Related papers: On parameter estimation in the physics lab based o…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
We aim at finding the value of an explanatory variable, through its expression in a large data-vector, without knowing the link function between the explanatory variable and the data-space. Sliced Inverse Regression (SIR) method allows for…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
Statistical estimation of the prediction uncertainty of physical models is typically hindered by the inadequacy of these models due to various approximations they are built upon. The prediction errors due to model inadequacy can be handled…
Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly…
Regression is one of the most commonly used statistical techniques. However, testing regression systems is a great challenge because of the absence of test oracle in general. In this paper, we show that Metamorphic Testing is an effective…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…
Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
This study investigated the problem posed by using ordinary least squares (OLS) to estimate parameters of simple linear regression under a specific context of special relativity, where an independent variable is restricted to an open…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
Measuring treatment effects in observational studies is challenging because of confounding bias. Confounding occurs when a variable affects both the treatment and the outcome. Traditional methods such as propensity score matching estimate…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analyzing data collected in three selected experiments taken from an introductory physics laboratory, which include a…
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…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…