arXiv subjects

Eduardo Ramos

Publications and source records attributed to Eduardo Ramos.

18 recordsLinked to original sources

arXiv2026

Noniterative Likelihood-Derived Estimation through Auxiliary Estimating Equations

Closed-form estimators are useful when parametric models are repeatedly refitted but likelihood maximization is iterative. We study a likelihood-derived construction of auxiliary estimating equations obtained by differentiating a positive auxiliary function and centering the derivatives under a baseline model. The resulting estimators are just-identified Z-estimators, or equivalently GMM estimators; the contribution is a constructive route to explicitly invertible equations rather than a replacement for general estimating-equation theory. We establish local existence, uniqueness and asymptotic normality of the selected root, characterize optimal linear combinations through Godambe information, and give constrained variants and influence-function diagnostics. Transformed exponential families, Beta, Weibull AFT regression, Wishart covariance estimation, zero-inflated counts, tail modelling and copula dependence illustrate the construction. Simulations and survival-tree split screening quantify the statistical-computational trade-off.

stat.ME↗

arXiv2024

On the posterior property of the Rician distribution

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles-Sustainable, Accurate, Fair, and Explainable-ensuring robustness, fairness, and transparency in predictive modeling.

stat.ME↗

arXiv2023

Objective Bayesian Analysis for the Differential Entropy of the Gamma Distribution

The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.

math.ST↗

arXiv2022

Rigorous Enclosures of Solutions of Neumann Boundary Value Problems

This paper is dedicated to the problem of isolating and validating zeros of non-linear two point boundary value problems. We present a method for such purpose based on the Newton-Kantorovich Theorem to rigorously enclose isolated zeros of two point boundary value problem with Neumann boundary conditions.

math.AP↗

arXiv2020

Posterior properties of the Weibull distribution for censored data

The Weibull distribution is one of the most used tools in reliability analysis. In this paper, assuming a Bayesian approach, we propose necessary and sufficient conditions to verify when improper priors lead to proper posteriors for the parameters of the Weibull distribution in the presence of complete or right-censored data. Additionally, we proposed sufficient conditions to verify if the obtained posterior moments are finite. These results can be achieved by checking the behavior of the improper priors, which are applied in different objective priors to illustrate the usefulness of the new results. As an application of our theorem, we prove that if the improper prior leads to a proper posterior, the posterior mean, as well as other higher moments of the scale parameter, are not finite and, therefore, should not be used.

math.ST↗

arXiv2020

On the feasibility and convergence of the inexact Newton method under minor conditions on the error terms

In this paper we introduce a semi-local theorem for the feasibility and convergence of the inexact Newton method, regarding the sequence $x_{k+1} = x_k - Df(x_k)^{-1}f(x_k) + r_k$, where $r_k$ represents the error in each step. Unlike the previous results of this type in the literature, we prove the feasibility of the inexact Newton method under the minor hypothesis that the error $r_k$ is bounded by a small constant to be computed, and moreover we prove results concerning the convergence of the sequence $x_k$ to the solution under this hypothesis. Moreover, we show how to apply this this method to compute rigorously zeros for two-point boundary value problems of Neumann type. Finally, we apply it to a version of the Cahn-Hilliard equation.

math.AP↗

arXiv2020

Power laws distributions in objective priors

The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the posterior distribution. However, these priors are typically improper and may lead to improper posterior. Here, we show, for a general family of distributions, that the obtained objective priors for the parameters either follow a power-law distribution or has an asymptotic power-law behavior. As a result, we observed that the exponents of the model are between 0.5 and 1. Understand these behaviors allow us to easily verify if such priors lead to proper or improper posteriors directly from the exponent of the power-law. The general family considered in our study includes essential models such as Exponential, Gamma, Weibull, Nakagami-m, Haf-Normal, Rayleigh, Erlang, and Maxwell Boltzmann distributions, to list a few. In summary, we show that comprehending the mechanisms describing the shapes of the priors provides essential information that can be used in situations where additional complexity is presented.

math.ST↗

arXiv2018

The Frechet distribution: Estimation and Application an Overview

In this article, we consider the problem of estimating the parameters of the Fréchet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood, method of moments, percentile estimators, L-moments, ordinary and weighted least squares, maximum product of spacings, maximum goodness-of-fit estimators and compare them with respect to mean relative estimates, mean squared errors and the 95\% coverage probability of the asymptotic confidence intervals using extensive numerical simulations. Next, we consider the Bayesian inference approach using reference priors. The Metropolis-Hasting algorithm is used to draw Markov Chain Monte Carlo samples, and they have in turn been used to compute the Bayes estimates and also to construct the corresponding credible intervals. Five real data sets related to the minimum flow of water on Piracicaba river in Brazil are used to illustrate the applicability of the discussed procedures.

