Related papers: Measurement Error Models in Astronomy
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
This article focuses on measurement error in covariates in regression analyses in which the aim is to estimate the association between one or more covariates and an outcome, adjusting for confounding. Error in covariate measurements, if…
This article reviews bias-correction models for measurement error of exposure variables in the field of nutritional epidemiology. Measurement error usually attenuates estimated slope towards zero. Due to the influence of measurement error,…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
In astronomy, there is an opportunity to enhance the practice of validating models through statistical techniques, specifically to account for measurement error uncertainties. While models are commonly used to describe observations, there…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
The paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the…
Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless.…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
A persistent challenge in astronomical machine learning is a systematic bias where predictions compress the dynamic range of true values-high values are consistently predicted too low while low values are predicted too high. Understanding…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
Data analysis methods have always been of critical importance for quantitative sciences. In astronomy, the increasing scale of current and future surveys is driving a trend towards a separation of the processes of low-level data reduction…
This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…
Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first (BCES) is a direct extension of the…
Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the…