Confidence Regions Research Articles

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems.

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) - approximately of first order -, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

High-Accuracy Confidence Regions for Distribution Parameters

With the help of today’s computers, it is always relatively easy to find maximum-likelihood estimators of one or more parameters of any specific statistical distribution, and use these to construct the corresponding approximate confidence interval/region, facilitated by the well-known asymptotic properties of the likelihood function. The purpose of this article is to make this approximation substantially more accurate by extending the Taylor expansion of the corresponding probability density function to include quadratic and cubic terms in several centralized sample means, and thus finding the corresponding -proportional correction to the original algorithm. We then demonstrate the new procedure’s usage, both for constructing confidence regions and for testing hypotheses, emphasizing that incorporating this correction carries minimal computational and programming cost. In our final chapter, we present two examples to indicate how significantly the new approximation improves the procedure’s accuracy.

Identifying Panel Inconsistency in Sensory Profiles using Multivariate Analysis of Variance (MANOVA) and follow–up Canonical Variate Analysis (CVA)

Inconsistency in sensory evaluation is a serious problem and it often leads to loss of large revenue. Screening tasters before the sensory evaluation is the only remedy to overcome this inconsistency. This paper aims at showing how the above requirement can be achieved by using Multivariate Analysis of Variance (MANOVA) and follow–up Canonical Variate Analysis (CVA). The approach was illustrated using sensory profiles of Sri Lankan tea. The principle behind the approach is that any discrepancy between assessors on several attributes is detected simultaneously using MANOVA, and the discrepancy interacts with the factors such as products or region is detected using CVA. Data used for the study consisted of sensory scores given by 8 tea tasters for 13 tea growing regions on 6 attributes; colour, brightness, strength, flavour, aroma, quality. Samples from four factories represented a region, and data were collected for a one–year period on a monthly basis. Data from each month were analyzed separately. The Wilk’s Lambda statistics of MANOVA revealed assessor effect as well as assessor × region interaction effect (P < 0.05) in every month indicating the inconsistency among assessors. The CVA for each region, specifically the 95% confidence regions of CV bi–plots, clearly identified clusters of assessors. Based on the location of these clusters in bi–plots, assessors who are suitable for different attributes were also identified. MANOVA followed by CVA, can effectively be used to identify discrepancies between assessors, discrepancy interacts with factors such as geographical region, and selecting consistent assessors depending on product or region and season.

Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity

The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region.

Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

Variational Bayesian calibration of low-cost gas sensor systems in air quality monitoring

Due to the impact of air quality on health, the use of low-cost gas sensor systems in air quality monitoring has increased. The deficiencies of low-cost gas sensors such as cross-sensitivities, interferences with environmental factors, and unit-to-unit variability have led to multidimensional calibration approaches with machine learning applied to field data. However, the trustworthiness of measurement results remains a concern, since sensor aging and concept drift are common problems. While most machine learning algorithms do not disclose the reliability and trustworthiness of measurement results, Bayesian models offer integrated sanity checking of predictions. Motivated by recent advancements in variational inference, this publication evaluates the potential of variational Bayesian linear regression and variational Bayesian neural networks for the calibration of low-cost gas sensors and sensor systems using laboratory as well as published field data. With the performed analysis, it can be shown that raw sensor measurements outside confidence regions, implicitly defined by the calibration input data, are detectable. In such situations, the uncertainty of the posterior predictive distribution increases, suggesting less trustworthy measurement results and necessity for maintenance.

Способы отождествления пеленгов в двухпозиционных угломерных системах радиомониторинга воздушного базирования.

For aeronautical goniometric systems for radio monitoring of radio emission sources (RES), one of the primary tasks is the identification of bearings. It is especially difficult to solve the problem of identifying bearings if there are several RESs in the observation area in the case when they are located in the same plane with the direction finders. In this case, the problem of identifying bearings in goniometric two-position systems is solved in the process of performing a two-stage procedure. At the first stage, the primary identification of single measurements of bearings is carried out separately at each receiving position (RP) when receiving radio signals from the RES, and at the second stage, the secondary (inter-positional) identification of bearings arriving from both RPs is carried out. In the initial identification, strobe and strobeless identification algorithms are used. In the secondary identification for selection of true and false points of intersection of bearings on the plane, it is proposed to use the kinematic parameters of the relative RES. However, this type of selection does not provide interposition identification with an arbitrary nature of the movement of the RES relative to the RP, and also assumes a constant angular position of the RP base on the plane. More practical are ways of identifying bearings with RES, in which the procedure for constructing a confidence region (CR) in the form of a circle with a certain radius is used. However, a more correct form of CR is an elliptical CR, since the errors in determining the position of the RES are characterized by an error ellipse, a particular case of which is a circle. Therefore, methods for identifying coordinate information have been developed, in which elliptical CRs are used. In this case, not only the bearings of the RES, but also other measured parameters, for example, estimates of the rectangular coordinates of the RES, calculated on the basis of the triangulation method, can be used as coordinate information. The purpose of the article is to systematize and analyze the developed methods for identifying bearings, which allow one to get a fairly general idea of how to solve the problem of identifying bearings and indirect measurements of the coordinates of radio emission sources in aviation goniometric two-position radio monitoring systems. As a result, a classification of identification methods is given. The existing possibilities and limitations of using various identification methods in solving radio monitoring problems are analyzed. The necessary information on the methods and algorithms for interpositional identification of coordinate information about the position of the RES, using ellipsoidal CRs in solving the identification problem, is given. The practical significance of the presented methods is to increase the likelihood of correct identification of coordinate information, as well as the accuracy of the positioning of RES due to the use of elliptical CRs, which more accurately reflect the regularity of the distribution of errors in determining the position of RES.

