Gaussian Confidence Intervals Research Articles

Consistent and accurate estimation of stellar parameters from HARPS-N Spectroscopy using Deep Learning

Consistent and accurate estimation of stellar parameters is of great importance for information retrieval in astrophysical research. The parameters span a wide range from effective temperature to rotational velocity. We propose to estimate the stellar parameters directly from spectral signals coming from the HARPS-N spectrograph pipeline before any spectrum-processing steps are applied to extract the 1D spectrum. We propose an attention-based model to estimate the stellar parameters, which estimate both mean and uncertainty of the stellar parameters through estimation of the parameters of a Gaussian distribution. The estimated distributions create a basis to generate data-driven Gaussian confidence intervals for the estimated stellar parameters. We show that residual networks and attention-based models can estimate the stellar parameters with high accuracy for low Signal-to-noise ratio (SNR) compared to previous methods. With an observation of the Sun from the HARPS-N spectrograph, we show that the models can estimate stellar parameters from real observational data.

Tail index estimation based on survey data

This paper is devoted to tail index estimation in the context of survey data. Assuming that the population of interest is described by a heavy-tailed statistical model, we prove that the survey scheme plays a crucial role in the design of consistent inference methods for extremes. As can be revealed by simulation experiments, ignoring the sampling plan generally induces a significant bias, jeopardizing the accuracy of the extreme value statistics thus computed. Focus is here on the celebrated Hill method for tail index estimation, it is shown how to modify it in order to take into account the survey design. Precisely, under specific conditions on the inclusion probabilities of first and second orders, we establish the consistency of the variant of the Hill estimator we propose. Additionally, its asymptotic normality is proved in a specific situation. Application of this limit result for building Gaussian confidence intervals is thoroughly discussed and illustrated by numerical results.

DIFFERENCING TRANSFORMATIONS AND INFERENCE IN PREDICTIVE REGRESSION MODELS

The limit distribution of conventional test statistics for predictability may depend on the degree of persistence of the predictors. Therefore, diverging results and conclusions may arise because of the different asymptotic theories adopted. Using differencing transformations, we introduce a new class of estimators and test statistics for predictive regression models with Gaussian limit distribution that is instead insensitive to the degree of persistence of the predictors. This desirable feature allows to construct Gaussian confidence intervals for the parameter of interest in stationary, nonstationary, and even locally explosive settings. Besides the limit distribution, we also study the efficiency and the rate of convergence of our new class of estimators. We show that the rate of convergence is$\sqrt n $in stationary cases, while it can be arbitrarily close tonin nonstationary settings, still preserving the Gaussian limit distribution. Monte Carlo simulations confirm the high reliability and accuracy of our test statistics.

Differencing Transformations and Robust Inference in Predictive Regression Models

The limit distribution of conventional test statistics for predictability may depend on the degree of persistence of the predictors. Therefore, diverging results and conclusions may arise because of the different asymptotic theories adopted. Using differencing transformations, we introduce a new class of estimators and test statistics for predictive regression models with Gaussian limit distribution that is instead insensitive to the degree of persistence of the predictors. This desirable feature allows to construct Gaussian confidence intervals for the parameter of interest in stationary, nonstationary, and even locally explosive settings. Besides the limit distribution, we also study the efficiency and the rate of convergence of our new class of estimators. We show that the rate of convergence is 'n' in stationary cases, while it can be arbitrarily close to 'n' in nonstationary settings, still preserving the Gaussian limit distribution. Monte Carlo simulations confirm the high reliability and accuracy of our test statistics.

Robust confidence intervals applied to crossover operator for real-coded genetic algorithms

In this work we propose a new approach to crossover operators for real-coded genetic algorithms based on robust confidence intervals. These confidence intervals are an alternative to standard confidence intervals. In this paper, they are used for localising the search regions where the best individuals are placed. Robust confidence intervals use robust localization and dispersion estimators that are highly recommendable when the distribution of the random variables is not known or is distorted. Both situations are likely when we are dealing with the best individuals of the population, especially if the problem under study is multimodal. The performance of the crossovers based on robust intervals is evaluated using a well characterised set of optimisation problems. We have chosen problems with different features of modality, separability, regularity, and correlation among their variables. The results show that the performance of the crossovers based on robust confidence intervals is less dependent on the problem than the performance of the crossovers based on Gaussian confidence intervals. We have also made comparisons between several standard crossovers that show very interesting results, which support the idea underlying the defined operators.

