This paper argues that two commonly-used discretization approaches, fixed k-interval discretization and entropy-based discretization have sub-optimal characteristics for naive-Bayes classification. This analysis leads to a new discretization method, Proportional k-Interval Discretization (PKID), which adjusts the number and size of discretized intervals to the number of training instances, thus...

Empirical Bayes modeling has a long and celebrated history in statistical theory and applications. After a brief review of the literature, we propose a new dynamic empirical Bayes modeling approach which provides flexible and computationally efficient methods for the analysis and prediction of longitudinal data from many individuals. This dynamic empirical Bayes approach pools the cross-section...

In this paper, we demonstrate that predicting stimulus cooccurrence patterns in a Bayes-optimal manner endogenously explains classical conditioning. Simulated experiments with a standard Bayesian implementation of this model show that it is capable of explaining a broader range of effects than any previous theory of classical conditioning. By simplifying the mathematical structure of statistica...

Many clinical decisions are made in uncertainty. When the diagnosis is uncertain, the goal is to establish a diagnosis or to treat even if the diagnosis remains unknown. If the diagnosis is known (e.g., breast cancer or prostate cancer) but the treatment is risky and its outcome uncertain, still a choice must be made. In researching the psychology of clinical judgment and decision making, the m...

1. Introduction. Compound decision theory and empirical Bayes methodology , acclaimed as " two breakthroughs " by Neyman (1962), are the most important contributions of Herbert Robbins to statistics. The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related developments. Robbins introduced compo...

Bayesian inference requires all unknowns to be represented by probability distributions, which awkwardly implies that the probability of an event for which we are completely ignorant (e.g., that the world’s greatest boxer would defeat the world’s greatest wrestler) must be assigned a particular numerical value such as 1/2, as if it were known as precisely as the probability of a truly random ev...

We suppose that the statistician observes some large number of estimates z(i), each with its own unobserved expectation parameter μ(i). The largest few of the z(i)'s are likely to substantially overestimate their corresponding μ(i)'s, this being an example of selection bias, or regression to the mean. Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach...

Let X|μ∼Np(μ,vxI ) and Y |μ∼Np(μ,vyI ) be independent p-dimensional multivariate normal vectors with common unknown mean μ. Based on only observing X = x, we consider the problem of obtaining a predictive density p̂(y|x) for Y that is close to p(y|μ) as measured by expected Kullback–Leibler loss. A natural procedure for this problem is the (formal) Bayes predictive density p̂U(y|x) under the unif...