Interval Width Research Articles

Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach.

The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the distance geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent geometry and may have benefits from the recent development of residue-specific force-fields.

Algorithmic Matching Attacks on Optimally Suppressed Tabular Data

The objective of the cell suppression problem (CSP) is to protect sensitive cell values in tabular data under the presence of linear relations concerning marginal sums. Previous algorithms for solving CSPs ensure that every sensitive cell has enough uncertainty on its values based on the interval width of all possible values. However, we find that every deterministic CSP algorithm is vulnerable to an adversary who possesses the knowledge of that algorithm. We devise a matching attack scheme that narrows down the ranges of sensitive cell values by matching the suppression pattern of an original table with that of each candidate table. Our experiments show that actual ranges of sensitive cell values are significantly narrower than those assumed by the previous CSP algorithms.

Assessing the Relative Biological Effectiveness of Neutrons across Organs of Varying Depth among the Atomic Bomb Survivors.

When assessing radiation-related risk among the atomic bomb survivors, choices in modeling approach can have an important impact on the results, which are then used to inform radiation protection standards throughout the world. The atomic bombings of Hiroshima and Nagasaki produced a mixed-field radiation exposure from two sources: neutrons and gamma rays. Neutrons are more densely ionizing and cause greater biological damage per unit absorbed dose, resulting in greater relative biological effectiveness (RBE) than gamma rays. To account for this, a combined weighted dose is typically calculated as the sum of the gamma-ray dose and 10 times the neutron dose in the Radiation Effects Research Foundation's reports of mortality, solid cancer incidence and other outcomes. In addition, the colon, which is often chosen as the whole-body representative organ in these analyses, is relatively deep in the body and therefore its dose calculation involves heavy body shielding of neutrons and a low neutron/gamma-ray ratio. With added follow-up and recently updated doses, we used a data-driven approach to determine the best-fitting neutron RBE for a range of organs of varying depth. Aggregated person-year tables of solid cancer incidence (1958-2009) from the Life Span Study were created with separate neutron and gamma-ray DS02R1 doses for several organs including breast, brain, thyroid, bone marrow, lung, liver and colon. Typical excess relative risk models estimating the linear effect of radiation dose were fitted using a range of neutron weights (1-250) to calculate combined dose for each organ, and model deviances were compared to assess fit. Furthermore, models using separate terms for gamma-ray and neutron dose were also examined, wherein the ratio of the neutron/gamma-ray linear terms indicated the best estimate of the RBE. The best-fitting RBE value for the traditional weighted colon dose was 80 [95% confidence interval (CI): 20-190], while the RBEs for other organs using weighted doses ranged from 25 to 60, with the best-fitting weights and confidence interval widths both incrementally increasing with greater depth of organ. Models using separate neutron- and gamma-ray-dose terms gave similar results to weighted linear combinations, with a neutron/gamma-ray term ratio of 79.9 (95% CI: 18.8-192.3) for colon. These results indicated that the traditionally modeled RBE of 10 may underestimate the effect of neutrons across the full dose range, although these updated estimates still have fairly wide confidence bounds. Furthermore, the colon is among the deepest of organs and may not be the best choice as a single surrogate organ dose, as it may minimize the role of the neutrons. Future work with more refined organ doses could shed more light on RBE-related information available in the Life Span Study data.

Sequential accuracy in parameter estimation for population correlation coefficients.

Correlation coefficients are effect size measures that are widely used in psychology and related disciplines for quantifying the degree of relationship of two variables, where different correlation coefficients are used to describe different types of relationships for different types of data. We develop methods for constructing a sufficiently narrow confidence interval for 3 different population correlation coefficients with a specified upper bound on the confidence interval width (e.g., .10 units) at a specified level of confidence (e.g., 95%). In particular, we develop methods for Pearson's r, Kendall's tau, and Spearman's rho. Our methods solve an important problem because existing methods of study design for correlation coefficients generally require the use of supposed but typically unknowable population values as input parameters. We develop sequential estimation procedures and prove their desirable properties in order to obtain sufficiently narrow confidence interval for population correlation coefficients without using supposed values of population parameters, doing so in a distribution-free environment. In sequential estimation procedures, supposed values of population parameters for purposes of sample size planning are not needed, but instead stopping rules are developed and once satisfied, they provide a rule-based stop to the sampling of additional units. In particular, data in sequential estimation procedures are collected in stages, whereby at each stage the estimated population values are updated and the stopping rule evaluated. Correspondingly, the final sample size required to obtain a sufficiently narrow confidence interval is not known a priori, but is based on the outcome of the study. Additionally, we extend our methods to the squared multiple correlation coefficient under the assumption of multivariate normality. We demonstrate the effectiveness of our sequential procedure using a Monte Carlo simulation study. We provide freely available R code to implement the methods in the MBESS package. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Calculation of narrower confidence intervals for tree mortality rates when we know nothing but the location of the death/survival events.