A two-dimensional index for marginal homogeneity in ordinal square contingency tables

For square contingency tables with ordered categories, indexes that represent the degree of departure from the marginal homogeneity (MH) model have been proposed. There are two types of directionalities of departure from MH. The existing indexes, however, can analyze either the degree of departure from MH or the directionality but not both. To address this issue, this study proposes a two-dimensional index, which combines the existing indexes, can simultaneously analyze both the degree and directionality of departure from MH. This study also evaluates the usefulness of the proposed index for visually comparing degrees of departure from MH in several square contingency tables using confidence region.

Confidence polytopes for quantum process tomography

In the present work, we propose a generalization of the confidence polytopes approach for quantum state tomography (QST) to the case of quantum process tomography (QPT). Our approach allows obtaining a confidence region in the polytope form for a Choi matrix of an unknown quantum channel based on the measurement results of the corresponding QPT experiment. The method uses the improved version of the expression for confidence levels for the case of several positive operator-valued measures. We then demonstrate how confidence polytopes can be employed for calculating confidence intervals for affine functions of quantum states (Choi matrices), such as fidelities and observables mean values, which are used both in QST and QPT settings. As we propose, this problem can be efficiently solved using linear programming tools. We also study the performance and scalability of the developed approach on the basis of simulation and experimental data collected using IBM cloud quantum processor.

Optimal rerandomization designs via a criterion that provides insurance against failed experiments

We present an optimized rerandomization design procedure for a non-sequential treatment-control experiment. Randomized experiments are the gold standard for finding causal effects in nature. But sometimes random assignments result in unequal partitions of the treatment and control group visibly seen as imbalance in observed covariates. There can additionally be imbalance on unobserved covariates. Imbalance in either observed or unobserved covariates increases treatment effect estimator error inflating the width of confidence regions and reducing experimental power. “Rerandomization” is a strategy that omits poor imbalance assignments by limiting imbalance in the observed covariates to a prespecified threshold. However, limiting this threshold too much can increase the risk of contracting error from unobserved covariates. We introduce a criterion that combines observed imbalance while factoring in the risk of inadvertently imbalancing unobserved covariates. We then use this criterion to locate the optimal rerandomization threshold based on the practitioner’s level of desired insurance against high estimator error. We demonstrate the gains of our designs in simulation and in a dataset from a large randomized experiment in education. We provide an open source R package available on CRAN named OptimalRerandExpDesigns which generates designs according to our algorithm.

Estimating the fundamental niche: Accounting for the uneven availability of existing climates in the calibration area

Studies that question important conceptual and methodological aspects of the field of ecological niche modeling (and species distribution modeling) have cast doubts on whether it is possible to estimate the fundamental niche of a species using presence-only data. The main limitation in niche estimation is that presence data come from the realized niche, which is only a subset of the fundamental niche. Most of the existing methods lack the ability to overcome this limitation and therefore fit niches that resemble the realized niche. To obtain a more accurate estimate of the fundamental niche, we propose using the geographic region that is accessible to a species (based on its dispersal ability) to determine a sampling distribution, in environmental space, from which we can quantify the likelihood of observing a particular environmental combination in a sample of presence points. We incorporate this sampling distribution into a multivariate normal model (i.e., a Mahalanobis distance model) by creating a weight function that modifies the probabilities of observing different environmental combinations in a sample of presences. This modification accounts for the uneven availability of environmental conditions. We show that the parameters of this weighted-normal model can be approximated with a maximum likelihood estimation approach; and then used to draw ellipsoids (confidence regions) that represent the fundamental niche of the species. We illustrate the application of our model with two worked examples. First, we use presence data for an invasive species and an accessible area that includes only its native range to evaluate whether the fitted model predicts confirmed establishments of the species outside its native range. Second, we use presence data for closely related species with known accessible areas to demonstrate how the different dispersal abilities of the species constrain a classic Mahalanobis distance model. Overall, we show that accounting for the distribution of environmental conditions that are accessible to a species indeed affects the estimation of the ellipsoids used to model its fundamental niche.

