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Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of molecules in living cells. Such inference allows to understand and determine the organization and function of the cell. The trajectories of particles (e.g., single molecules or proteins) in living cells, computed with the help of object tracking methods, can be modeled with diffusion processes. Three types of diffusion are considered : (i) free diffusion (equivalently Brownian motion); (ii) subdiffusion and (iii) superdiffusion. The Mean Square Displacement (MSD) is generally used to discriminate the three types of particle dynamics.
In the first part, I propose a non-parametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis H0 (free diffusion) is accompanied by claims of the direction of the alternative (subdiffusion or superdiffusion).
In the second part, I derive an algorithm to estimate the times at which the particle changes from one type of diffusion (superdiffusion, subdiffusion or Brownian motion) to another type of diffusion. This algorithm uses the statistic of the aforementioned test in a multiple testing context to detect the changes points.