Model specification via sequential coherence and backward induction

TL;DR

This paper introduces a backward induction method for specifying probability models that ensures coherence and prior-free uncertainty quantification, with applications to kernel density estimation and credible interval computation.

Contribution

It presents a novel backward induction approach for model specification that improves uncertainty assessment and simplifies credible interval calculation in nonparametric density estimation.

Findings

Enables accurate posterior mean density approximation without Monte Carlo methods

Provides concentration bounds as a function of sample size

Offers a coherent, prior-free framework for uncertainty quantification

Abstract

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.