A kernel method for realizing Bayes’ rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The poste...

In this project, a modified version of the curvelet transform is proposed for image denoising. We introduced the complex Gaussian scale mixture (CGSM) for modeling the distribution of complex curvelet coefficients. The statistical model is then used to obtain the denoised coefficients from the noisy image decomposition by Bayes least squares estimator. Performance of the denoised images using t...

In this paper, we propse Bayes estimators of the parameters of Marshall Olkin extended exponential distribution (MOEED) introduced by Marshall-Olkin [2] for complete sample under squared error loss function (SELF). We have used different approximation techniques to obtain the Bayes estimate of the parameters. A Monte Carlo simulation study is carried out to compare the performance of proposed e...

This paper deals with the task of pameter identification using the Bayes estimation method, which makes it possible to take into account the differing consequences of positive and negative estimation errors. The calculation procedures are based on the kernel estimators technique. The final result constitutes a complete algorithm usable for specifying the value of the Bayes estimator on the basi...

The main purpose of this article is to study the wavelet shrinkage method from a Bayesian viewpoint. Nonparametric mixed-effects models are proposed and used for interpretation of the Bayesian structure. Bayes and empirical Bayes estimation are discussed. The latter is shown to have the Gauss-Markov type optimality (i.e., BLUP), to be equivalent to a method of regularization estimator (MORE), a...

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

A number of recent algorithms in signal and image processing are based on the empirical distribution of localized patches. Here, we develop a nonparametric empirical Bayesian estimator for recovering an image corrupted by additive Gaussian noise, based on fitting the density over image patches with a local exponential model. The resulting solution is in the form of an adaptively weighted averag...

This paper deals with the estimation of the stress-strength parameter R = P (Y < X) when X and Y are independent Lindley random variables with different shape parameters. The uniformly minimum variance unbiased estimator has explicit expression, however, its exact or asymptotic distribution is very difficult to obtain. The maximum likelihood estimator of the unknown parameter can also be obtain...

Regularized techniques, also named as kernel-based are the major advances in system identification last decade. Although many promising results have been achieved, their theoretical analysis is far from complete and there still key problems to be solved. One of them asymptotic theory, which about convergence properties model estimators sample size goes infinity. The existing related for regular...