Phase transition in statistical inference of spatial information from single-cell sequencing data

A process of statistical inference can exhibit a phase transition as a function of the quantity or quality of the data used for the inference. In the "reconstructing" phase, the data is rich enough to enable the parameters to be inferred accurately, while in the "non-reconstructing" phase the data is sufficiently poor that errors in the inferred parameters grow extensively with the system size. Here we demonstrate this phase transition in a process of spatial genomics, in which the positions of cells in a biological tissue are reconstructed from single-cell sequencing data by examining correlations between the levels of DNA barcodes present within the cells. We provide analytical and numerical evidence for the transition and its critical properties using both simulated data and real experimental data collected by experiments at the Broad Institute.