The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in t...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i), its probability of type I error is below a pre-specifi...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specifie...

For the measurement of Ns signals in N events rigorous confidence bounds on the true signal probability pexact were established in a classical paper by Clopper and Pearson [Biometrica 26, 404 (1934)]. Here, their bounds are generalized to the HEP situation where cuts on the data tag signals with probability Ps and background data with likelihood Pb < Ps. The Fortran program which, on input of P...

The Chi-Square test (χ 2 test) is a family of tests based on a series of assumptions and is frequently used in the statistical analysis of experimental data. The aim of our paper was to present solutions to common problems when applying the Chi-square tests for testing goodness-of-fit, homogeneity and independence. The main characteristics of these three tests are presented along with various p...

BACKGROUND This work aimed to identify altered pathways in congenital heart defects (CHD) in Down syndrome (DS) by systematically tracking the dysregulated modules of reweighted protein-protein interaction (PPI) networks. MATERIAL AND METHODS We performed systematic identification and comparison of modules across normal and disease conditions by integrating PPI and gene-expression data. Based...

To clarify clinical significance of high mobility group box 1 level in inflammation asthma-chronic obstructive pulmonary disease overlap syndrome. A total 124 asthma patients acute attack (asthma group), chronic exacerbation (chronic group) and syndrome (asthma-chronic hospitalized the department geriatric respiratory medicine second our hospital from January 2020 to June 2022 were enrolled. Th...

Karl Pearson was a man of many parts: the applied mathematician who completed Todhunter's History of the Theory of Elasticity; the philosopher of science whom Lenin described as 'this conscientious and honest opponent of materialism' (1970, p. 170); the statistician who espoused the cause of evolution and edited Biometrika for 35 years; the innovator and administrator whose Department became fa...