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Motivated by the problem of colocalization analysis in fluorescence microscopic imaging, we study in this paper structured detection of correlated regions between two random processes observed on a common domain. We argue that although intuitive, direct use of the maximum log-likelihood statistic suffers from potential bias and substantially reduced power, and introduce a simple size-based normalization to overcome this problem. We show that scanning with the proposed size-corrected likelihood ratio statistics leads to optimal correlation detection over a large collection of structured correlation detection problems.
Colocalization analysis aims to study complex spatial associations between bio-molecules via optical imaging techniques. However, existing colocalization analysis workflows only assess an average degree of colocalization within a certain region of in
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional manifold a
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. The formal equivalence of compositional data with discrete probability
Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial align
Colocalization is a powerful tool to study the interactions between fluorescently labeled molecules in biological fluorescence microscopy. However, existing techniques for colocalization analysis have not undergone continued development especially in