Statistics

2503 Submissions

[6] viXra:2503.0127 [pdf] submitted on 2025-03-21 20:54:38

Notes on the Jellinek-Berry Thermostated Ideal Gas

Authors: Leo T. Butler, Alireza Sharifi
Comments: 12 Pages.

This note studies Hamiltonian systems which are thermostated using the Jellinek—Berry thermostat (J. Chem. Phys. 1988; Phys. Rev. A 1988). Jellinek & Jellinek and Berry propose an extension of Nosé's thermostat (J. Chem. Phys. 1984). They introduce multiple functional parameters in order to achieve ergodicity of the thermostatted dynamics. This family of Hamiltonian thermostats aim to simulate the macro canonical ensemble of a Hamiltonian $H$ by coupling $H$ to a 1-d heat reservoir with potentialenergy $v(s)$ and kinetic energy $p^2/2Q(s)$. Our note derives a normal form for the reservoir’s potential energy; investigates when the Jellinek—Berry thermostated system admits a Nosé—Hoover reduction; and, we demonstrate that a Jellinek—Berry thermostated periodic ideal gas is completely integrable and satisfies a KAM twist condition called Rüssmann non-degeneracy. This is used to deduce that a thermostated, collision-less, non-ideal gas (i.e. one with a smooth potential energy) at sufficiently high temperatures of the reservoir has a positive measure set of invariant tori—hence, the thermostated dynamics are non-ergodic.
Category: Statistics

[5] viXra:2503.0117 [pdf] submitted on 2025-03-19 14:35:15

A Note on Gradient-Based Parameter Estimation for Energy-Based Models

Authors: L. Martino, S. Ingrassia, S. Mangano, L. Scaffidi
Comments: 12 Pages.

Energy-based models (EBMs) are an important family of models where a piece of the likelihood is intractable, and hence unknown. For this reason, the parameter estimation in EBMs is a challengefor the standard estimation methods. In this paper, we present a critical discussion of gradient-based approaches for inference in energy-based models. We provide many details of different derivations, clarify connections and differences. We give practical suggestions for the application of the different schemes. Specifically, we focus on a suitable choice of the proposal/reference density that is crucial for the performance of the gradient-based procedures.
Category: Statistics

[4] viXra:2503.0116 [pdf] submitted on 2025-03-19 15:09:21

Multioutput Feature Selection for Emulation and Sensitivity Analysis

Authors: J. Vicent, L. Martino, J. Verrelst, J. P. Rivera Caicedo, G. Camps-Valls
Comments: 26 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-11, 2024

Statistical regression methods are widely used in remote sensing applications but tend to lack physical interpretability. In this paper, we introduce a methodological framework to improve modelemulation and its understanding with machine learning feature selection. Our wrapper-forward feature selection method seamlessly integrates physics knowledge into model emulation, improving the tradeoff between accuracy and interpretability. We illustrate our methodology by applying it to atmospheric radiative transfer models in the context of global sensitivity analysis (GSA) and emulation. Our approach consistently aligns with variance-based GSA, pinpointing the critical features of aerosol properties, solar zenith angle, and water vapor. While our physically-based emulators yield only a modest accuracy improvement of 0.2% over conventional Gaussian Processes emulators, its introduction signifies a step forward to physics-aware machine learning-based emulation. The emulator performance remains steadfast, unaffected by substantial changes, further underscoring the reliability of our approach.
Category: Statistics

[3] viXra:2503.0115 [pdf] submitted on 2025-03-19 20:03:15

Multi-fidelity Gaussian Process Emulation for Atmospheric Radiative Transfer Models

Authors: J, Vicent, L. Martino, J. Verrelst, G. Camps-Valls
Comments: 28 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-10, 2023.

Atmospheric radiative transfer models (RTMs) are widely used in satellite data processing to correct for the scattering and absorption effects caused by aerosols and gas molecules in the Earth’s atmosphere. As the complexity of RTMs grows and the requirements for future Earth Observation missions become more demanding, the conventional Look-Up Table (LUT) interpolation approach faces important challenges. Emulators have been suggested as an alternative to LUT interpolation, but they arestill too slow for operational satellite data processing. Our research introduces a solution that harnesses the power of multi-fidelity methods to improve the accuracy and runtime of Gaussian Process (GP) emulators. We investigate the impact of the number of fidelity layers, dimensionality reduction, and training dataset size on the performance of multi-fidelity GP emulators. We find that an optimal multi-fidelity emulator can achieve relative errors in surface reflectance below 0.5% and performs atmospheric correction of hyperspectral PRISMA satellite data (one million pixels) in a few minutes. Additionally, we provide a suite of functions and tools for automating the creation and generation of atmospheric RTM emulators.
Category: Statistics

[2] viXra:2503.0080 [pdf] submitted on 2025-03-13 20:56:57

Bayesian Approach to Hypothesis-Based Randomness Estimation

Authors: Alexander Rozenkevich
Comments: 6 Pages.

A Bayesian method for dynamic hypothesis-based randomness estimation of a sequence of experimental data is proposed. Examples of pseudorandom number generator testing are given.
Category: Statistics

[1] viXra:2503.0079 [pdf] submitted on 2025-03-13 20:56:30

Bayesian Approach to Hypothesis-Based Randomness Estimation (in Russian)

Authors: Alexander Tozenkevich
Comments: 6 Pages.