Related papers: Model error and its estimation, with particular ap…

In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…

We study the well known difficult problem of prediction in measurement error models. By targeting directly at the prediction interval instead of the point prediction, we construct a prediction interval by providing estimators of both the…

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

Model development often takes data structure, subject matter considerations, model assumptions, and goodness of fit into consideration. To diagnose issues with any of these factors, it can be helpful to understand regression model estimates…

A new type of robust estimation problem is introduced where the goal is to recover a statistical model that has been corrupted after it has been estimated from data. Methods are proposed for "repairing" the model using only the design and…

This paper considers the problem of forecasting mortality rates. A large number of models have already been proposed for this task, but they generally have the disadvantage of either estimating the model in a two-step process, possibly…

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

Deep learning models are widely used across computer vision and other domains. When working on the model induction, selecting the right architecture for a given dataset often relies on repetitive trial-and-error procedures. This procedure…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

The a posteriori analysis of the discretization error and the modeling error is studied for a compliance cost functional in the context of the optimization of composite elastic materials and a two-scale linearized elasticity model. A…

Leasing is a popular channel to market new cars. Pricing a leasing contract is complicated because the leasing rate embodies an expectation of the residual value of the car after contract expiration. To aid lessors in their pricing…

In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive…

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…

Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…