Statistics

2601 Submissions

[2] viXra:2601.0127 [pdf] replaced on 2026-02-08 00:15:36

Neutrinos De-mystified[:] Do Energetic, Negligible Mass Neutrinos Violate Einstein's E=mCC?

Authors: Carl Littmann
Comments: 8 Pages.

Einstein’s Relativity Theory emphasizes that "if a body radiates a given amount of Energy, that emitting body loses a Mass equal to that emitted Energy divided by the speed of light squared". But if that lost mass can’t be fully found by adding up all the resulting products, including negligible-mass high-energy Neutrinos; where did that mass go? My paper asserts that the lost (hidden) mass was ‘injected’ into the ‘aether’, increasing aether’s mass. As Einstein even said, in 1930, "Space is Eating-Up matter!" I use that "Einstein Statement" to estimate a minimum mass density of aether in Space, i.e., a key estimate but still likely much too low. And I also show that Neutrino propagation is likely an Ethereal Pulse or Stress, like a Twisting Spring Pulse (wave), instead of a forward or backward pulse. Thus, not likely a Particle mass flying through space, like a bullet or ‘baseball’. And I give more details, and address related questions.
Category: Statistics

[1] viXra:2601.0065 [pdf] replaced on 2026-02-24 22:06:15

Importance Sampling and Contrastive Learning Schemes for Parameter Estimation in Non-Normalized Models

Authors: L. Martino, L. Scaffidi, S. Mangano
Comments: 30 Pages.

Likelihood-approximation methods and contrastive learning (CL) are two prominent approaches for inference in models with unknown partition function. In this work, we provide a detailed comparison between the likelihood approximation by Geyer's approach (GA) and CL. Rather than increasing the complexity of Geyer's method to enable comparison, as proposed in [1], we adopt the opposite strategy by simplifying CL. We introduce a class of IS-within-CL schemes that estimate the partition function via importance sampling (IS) and reduce the optimization problem to the original parameter space. This perspective motivates the development of novel variants, whose theoretical properties are analyzed and empirically compared in a replicable experimental study. The described IS-within-CL schemes yield an entire approximation of the partition function, so enabling a possible efficient Bayesian inference. An optimal independent proposal density for IS-within-CL methods and the GA is also introduced. Overall, this work contributes to a clearer unification of likelihood-approximation and CL approaches, offering both theoretical understanding and practical tools for inference in energy-based and non-normalized models. Related MATLAB and R codes are also made freely available to help the reproducibility of the results.
Category: Statistics