We first consider a Bayesian formalism in the wavelet domain that gives rise to the regularised linear wavelet estimator obtained in the standard nonparametric regression setting when the unknown response function belongs to a Sobolev space with non-integer regularity s > 1/2. We then use the posterior distribution of the wavelets coefficients to construct pointwise Bayesian credible intervals ...

In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using variou...

The paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis. Our method incorporates a Bayesian mixture prior for these wavelet coefficients into a Gibbs sampler to generate a complete posterior distribution for the variable of interest. Intuitively, the estimator operates by borrowing strength from those observed ne...

When making estimates of a quantum state, point estimators express one’s best guess of the true state, but estimator regions are important to express the uncertainty associated with the estimate. Employing the Bayesian approach, we discuss the use of smallest credible regions (SCRs), the smallest possible regions for given credibilities, as optimal estimator regions. However, constructing the S...

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy-like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where oth...

Abstract Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an analytical framework for drawing objective and accurate inferences on the FS of time series. The technique exploits the scaling property of the diffusion associated to a tim...

`Bussgang ' deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequence deened on the basis of channel/equalizer cascade model which involves the deenition of deconvolution noise. In this paper we consider four`Bussgang' blind deconvolution algorithms for uniformly-distributed source signals and investigate their numerical performances as...

The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the ...

‘Bussgang’ deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequence de1ned on the basis of channel=equalizer cascade model which involves the de1nition of deconvolution noise. In this paper we consider four ‘Bussgang’ blind deconvolution algorithms for uniformly distributed source signals and investigate their numerical performances as...

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...