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A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets…
In this paper we explore the possibility of using bibliographic databases for tracking the geographic origin of surnames. Surnames are used as a proxy to determine the ethnic, genetic or geographic origin of individuals in many fields such…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection,…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
The necessary conditions (NC) that reconcile canonical probability distributions obtained from the q-maximum entropy principle, subjected to both i) the additive duality of generalized statistics and ii) normal averages expectations with…
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…
We show that the principle of entropy increase may be exactly founded on a few axioms valid not only for quantum and classical statistics, but also for a wide range of statistical processes.
Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the…
Population genetics lies at the heart of evolutionary theory. This topic forms part of many biological science curricula but is rarely taught to physics students. Since physicists are becoming increasingly interested in biological…
Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this brief report we show that the generalized canonical…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…