Related papers: Random irregular histograms
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
This paper devises a fully Bayesian sample size determination method for hierarchical model-based small area estimation with a decision risk approach. A new loss function specified around a desired maximum posterior variance target…
Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms…
The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…