We develop priors for Bayes estimation of quantum states that provide minimax state estimation. The relative entropy from the true density operator to a predictive density operator is adopted as a loss function. The proposed prior maximizes the conditional Holevo mutual information, and it is a quantum version of the latent information prior in classical statistics. For one qubit system, we pro...

Current psychological theories of human causal learning and judgment focus primarily on long-run predictions: two by estimating parameters of a causal Bayes nets (though for different parameterizations), and a third through structural learning. This paper focuses on people's short-run behavior by examining dynamical versions of these three theories, and comparing their predictions to a real-wor...

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...

This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positive-part JamesStein estimator under the choice of an uninformative prior. A new approach for estimating parameters and hyperparameters in general hierarchical Bayes mod...

We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under logarithmic loss, we show that in the finite space setting, when it is possible to construct an estimator of the limits with vanishing error with n samples, it...

Classical approaches to estimating the rate of occurrence of events perform poorly when data are few. Maximum Likelihood Estimators result in overly optimistic point estimates of zero for situations where there have been no events. Alternative empirical based approaches have been proposed based on median estimators or noninformative prior distributions. While these alternatives offer an improve...

The naive Bayes classifier has proved to be very effective on many real data applications. Its performance usually benefits from an accurate estimation of univariate conditional probabilities and from variable selection. However, although variable selection is a desirable feature, it is prone to overfitting. In this paper, we introduce a Bayesian regularization technique to select the most prob...

A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is the point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not an inner product space and conventional Bayes estimators therefore stand without their usual decision theoretic foundation. W...

Bayes filtering techniques have been successfully used for a variety of tasks, for instance to navigate a robot through a museum [27] or to track diverse objects [10]. Many of these probabilistic search techniques are based on Markov and Monte-Carlo methods and allow the robust tracking of multiple hypotheses. The basis of every Bayes-based filtering technique is its likelihood model. For visio...

The empirical Bayes estimator is applied to software failures production. The time between failures data registered up to a given time, are used in order to estimate the probability of failure appearance during the next interval time. This method is similar to the estimation of n-grams in natural language processing. A modified expression to the estimator usually used in language and speech pro...