Related papers: Additive interaction modelling using I-priors

The usage of machine learning methods in traditional surveys including official statistics, is still very limited. Therefore, we propose a predictor supported by these algorithms, which can be used to predict any population or subpopulation…

Scale-mixture shrinkage priors have recently been shown to possess robust empirical performance and excellent theoretical properties such as model selection consistency and (near) minimax posterior contraction rates. In this paper, the…

Quadratic regression goes beyond the linear model by simultaneously including main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive…

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…

The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the…

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function…

We propose a multi-threshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of covariates and thus…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

This two-part paper presents a new approach to predictive analysis for social processes. In Part I, we begin by identifying a class of social processes which are simultaneously important in applications and difficult to predict using…

The article develops marginal models for multivariate longitudinal responses. Overall, the model consists of five regression submodels, one for the mean and four for the covariance matrix, with the latter resulting by considering various…

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the…

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

Additive Gaussian process (GP) models offer flexible tools for modelling complex non-linear relationships and interaction effects among covariates. While most studies have focused on predictive performance, relatively little attention has…

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

We have built PRISM, a "Probabilistic Regression Instrument for Simulating Models". PRISM uses the Bayes linear approach and history matching to construct an approximation ('emulator') of any given model, by combining limited model…

Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

Designing reward functions is a challenging problem in AI and robotics. Humans usually have a difficult time directly specifying all the desirable behaviors that a robot needs to optimize. One common approach is to learn reward functions…