In a classical parametric setup, a key factor in the implementation of the Empirical Bayes methodology is the incorporation of a suitable prior that is compatible with the parametric setup and yet lends to the estimation of the Bayes (shrinkage) factor in an empirical manner. The situation is more complex in semi-parametric and (ev,:,n more in) nonparametric models. Although the Dirichlet prior...

The convergence properties of a nearest neighbor rule that uses an editing procedure to reduce the number of preclassified samples and to improve the performance of the rule are developed. Editing of the preclassified samples using the three-nearest neighbor rule followed by classification using the single-nearest neighbor rule with the remaining preclassified samples appears to produce a decis...

We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain par...

This paper proposes a novel method for detecting foreground objects in nonstationary complex environments containing moving background objects. We derive a Bayes decision rule for classification of background and foreground changes based on inter-frame color co-occurrence statistics. An approach to store and fast retrieve color co-occurrence statistics is also established. In the proposed metho...

The paper undertakes a conceptual scrutiny of Bayes’ rule in terms of the nature and interpretation of its probabilistic components, which reveals that there is nothing obvious or self-evident about it. First, it is not an instantiation of the conditional probability formula because (i) it involves conditioning on the unobservable event (a hypothesis), and (ii) it ignores the gap between Plato...

In this paper, we consider the hypothesis-testing problem in the continuous one-parameter exponential family using the nonparametric empirical Bayes approach. In order to estimate an unknown marginal density and its derivative, a kernel sequence method is introduced. This method uses a sequence of kernel functions and allows the kernel index and window bandwidth to vary simultaneously. Thus imp...

a two-factor experiment with interaction between factors wherein observations follow an inverse gaussian model is considered. analysis of the experiment is approached via an empirical bayes procedure. the conjugate family of prior distributions is considered. bayes and empirical bayes estimators are derived. application of the procedure is illustrated on a data set, which has previously been an...

In the general classification context the recourse to the so-called Bayes decision rule requires to estimate the class conditional probability density functions. In this paper we propose a mixture model for the observed variables which is derived by assuming that the data have been generated by an independent factor model. Independent factor analysis is in fact a generative latent variable mode...

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten & Tibshirani 2011, Cai & Liu 2011, Mai et al. 2012, Fan et al. 2012). In this paper, we develop high-dimensional semiparametric sparse discriminant analysis (HD-SeSDA) that generalizes the normal-theory discriminant...

We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value ∞. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we prov...