Related papers: Shape restricted regression with random Bernstein …

This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

We consider the problem of shape restricted nonparametric regression on a closed set X ?\in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a…

The Bayesian probit regression model (Albert and Chib (1993)) is popular and widely used for binary regression. While the improper flat prior for the regression coefficients is an appropriate choice in the absence of any prior information,…

To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing…

Noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing. The methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing…

There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess…

Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…

Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…

Forward regression is a classical and effective tool for variable screening in ultra-high dimensional linear models, but its standard projection-based implementation can be computationally costly and numerically unstable when predictors are…

We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

Interval-censored data are common in fields such as epidemiology and demography. When the failure event of interest is relatively rare and the collection of covariates is costly, researchers often adopt the case-cohort design to reduce…

Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…