This paper is concerned with the prediction of the conditional mean which involves the fixed and random effects based on the natural exponential family with a quadratic variance function. The best predictor is interpreted as the Bayes estimator in the Bayesian context, and the empirical Bayes estimator (EB) is useful for small area estimation in the sense of increasing precision of prediction f...

The practice of capture-recapture to estimate the diversity is well known to many animal groups, however this practice in the larval phase of anuran amphibians is incipient. We aimed at evaluating the Lincoln estimator, Venn diagram and Bayes theorem in the inference of population size of a larval phase anurocenose from lotic environment. The adherence of results was evaluated using the Kolmogo...

A simulation study was carried out for a separable fish stock assessment model including commercial and survey catch-at-age and effort data. All catches are considered stochastic variables subject to sampling and process variations. The results showed that the Bayes estimator of spawning biomass is a useful but slightly biased estimator for which the frequentist variance can be estimated by the...

Modelling and reducing uncertainty are two essential problems with mobile robot localisation. In this paper, a new robot position estimator, the Gaussian mixture of Bayes (GMB) which utilises a density estimation technique, is introduced in particular. The proposed system, namely the GMB robot position estimator, which allows a robot's position to be modelled as a probability distribution, and ...

We investigate the statistical convergence rate of a Bayesian low-rank tensor estimator, and derive the minimax optimal rate for learning a lowrank tensor. Our problem setting is the regression problem where the regression coefficient forms a tensor structure. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatiotemporal dat...

Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is often low, the usual unbiased estimator of the error variance can be unreliable. Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in r...

Abstract: We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular we establish the admissibility of generalized Bayes estim...

This work presents a new general purpose classifier named Averaged Extended Tree Augmented Naive Bayes (AETAN), which is based on combining the advantageous characteristics of Extended Tree Augmented Naive Bayes (ETAN) and Averaged One-Dependence Estimator (AODE) classifiers. We describe the main properties of the approach and algorithms for learning it, along with an analysis of its computatio...

Let y = Aβ + ε, where y is an N × 1 vector of observations, β is a p× 1 vector of unknown regression coefficients, A is an N × p design matrix and ε is a spherically symmetric error term with unknown scale parameter σ. We consider estimation of β under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer. Statist. Assoc. 73 (1978) 623–627] and Casella [A...

Identification of suitable biomarkers for accurate prediction of phenotypic outcomes is a goal for personalized medicine. However, current machine learning approaches are either too complex or perform poorly. Here, a novel two-step machine-learning framework is presented to address this need. First, a Naïve Bayes estimator is used to rank features from which the top-ranked will most likely cont...