Related papers: Bayesian Nonparametric Monotone Regression
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
We propose a Bayesian nonparametric model for mixed-type bounded data, where some variables are compositional and others are interval-bounded. Compositional variables are non-negative and sum to a given constant, such as the proportion of…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
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 consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…
We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…
In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the…
The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…
This paper proposes a novel framework for manifold-valued regression and establishes its consistency as well as its contraction rate. It assumes a predictor with values in the interval $[0,1]$ and response with values in a compact…
In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…
Bayesian hierarchical methods implemented for small area estimation focus on reducing the noise variation in published government official statistics by borrowing information among dependent response values. Even the most flexible models…
In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…