Adaptive Piecewise-constant Modeling of Signals in Multidimensional Spaces

This contribution describes an analysis method for the class of problems in which data elements { e.g. mea-surements, event detections, etc. { are distributed over some region of space and/or time, or other coordinates(e.g., energy, redshift, category), with the goal of estimating the variation of some physical quantity. The non-parametric model is simply that the physical variable is constant over a nite set of segments of the data space.A dynamic programming algorithm implements such modeling of 1D data by yielding the optimal partitionof an interval. Any tness function that is additive on the partition elements can be used, but the Bayesianposterior probability distribution over partitions|marginalized over all but the geometrical parameters de ningthe partition|has proved particularly e ective. The resulting maximum a posteriori piecewise constant modelis readily extended to data spaces of higher dimension.