Related papers: Quantile pyramids for Bayesian nonparametrics
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random…
Despite the practicality of quantile regression (QR), simultaneous estimation of multiple QR curves continues to be challenging. We address this problem by proposing a Bayesian nonparametric framework that generalizes the quantile pyramid…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…
Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the…
Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
We introduce a comprehensive Bayesian multivariate predictive inference framework. The basis for our framework is a hierarchical Bayesian model, that is a mixture of finite Polya trees corresponding to multiple dyadic partitions of the unit…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
This work studies the variation in Kullback-Leibler divergence between random draws from some popular nonparametric processes and their baseline measure. In particular we focus on the Dirichlet process, the P\'olya tree and the frequentist…