Structure and timing of recirculation around Georges Bank: an observational and modeling study at the Great South Channel: Part I––ensemble smoother

An ensemble smoother is used to assimilate moored temperature, salinity, and velocity data into a local area primitive equation model. The overall goal of the analysis is to estimate variability of Georges Bank recirculation, i.e., northward flow through the Great South channel in support of the US Global Ocean Ecosystem Dynamics (GLOBEC) Georges Bank experiment. Here, identical twin experiments are carried out to test the ensemble smoother with a finite-element circulation model of the Great South Channel, based on a previous formulation designated QUODDY. The ensemble smoother utilizes a finite number of Monte Carlo model simulations to estimate model error covariance. The prior distribution from which the ensemble members are simulated is implicitly defined by the forward model by adding spatially correlated Gaussian random variables to the initial conditions, and time-dependent boundary elevations. Atmospheric forcing (wind stress) is derived from buoy measurements and is assumed to be known with certainty. The accuracy of the estimator depends on the state space variable being estimated and proximity to the data. In these twin experiments the domain-wide mean error variance of temperature, salinity, and velocity were reduced 96%, 93%, and 89%, respectively. The prediction statistics for the estimate are accurate throughout the domain. Non-linearity of the forward model and subsequent skewness of the posterior probability density function (pdf) are investigated. It is found that the posterior distribution is sufficiently Gaussian to use Gaussian confidence intervals. These results give confidence for using the numerical formulation and ensemble smoother to examine variability in circulation at Great South Channel with available data.

EMLK2D: a computer program for spatial estimation using empirical maximum likelihood kriging

The authors describe a Fortran-90 program for empirical maximum likelihood kriging. More efficient estimates are obtained by solving the estimation problem in the ‘Gaussian domain’ (i.e., using the normal scores of the experimental data), where the simple kriging estimate is equivalent to the maximum likelihood estimate and to the conditional expectation. The transform to normality is done using the empirical cumulative probability distribution function. A Bayesian approach is adopted to ensure a conditionally unbiased estimate, which is obtained as the mean of the posterior distribution. The posterior distribution also provides a complete specification of the probability of the variable and thus provides the basis for a more realistic evaluation of uncertainty by various methods: inverting Gaussian confidence intervals, confidence intervals measured from the posterior distribution, variance measured from the posterior distribution or intervals obtained using the likelihood ratio statistic. A detailed case study is used to demonstrate the use of the program.

Vascular plant compositional gradients within and between Iowa fens

AbstractQuestion: What is the nature and relative importance of compositional gradients within‐ and between fens?Location: Iowa, USA.Methods: 506 0.5 m × 0.5 m quadrats were sampled from 31 fens across a 550 km extent. Presence/absence of all vascular plant taxa, plus the non‐vascular genera Sphagnum and Chara, and values for 24 environmental variables were noted. Global Non‐Metric Multidimensional Scaling and Monte Carlo tests were used to describe compositional variation and identify significant environmental co‐variables. Model‐based cluster analysis was used to identify the optimal number of groups supported by the data, while k‐means clustering was used to assign each quadrat to a group. The number of occurrences (and frequency) of each species within each group was calculated. Two‐dimensional 95% Gaussian confidence intervals, ANOVA, correlation coefficient homogeneity tests, log‐linear modelling, and Fisher's exact tests were used to document patterns of compositional change.Results: Two stable axes of variation were identified: the first being most closely correlated with soil pH, Mg, Ca, P, S, vegetation height, surface and −10 cm soil temperature, site area, perimeter, perimeter/area ratio, growing season, and air temperature, with the second being most correlated to soil moisture, N, disturbance level, % organic matter, hummock height, N‐S coordinate, and precipitation. Individual sites harboured between 20–47% of total compositional variation, with 28% of Axis 1 and 55% of Axis 2 scores being contained within‐sites. Five compositional regions were identified that differed in the proportion of calciphile and hydrophile species. Compositional groups differed significantly between geologic types.Conclusions: While the principal axis of variation (corresponding to the rich‐poor fen gradient) is present largely between sites, the second axis (corresponding to water level) is largely repeated within sites. Documentation and protection of vegetation patterns and species diversity within Iowa fens will thus require consideration of multiple sites across the landscape.

Vascular plant compositional gradients within and between Iowa fens

Abstract Question: What is the nature and relative importance of compositional gradients within- and between fens? Location: Iowa, USA. Methods: 506 0.5 m × 0.5 m quadrats were sampled from 31 fens across a 550 km extent. Presence/absence of all vascular plant taxa, plus the non-vascular genera Sphagnum and Chara, and values for 24 environmental variables were noted. Global Non-Metric Multidimensional Scaling and Monte Carlo tests were used to describe compositional variation and identify significant environmental co-variables. Model-based cluster analysis was used to identify the optimal number of groups supported by the data, while k-means clustering was used to assign each quadrat to a group. The number of occurrences (and frequency) of each species within each group was calculated. Two-dimensional 95% Gaussian confidence intervals, ANOVA, correlation coefficient homogeneity tests, log-linear modelling, and Fisher's exact tests were used to document patterns of compositional change. Results: Two stable...

Convergence to equilibrium for granular media equations and their Euler schemes

We introduce a new interacting particle system to investigate the behavior of the nonlinear, nonlocal diffusive equation already studied by Benachour et al. [3, 4]. We first prove an uniform (with respect to time) propagation of chaos. Then, we show that the solution of the nonlinear PDE converges exponentially fast to equilibrium recovering a result established by an other way by Carrillo, McCann and Vilanni [7]. At last we provide explicit and Gaussian confidence intervals for the convergence of an implicit Euler scheme to the stationary distribution of the nonlinear equation.