Related papers: Bias-Variance Trade-off and Model Selection for Pr…
[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to…
Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior…
The methods of Bayesian statistics are used to extract the value of the proton radius from the elastic $ep$ scattering data in a model independent way. To achieve that goal a large number of parametrizations (equivalent to neural network…
Background: The "proton radius puzzle" refers to an eight-year old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using…
Extracting the proton charge radius from electron scattering data requires determining the slope of the charge form factor at $Q^2$ of zero. But as experimental data never reach that limit, numerous methods for making the extraction have…
A puzzling discrepancy exists between the values of the proton charge radius obtained using different experimental techniques: elastic electron-proton scattering and spectroscopy of electronic and muonic hydrogen. The proton radius is…
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
This paper applies the minimum message length principle to inference of linear regression models with Student-t errors. A new criterion for variable selection and parameter estimation in Student-t regression is proposed. By exploiting…
For many classification and regression problems, a large number of features are available for possible use - this is typical of DNA microarray data on gene expression, for example. Often, for computational or other reasons, only a small…
Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.We study several hypotheses that enable robust estimations of the column densities and…
While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…
In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved…
Recently a high-precision measurement of the Lamb shift in muonic hydrogen has been performed. An accurate value of the proton charge radius can be extracted from this datum with a high accuracy. To do that a sufficient accuracy should be…
Regression machine learning is widely applied to predict various materials. However, insufficient materials data usually leads to a poor performance. Here, we develop a new voting data-driven method that could generally improve the…
Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and…
We perform a new analysis of electron-proton scattering data to determine the proton electric and magnetic radii, enforcing model-independent constraints from form factor analyticity. A wide-ranging study of possible systematic effects is…
We show that in previous analyses of electron-proton scattering, the uncertainties in the statistical procedure to extract the proton charge radius are underestimated. Using a fit function based on a conformal mapping, we can describe the…
A bias correction to Akaike's information criterion (AIC) is derived for seemingly unrelated regressions models. The correction is of particular use when the sample size is not much larger than the number of fitted parameters. A…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…