Related papers: Dimensional Analysis in Statistical Modelling
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Measurement bridges theory and empirics. Without measures that appropriately capture theoretical concepts, description will fail to represent reality and true causal inference will be impossible. Yet, the social sciences traffic in complex…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of…
A study is made, of families of Hamiltonians parameterized over open subsets of Banach spaces in a way which renders many interesting properties of eigenstates and thermal states analytic functions of the parameter. Examples of such…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
The behavior of photons is controlled by quantum mechanics, not as deterministic as classical optics shows. To this end, we defined a new statistic $Z$, which is equal to the variance minus the expectation or mean. Then, we established a…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…