Mathematics – Numerical Analysis
Scientific paper
2001-11-11
Mathematics
Numerical Analysis
19 pages, MAXENT2001: Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Scientific paper
10.1063/1.1477046
This paper describes an extension, to higher dimensions, of the Bayesian Blocks algorithm for estimating signals in noisy time series data (Scargle 1998, 2000). The mathematical problem is to find the partition of the data space with the maximum posterior probability for a model consisting of a homogeneous Poisson process for each partition element. For model M_{n}, attributing the data within region n of the data space to a Poisson process with a fixed event rate lambda_{n}, the global posterior is: P(M_{n}) = Phi(N,V) = Gamma(N+1)Gamma(V-N+1) / Gamma(V+2) = N!(V-N)!/(V+1)! . Note that lambda_{n} does not appear, since it has been marginalized, using a flat, improper prior. Other priors yield similar formulas. This expression is valid for a data space of any dimension. It depends on only N, the number of data points within the region, and V, the volume of the region. No information about the actual locations of the points enters this expression. Suppose two such regions, described by N_{1},V_{1} and N_{2},V_{2}, are candidates for being merged into one. From the above equation, construct a Bayes merge factor, giving the ratio of posteriors for the two regions merged and not merged, respectively: P(Merge) = Phi(N_{1}+N_{2},V_{1}+V_{2}) / Phi(N_{1},V_{1}) Phi(N_{2},V_{2}) . Then collect data points into blocks with a greedy cell coalescence algorithm.
No associations
LandOfFree
Bayesian Blocks in Two or More Dimensions: Image Segmentation and Cluster Analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bayesian Blocks in Two or More Dimensions: Image Segmentation and Cluster Analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bayesian Blocks in Two or More Dimensions: Image Segmentation and Cluster Analysis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-296887