A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rateoptimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequen...

Motivated by applications in microwave engineering and diffusion tensor imaging, we study the problem of deconvolution density estimation on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools...

In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables plus a perturbation which is asymptotic...

The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to innuence the accuracy of the binned kernel estimators. Our results are used to compare commonly used binni...

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function and the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rateoptimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian seque...

Diffusion tensor imaging can be studied as a deconvolution density estimation problem on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the common density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools for analysis of compositions of random posit...

In the present research, free convection heat transfer from isothermal concave and convex body shapes is studied numerically. The body shapes investigated here, are bi-sphere, cylinder, prolate and cylinder with hemispherical ends; besides, they have the same height over width (H/D = 2). A Numerical simulation is implemented to obtain heat transfer and fluid flow from all of the geometries in a...

In this paper we consider two important topics: density estimation and random variate generation. We present a framework that is easily implemented using the familiar multilayer neural network. First, we develop two new methods for density estimation, a stochastic method and a related deterministic method. Both methods are based on approximating the distribution function, the density being obta...