Multiscale Data Analysis through Optimal Segmentation: From Photons and Stars to Galaxies and the Large Scale Structure of the Universe

Jeff Scargle
NASA Ames Research Center

A optimal segmentation algorithm, new but with a dynamic programming heritage dating back to Richard Bellman in the 1950's, can be used to detect time series structure on any scale. When the cost function to be optimized is the marginal posterior of the piece-wise constant model, the method (called Bayesian Blocks) has been applied to a number of problems in 1D astronomical data analysis. We have recently explored several other cost functions, such as a simple maximum likelihood quantity that has a useful scaling property.

For cost functions that have a simple convexity property, extension to higher dimensional data spaces is immediate. We detail this extension and show examples, such as the analysis of photon maps prevalent in high-energy astrophysics, edge detection in images, and the detection and characterization of 3D multiscale structure in galaxy redshift survey data.

Presentation (PDF File)

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