Physics – Data Analysis – Statistics and Probability
Scientific paper
2000-09-09
Physics
Data Analysis, Statistics and Probability
15 pages, LaTeX; 19th International Workshop on Bayesian Inference and Maximum Entropy Methods (MaxEnt '99), August 2-6, 1999,
Scientific paper
Identification of local structure in intensive data -- such as time series, images, and higher dimensional processes -- is an important problem in astronomy. Since the data are typically generated by an inhomogeneous Poisson process, an appropriate model is one that partitions the data space into cells, each of which is described by a homogeneous (constant event rate) Poisson process. It is key that the sizes and locations of the cells are determined by the data, and are not predefined or even constrained to be evenly spaced. For one-dimensional time series, the method amounts to Bayesian changepoint detection. Three approaches to solving the multiple changepoint problem are sketched, based on: (1) divide and conquer with single changepoints, (2) maximum posterior for the number of changepoints, and (3) cell coalescence. The last method starts from the Voronoi tessellation of the data, and thus should easily generalize to spaces of higher dimension.
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