Bayesian nonparametric density estimation for doubly-truncated data

Nonparametric analysis of doubly truncated data

One of the principal goals of the quasar investigations is to study luminosity evolution. A convenient one-parameter model for luminosity says that the expected log luminosity, T ∗, increases linearly as θ0 · log(1+ Z∗), and T ∗(θ0) = T ∗ − θ0 · log(1 + Z∗) is independent of Z∗, where Z∗ is the redshift of a quasar and θ0 is the true value of evolution parameter. Due to experimental constraints...

Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

Nonparametric Functional Data Analysis through Bayesian Density Estimation

In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivitytemperature-depth (CTD) data in oceanography, dose-response models in epidemiology and time-course microarray experiments in biology and medicine. In this paper we propose a hierarchical model that allows us...

Categorization as nonparametric Bayesian density estimation 1 Running head: CATEGORIZATION AS NONPARAMETRIC BAYESIAN DENSITY ESTIMATION Categorization as nonparametric Bayesian density estimation

Convergence Rates in Nonparametric Bayesian Density Estimation

We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for α-smooth densities for 0 < α ≤ 2 and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts...