Related papers: On parameter estimation in the physics lab based o…

Measurement uncertainty and experimental error are important concepts taught in undergraduate physics laboratories. Although student ideas about error and uncertainty in introductory classical mechanics lab experiments have been studied…

Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

The impact of machine learning models on healthcare will depend on the degree of trust that healthcare professionals place in the predictions made by these models. In this paper, we present a method to provide people with clinical expertise…

Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating…

The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of both aleatoric and epistemic uncertainty by variational Bayesian inference with Monte Carlo dropout to…

We introduce linear regression using physics-based basis functions optimized through the geometry of an inner product space. This method addresses the challenge of surrogate modeling with high-dimensional input, as the physics-based basis…

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of…

Machine learning algorithms have recently been used to predict students' performance in an introductory physics class. The prediction model classified students as those likely to receive an A or B or students likely to receive a grade of C,…

Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…

Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…

We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an…

The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random,…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

Computation is a central aspect of 21st century physics practice; it is used to model complicated systems, to simulate impossible experiments, and to analyze mountains of data. Physics departments and their faculty are increasingly…

We consider the problem of learning linear prediction models with model misspecification bias. In such case, the collinearity among input variables may inflate the error of parameter estimation, resulting in instability of prediction…