Related papers: Standard vs. Generalized Chiral Perturbation Theor…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
A brief introduction to the low-energy effective field theory of the standard model, chiral perturbation theory, is presented.
Universal outlier hypothesis testing refers to a hypothesis testing problem where one observes a large number of length-$n$ sequences -- the majority of which are distributed according to the typical distribution $\pi$ and a small number…
We analyze the baryon mass differences up to second order in chiral perturbation theory, including the effects of decuplet intermediate states. We show that the Coleman--Glashow relation has computable corrections of order $(m_d - m_u)…
The $T$-test is probably the most popular statistical test; it is routinely recommended by the textbooks. The applicability of the test relies upon the validity of normal or Student's approximation to the distribution of Student's statistic…
Pearson's chi-square tests are among the most commonly applied statistical tools across a wide range of scientific disciplines, including medicine, engineering, biology, sociology, marketing and business. However, its usage in some areas is…
We present a detailed analysis of epsilon'/epsilon within the Standard Model, taking into account the strong enhancement through final-state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at…
Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still…
Relational models generalize log-linear models to arbitrary discrete sample spaces by specifying effects associated with any subsets of their cells. A relational model may include an overall effect, pertaining to every cell after a…
Elastic pion-pion and pion-nucleon scattering are reviewed in the context of chiral perturbation theory. Theoretical results from systematic low-energy expansions to O(p^6) for pion-pion and to O(p^3) for pion-nucleon scattering are…
We present a dispersive method which allows to investigate the low-energy couplings of chiral perturbation theory at the next-to-leading order (NLO) in the 1/N(C) expansion, keeping full control of their renormalization scale dependence.…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
The score test statistic using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the…
We discuss the potential of Ginsparg-Wilson fermion simulations in the epsilon-regime of chiral perturbation theory, regarding the determination of the leading low energy constants of the effective chiral Lagrangian. It turns out to be very…
The scaling behavior of the order parameter at the chiral phase transition, the so-called magnetic equation of state, of strongly interacting matter is studied within effective models. We explore universal and nonuniversal structures near…
We extend our previous study of elastic pion-nucleon scattering in the framework of chiral perturbation theory by performing a combined analysis of the reactions $\pi N \to \pi N$ and $\pi N \to \pi \pi N$. The calculation is carried out to…
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for…