Directions Old and New: Palaeomagnetism and Fisher (1953) Meet Modern Statistics

SummaryMost modern articles in the palaeomagnetism literature are based on statistics developed by Fisher's 1953 paper ‘Dispersion on a sphere’, which assumes independent and identically distributed (iid) spherical data. However, palaeomagnetic sample designs are usually hierarchical, where specimens are collected within sites and the data are then combined across sites to calculate an overall mean direction for a geological formation. The specimens within sites are typically more similar than specimens between different sites, and so the iid assumptions fail. This article has three principal goals. The first is to review, contrast and compare both the statistics and geophysics literature on the topic of analysis methods for clustered data on spheres. The second is to present a new hierarchical parametric model, which avoids the unrealistic assumption of rotational symmetry in Fisher's 1953 paper ‘Dispersion on a sphere’ and may be broadly useful in the analysis of many palaeomagnetic datasets. To help develop the model, we use publicly available data as a case study collected from the Golan Heights volcanic plateau. The third goal is to explore different methods for constructing confidence regions for the overall mean direction based on clustered data. Two bootstrap confidence regions that we propose perform well and will be especially useful to geophysics practitioners.

A WILD BOOTSTRAP FOR DEPENDENT DATA

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is established when data are assumed to satisfy a near epoch dependent condition and under the framework of the smooth function model. The WBDD offers a viable alternative to the existing non parametric bootstrap methods for dependent data. It preserves the second-order correctness property of blockwise bootstrap (provided we choose the external random variables appropriately), for stationary time series and smooth functions of the mean. This desirable property of any bootstrap method is not known for extant wild-based bootstrap methods for dependent data. Simulation studies illustrate the finite-sample performance of the WBDD.

Abstract 14467: Machine Learning for Identifying Salient Regions on the Coronary Artery on CT for Radiomic Feature Extraction and Characterization of CAD

Introduction: Radiomics is a quantitative approach that allows for high throughput extraction of image features such as texture. It has been used for characterization of coronary artery disease (CAD). However, the reliability of radiomic features (RFs) varies with the image segmentation quality. We present a new strategy to establish a segmentation confidence map spatially across the coronary arteries in the dataset. We then evaluate the quality of RFs in salient (high confidence) and non-salient (low confidence) regions in the coronary artery. Purpose: To identify salient regions in the coronary artery, providing high segmentation certainty as well as a site for informative radiomic feature extraction, useful in CAD characterization. Methods: In our approach, we first applied a deep learning-based segmentation model (U-Net with ResNet backbone) to segment the coronary arteries (Fig. 1a). Next, we constructed a mean probability atlas from the segmentation probability maps, using fiducial registration (Fig. 1b). Finally, we identified salient and non-salient regions within the segmentation (Fig. 1c) by masking the mean probability atlas with the predicted segmentation and then thresholding them. Human expert-generated manual segmentation was used as ground truth. RFs—shape (26), first order (19) and second order (75)—were extracted from salient and non-salient regions for comparative correlation analysis with features from ground truth segmentation. A higher correlation implies that these features are equally informative as those from the manual segmentation. Results: The model achieved a dice score of 79.8% on the hold-out set. The RFs extracted only from the salient regions (Proximal portion of RCA and LAD) of the coronary artery display strong correlations with RFs extracted from manual segmentations (Fig 1d). Conclusion: We present a framework to identify regions for optimal extraction of RFs for improved CAD characterization.

Received Signal Strength Indicator-Based Recursive Set-Membership Localization With Unknown Transmit Power and Path Loss Exponent

In most of the existing localization schemes based on received signal strength indicator (RSSI), the target location is calculated based on typical parameters and the statistical information of measurement noise is needed. This article addresses these problems of localization by implementing recursive set-membership filtering under unknown-but-bounded (UBB) parameters, process and measurement noise. First, a new prediction scheme is developed to confine the real location included in a reliable confidence region at each instant. Second, the nonlinear remainder bound of the Taylor series expansion of the measurement function is obtained analytically on-line. Furthermore, an efficient optimization procedure is developed. Third, an alternating iterative recursive convex optimization algorithm is given to derive a set of optimized ellipsoids and intervals which confine real location and parameters, respectively. Finally, experimental validation and numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method.

Asymptotic Results for Multinomial Models

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.

