  This paper describes how to specify probability models for data analysis via
a backward induction procedure. The new approach yields coherent, prior-free
uncertainty assessment. After presenting some intuition-building examples, the
new approach is applied to a kernel density estimator, which leads to a novel
method for computing point-wise credible intervals in nonparametric density
estimation. The new approach has two additional advantages; 1) the posterior
mean density can be accurately approximated without resorting to Monte Carlo
simulation and 2) concentration bounds are easily established as a function of
sample size.
