. This model allows us to assess the evidence for/against differences in correlations between experimental conditions in a more robust and credible way. We demonstrate the use of this method by applying it to data from two studies of spontaneous retinal activity. We believe however the framework to be rather more general and that it can be used in a wide range of datasets where distance and correlation are substitute for other independent and dependent variables from experiments.