Asymptotic Analysis for a Stochastic Second-Order Cone Programming and Applications

Stochastic second-order cone programming (SSOCP) is an extension of deterministic second-order cone programming, which demonstrates underlying uncertainties in practical problems arising in economics engineering and operations management. In this paper, asymptotic analysis of sample average approximation estimator for SSOCP is established. Conditions ensuring the asymptotic normality of sample average approximation estimators for SSOCP are obtained and the corresponding covariance matrix is described in a closed form. Based on the analysis, the method to estimate the confidence region of a stationary point of SSOCP is provided and three examples are illustrated to show the applications of the method.

Semianalytical approach for sky localization of gravitational waves

Rapid sky localization of gravitational wave sources is crucial to enable prompt electromagnetic follow-ups. In this article, we present a novel semianalytical approach for sky localization of gravitational waves from compact binary coalescences. We use the Bayesian framework with an analytical approximation to the prior distributions for a given astrophysical model. We derive a semianalytical solution to the posterior distribution of source directions. This method only requires one-fold numerical integral that marginalizes over the merger time, compared to the five-fold numerical integration otherwise needed in the Bayesian localization method. The performance of the method is demonstrated using a set of binary neutron stars (BNS) injections on Gaussian noise using LIGO-Virgo's design and O2 sensitivity. We find the median of 90% confidence area in O2 sensitivity to be $\mathcal{O}(10^2) ~\mathrm{deg}^2$, comparable to that of the existing LIGO-Virgo online localization method Bayestar and parameter estimation toolkit LALInference. In the end, we apply this method to localize the BNS event GW170817 and find the 50% (90%) confidence region of 11 $\mathrm{deg}^2$ (50 $\mathrm{deg}^2$). The detected optical counterpart of GW170817 resides within our 50% confidence area.

Process Quality Evaluation Model with Taguchi Cost Loss Index

Process Capability Indices (PCIs) are not only a good communication tools between sales departments and customers but also convenient tools for internal engineers to evaluate and analyze process capabilities of products. Many statisticians and process engineers are dedicated to research on process capability indices, among which the Taguchi cost loss index can reflect both the process yield and process cost loss at the same time. Therefore, in this study the Taguchi cost loss index was used to propose a novel process quality evaluation model. After the process was stabilized, a process capability evaluation was carried out. This study used Boole’s inequality and DeMorgan’s theorem to derive the (1−α)×100% confidence region of (δ,γ2) based on control chart data. The study adopted the mathematical programming method to find the (1−α)×100% confidence interval of the Taguchi cost loss index then employed a (1−α)×100% confidence interval to perform statistical testing and to determine whether the process needed improvement.

LMC N132D: A mature supernova remnant with a power-law gamma-ray spectrum extending beyond 8 TeV

Context. Supernova remnants (SNRs) are commonly thought to be the dominant sources of Galactic cosmic rays up to the knee of the cosmic-ray spectrum at a few PeV. Imaging Atmospheric Cherenkov Telescopes have revealed young SNRs as very-high-energy (VHE, >100 GeV) gamma-ray sources, but for only a few SNRs the hadronic cosmic-ray origin of their gamma-ray emission is indisputably established. In all these cases, the gamma-ray spectra exhibit a spectral cutoff at energies much below 100 TeV and thus do not reach the PeVatron regime. Aims. The aim of this work was to achieve a firm detection for the oxygen-rich SNR LMC N132D in the VHE gamma-ray domain with an extended set of data, and to clarify the spectral characteristics and the localization of the gamma-ray emission from this exceptionally powerful gamma-ray-emitting SNR. Methods. We analyzed 252 h of High Energy Stereoscopic System (H.E.S.S.) observations towards SNR N132D that were accumulated between December 2004 and March 2016 during a deep survey of the Large Magellanic Cloud, adding 104 h of observations to the previously published data set to ensure a > 5σ detection. To broaden the gamma-ray spectral coverage required for modeling the spectral energy distribution, an analysis of Fermi-LAT Pass 8 data was also included. Results. We unambiguously detect N132D at VHE with a significance of 5.7σ. We report the results of a detailed analysis of its spectrum and localization based on the extended H.E.S.S. data set. The joint analysis of the extended H.E.S.S and Fermi-LAT data results in a spectral energy distribution in the energy range from 1.7 GeV to 14.8 TeV, which suggests a high luminosity of N132D at GeV and TeV energies. We set a lower limit on a gamma-ray cutoff energy of 8 TeV with a confidence level of 95%. The new gamma-ray spectrum as well as multiwavelength observations of N132D when compared to physical models suggests a hadronic origin of the VHE gamma-ray emission. Conclusions. SNR N132D is a VHE gamma-ray source that shows a spectrum extending to the VHE domain without a spectral cutoff at a few TeV, unlike the younger oxygen-rich SNR Cassiopeia A. The gamma-ray emission is best explained by a dominant hadronic component formed by diffusive shock acceleration. The gamma-ray properties of N132D may be affected by an interaction with a nearby molecular cloud that partially lies inside the 95% confidence region of the source position.