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Neural Computation

November 2007, Vol. 19, No. 11, Pages 2871-2880
(doi: 10.1162/neco.2007.19.11.2871)
© 2007 Massachusetts Institute of Technology
On the Consistency of Bayesian Function Approximation Using Step Functions
Article PDF (90.47 KB)
Abstract

We consider the problem of estimating a step function with an unknown number of jumps under noisy observations on a grid. Under mild assumptions, the Bayesian approach is shown to produce a consistent estimate, even when the underlying true function is not piecewise constant. A simple prior is constructed to illustrate our assumptions.