Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior i...

This paper is about constructing and evaluating pointwise confidence bounds on an ROC curve. We describe four confidencebound methods, two from the medical field and two used previously in machine learning research. We evaluate whether the bounds indeed contain the relevant operating point on the “true” ROC curve with a confidence of 1−δ. We then evaluate pointwise confidence bounds on the regi...

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a 27 year old patient presented with primary infertility of 3 years' duration and also a history of myomectomy (5 years ago) was referred to our infertility clinic for investigation of infertility. the latest hysterosalpingography (hsg) revealed an obstructed left fallopian tube with apparently a unicornuate uterus with luminal contour irregularity and normal left fallopian tube (figure 1). sig...

This paper proposes a method of estimating and simulating a maximum entropy distribution given moment conditions based on MonteCarlo approach. The method provides an simple alternative to conventional calculation methods of maximum entropy densities which involve complex numerical integration and are subject to occasional failure. We first show that maximum entropy density on a random sample co...

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...