stat.AP↗

arXiv2012

The short life of a droplet

This is the companion paper of the Fluid Dynamics Video "The short life of a drop" where it is argued that the geometry of the sediment of a drop of water with particles in suspension can be correlated with the dynamics of the fluid inside the drop during the drying process.

physics.flu-dyn↗

arXiv2004

Complex dynamics in simple systems with seasonal parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of $ε$-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative non-trivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

nlin.CD↗

arXiv1998

Massive spinning particles and the geometry of null curves

We study the simplest geometrical particle model associated with null paths in four-dimensional Minkowski space-time. The action is given by the pseudo-arclength of the particle worldline. We show that the reduced classical phase space of this system coincides with that of a massive spinning particle of spin $s=α^2/M$, where $M$ is the particle mass, and $α$ is the coupling constant in front of the action. Consistency of the associated quantum theory requires the spin $s$ to be an integer or half integer number, thus implying a quantization condition on the physical mass $M$ of the particle. Then, standard quantization techniques show that the corresponding Hilbert spaces are solution spaces of the standard relativistic massive wave equations. Therefore this geometrical particle model provides us with an unified description of Dirac fermions ($s=1/2$) and massive higher spin fields.

hep-th↗

arXiv1997

The reduced covariant phase space quantization of the three dimensional Nambu-Goto string

The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three translational zero modes. The symplectic structure induced trough the Enneper-Weierstrass map can be explicitly computed. Quantization is then straightforward, yielding as a result a target-space Euclidean-invariant, positive-definite, two-dimensional quantum field theory. The physical states are shown to correspond with particles states of integer spin and arbitrary mass.

hep-th↗

arXiv1997

Three dimensional strings. I. Classical theory

I consider a three-dimensional string theory whose action, besides the standard area term, contains one of the form $\int_Σ ε_{μνσ} X^μ d X^ν \wedge d X^σ$. In the case of closed strings this extra term has a simple geometrical interpretation as the volume enclosed by the surface. The associated variational problem yields as solutions constant mean curvature surfaces. One may then show the equivalence of this equation of motion to that of an SU(2) principal chiral model coupled to gravity. It is also possible by means of the Kemmotsu representation theorem, restricted to constant curvature surfaces, to map the solution space of the string model into the one of the $CP^1$ nonlinear sigma model. I also show how a description of the Gauss map of the surface in terms of SU(2) spinors allows for yet a different description of this result by means of a Gross-Neveu spinorial model coupled to 2-D gravity. The standard three-dimensional string equations can also be recovered by setting the current-current coupling to zero.

hep-th↗

arXiv1995

The Constrained KP Hierarchy and the Generalised Miura Transformation

Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.

q-alg↗

arXiv1994

On the Supersymmetric BKP-Hierarchy

We prove that the supersymmetric BKP-hierarchy of Yu (SBKP_2) is hamiltonian with respect to a nonlinear extension of the N=1 Super-Virasoro algebra (W_SBKP) by fields of spin k, where k>3/2 and 2k = 0,3 mod 4. Moreover, we show how to associate in a similar manner an N=1 W-superalgebra with every integrable hierarchy of the SKdV-type. We also show using dressing transformations how to extend, in a way which is compatible with the hamiltonian structure, the SBKP_2-hierarchy by odd flows, as well as the equivalence of this extended hierarchy to the SBKP-hierarchy of Manin-Radul.

hep-th↗

arXiv1993

Diffeomorphisms from higher dimensional W-algebras

Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a tower of infinitely many fields transforming under this subalgebra as symmetric tensorial one-densities. We also unravel a structure isomorphic to the Schouten symmetric bracket, providing a natural generalization of w_\infty in higher dimensions.

hep-th↗

arXiv1992

Higher Dimensional Classical W-Algebras

Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These $W$-algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). The two dimensional case is worked out explicitly and it is shown that the role of Diff$S(1)$ is taken by the algebra of generators of local diffeomorphisms in two dimensions.

hep-th↗

arXiv1992

The Classical Limit of W-Algebras

We define and compute explicitly the classical limit of the realizations of $W_n$ appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of pseudodifferential operators. These algebras---denoted $w_n$---have free field realizations in which the generators are given by the elementary symmetric polynomials in the free fields. We compute the algebras explicitly and we show that they are all reductions of a new algebra $w_{\rm KP}$, which is proposed as the universal classical $W$-algebra for the $w_n$ series. As a deformation of this algebra we also obtain $w_{1+\infty}$, the classical limit of $W_{1+\infty}$.

hep-th↗