Statistics

2110 Submissions

[2] viXra:2110.0128 [pdf] submitted on 2021-10-22 04:13:21

Violating the Second Law of Thermodynamics in a Dynamical System Through Equivalence Closure Via Mutual Information Carriers of a 5-Tuple Measure Space

Authors: Deep Bhattacharjee
Comments: 22 Pages, 5 Figures, TechRxiv (Computations), Ergodic Theory

Time and space average of an ergodic systems following the 5-tuple relations (A,~,J,Σ,μ) through the initial increment from a+bθ to a+c+bθ indicates the entropy to be reserved in the deterministic yet dynamical and conservative systems to hold for the set S_p= S_1 ∑_(i=2)^∞_S_i keeping S as the entropy ∃(S_∞=⋯S_3=S_2 )>S_1 obeying the Poincare ́ recurrence theorem throughout the constant attractor A. This in turn states the facts of the equivalence closure as the property of the induced systems to resemblance an entropy conserving scenarios.
Category: Statistics

[1] viXra:2110.0032 [pdf] replaced on 2022-06-10 12:08:11

On the Safe Use of Prior Densities for Bayesian Model Selection

Authors: F. Llorente, L. Martino, E. Curbelo, J. Lopez-Santiago, D. Delgado
Comments: 38 Pages.

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even di use priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.
Category: Statistics