On the consistency of Bayesian function approximation using step functions.
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.
Lian
Heng
H
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. Heng_Lian@brown.edu
D001499:Bayes Theorem; D018709:Statistics, Nonparametric