Related papers: Functional Uniform Priors for Nonlinear Modelling

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…

Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…

We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. These parameter distributions are developed in the context of non-parametric regression…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…

Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…

We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…

We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for…

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical…

The use of flat or weakly informative priors is popular due to the objective a priori belief in the absence of strong prior information. In the case of the Weibull model the improper uniform, equal parameter gamma and joint Jeffrey's priors…

The term structure of credit spreads is studied with an aim to predict its future movements. A completely new approach to tackle this problem is presented, which utilizes nonlinear parametric models. The Brain-Cousens regression model with…

We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…

In multi-parameter models, reference priors typically depend on the parameter or quantity of interest, and it is well known that this is necessary to produce objective posterior distributions with optimal properties. There are, however,…

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…