Double Cox cluster processes - with applications to photoactivated localization microscopy

Photoactivated localization microscopy (PALM) is an ingenious super-resolution imaging technique that produces 2D point patterns of proteins. Individual proteins may appear as small artificial clusters of points, due to multiple blinking of individual fluorophores. The proteins may also cluster together, and in such cases a pertinent model for a PALM point pattern describes clustering at two different scales. Despite the importance of the imaging technique, statistical methods for analysingPALM data have remained relatively under-studied. In the present paper, we develop a model-based framework for analysis of PALM data. We focus on a subclass of independent cluster processes, denoted double Cox cluster processes (DCCPs), for which both the parent process (of proteins) and the observed process are Cox cluster processes. Parametric models for DCCPs with a Neyman–Scott process as parent process are developed together with statistical inference procedures, based on moment methods. To illustrate the proposed methodology, we analyse a data set from a PALM acquisition. In contrast to earlier model-free methods, the analysis provides information, directly relating to the performance of the proteins. The paper also represents an independent contribution to point process theory.