Many ecological applications, like the study of mortality rates, require the estimation of proportions and confidence intervals for them. The traditional way of doing this applies the binomial distribution, which describes the outcome of a series of Bernoulli trials. This distribution assumes that observations are independent and the probability of success is the same for all the individual observations. Both assumptions are obviously false in many cases.I show how to apply bootstrap and the Poisson binomial distribution (a generalization of the binomial distribution) to the estimation of proportions. Any information at the individual level would result in better (narrower) confidence intervals around the estimation of proportions. As a case study, I applied this method to the calculation of mortality rates in a forest plot of tropical trees in Lambir Hills National Park, Malaysia.I calculated central estimates and 95% confidence intervals for species‐level mortality rates for 1,007 tree species. I used a very simple model of spatial dependence in survival to estimate individual‐level risk of mortality. The results obtained by accounting for heterogeneity in individual‐level risk of mortality were comparable to those obtained with the binomial distribution in terms of central estimates, but the precision increased in virtually all cases, with an average reduction in the width of the confidence interval of ~20%.Spatial information allows the estimation of individual‐level probabilities of survival, and this increases the precision in the estimates of mortality rates. The general method described here, with modifications, could be applied to reduce uncertainty in the estimation of proportions related to any spatially structured phenomenon with two possible outcomes. More sophisticated approaches can yield better estimates of individual‐level mortality and thus narrower confidence intervals.

A new model for evaluating subjective online ratings with uncertain intervals

We formalize the information acquisition and choice structure of a decision maker (DM) when the main characteristics defining the alternatives are not directly observed but numerical evaluations of unknown quality are provided by external raters. The DM observes the overall numerical value assigned by the raters to an alternative and defines an uncertain interval within which the evaluation observed is contained. The width of the interval is determined by the subjective perception and evaluation differences existing between the DM and the raters transmitting the information. We analyze the incentives of the DM to improve upon an evaluation contained within an uncertain interval by retrieving further information from the raters of other alternatives. Different scenarios will be developed based on the ability of the DM to fully assimilate uncertainty and the introduction of heuristic approximations to account for the potential frictions arising from uncertainty. One of the main qualities of the current framework is its capacity to formalize interactions among alternatives determined by interval width differences across their characteristics, providing an analytical advantage over the operational complexity involved in the use of fuzzy and intuitionistic fuzzy sets. The same remark applies to the formalization of the interactions across attributes that must be considered when defining sequential decision processes or dynamical systems while dealing with multiple sources of uncertainty. Numerical simulations are provided to compare the different scenarios developed and describe the main consequences derived from ignoring the uncertainty inherent to the evaluations received. In particular, we illustrate the ranking consequences derived from increasing the spread of the evaluation uncertainty, an effect that can be easily combined with the risk attitude exhibited by DMs. The inclusion of both these features bridges the gap between economics, psychology and multiple criteria decision making, whose techniques do not generally account for these differences among DMs.

A Preferential Interval-Valued Fuzzy C-Means Algorithm for Remotely Sensed Imagery Classification

Remotely sensed imagery classification have a large amount of uncertainty related to the intraclass heterogeneity and the interclass ambiguity of objects. Fuzzy set theory can address the uncertainty effectively, while interval-valued model can improve the separability of samples. Therefore, we propose a novel interval-valued fuzzy c-means algorithm, which integrates the interval-valued model and preferential adaptive method. It preferentially adjusts the interval width according to MSE (mean-square-error) and boundary factor for determining the optimal set of features for the data. In this paper, it is proved that the method can make the intraclass MSE and boundary factor always proportional to the separability of objects, so that it can dynamically adjust the interval-valued separability by controlling the interval width. Experimental data consisting of SPOT5 (10-m spatial resolution) satellite data for three case study areas in China are used to test this algorithm. Compared with other state-of-the-art fuzzy classification methods, our algorithm demonstrates the markedly improved overall accuracy and Kappa coefficients.

Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles

SummaryQuantile estimation is important for a wide range of applications. While point estimates based on one or two order statistics are common, constructing confidence intervals around them, however, is a more difficult problem. This paper has two goals. First, it surveys the numerous distribution‐free methods for constructing approximate confidence intervals for quantiles. These techniques can be divided roughly into four categories: using a pivotal quantity, resampling, interpolation, and empirical likelihood methods. Second, a method based on the pivotal quantity that has received limited attention in the past is extended. Comprehensive simulation studies are used to compare performance across methods. The proposed method is simple and performs similarly to linear interpolation methods and a smoothed empirical likelihood method. While the proposed method has slightly wider interval widths, it can be calculated for more extreme quantiles even when there are few observations.

Interval state estimation for uncertain polytopic systems

The aim of this article is the state estimation of uncertain polytopic dynamic systems. The parametric uncertainties affecting the system are time varying, unknown and bounded with known bounds. The objective is to determine the state estimates consisting in the smallest interval containing the real-state value caused by the parametric uncertainties. This set will be characterised by the lower and upper bounds of the state trajectory. Given the uncertainty bounds, the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a Luenberger-type observer, fed with the system measurements. The proposed observer is designed to minimise the interval width of the estimates. The observer gains are obtained by solving an optimisation problem under LMI constraints. The efficiency of the proposed approach is illustrated by numerical examples.

On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and non-informative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability ( $$C_{p}$$ ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

This paper deals with construction of confidence intervals for process capability index using bootstrap method (proposed by Chen and Pearn in Qual Reliab Eng Int 13(6):355–360, 1997) by applying simulation technique. It is assumed that the quality characteristic follows type-II generalized log-logistic distribution introduced by Rosaiah et al. in Int J Agric Stat Sci 4(2):283–292, (2008). Discussed different bootstrap confidence intervals for process capability index. Maximum likelihood method is considered for obtaining the estimators of the parameter. Monte Carlo simulation technique is applied to find out the coverage probabilities and average widths of the bootstrap confidence intervals. The results are illustrated with real data sets.

Estimating prevalence of type I and type II diabetes using incidence rates: the SEARCH for diabetes in youth study

PurposeMost surveillance efforts in childhood diabetes have focused on incidence, whereas prevalence is rarely reported. This study aimed to assess whether a mathematical illness-death model accurately estimated future prevalence from baseline prevalence and incidence rates in children. MethodsSEARCH for Diabetes in Youth is an ongoing population-based surveillance study of prevalence and incidence of diabetes and its complications among youth in the United States. We used age-, sex-, and race/ethnicity-specific SEARCH estimates of the prevalence of type I and type II diabetes in 2001 and incidence from 2002 to 2008. These data were used in a partial differential equation to estimate prevalence in 2009 with 95% bootstrap confidence intervals. Model-based prevalence was compared with the observed prevalence in 2009. ResultsMost confidence intervals for the difference between estimated and observed prevalence included zero, indicating no evidence for a difference between the two methods. The width of confidence intervals indicated high precision for the estimated prevalence when considering all races/ethnicities. In strata with few cases, precision was reduced. ConclusionsFuture prevalence of type I and type II diabetes in youth may be accurately estimated from baseline prevalence and incidence. Diabetes surveillance could benefit from potential cost savings of this method.

Short-Term Wind Speed Interval Prediction Based on Ensemble GRU Model

Wind speed interval prediction is playing an increasingly important role in wind power production. The intermittent and fluctuant characteristics of wind power make high-quality prediction interval challenging. In this paper, a novel hybrid model based on a gated recurrent unit neural network and variational mode decomposition is proposed for wind speed interval prediction. Initially, variational mode decomposition is employed to decompose the complex wind speed time series into simplified modes. Interval prediction model and a point prediction model based on a gated recurrent unit neural network are designed to conduct interval prediction in primary mode and point prediction in rest modes, respectively, before the composition and construction of the prediction interval. Then, an error prediction model based on a gated recurrent unit neural network is proposed to enhance the model performance by error correction. Eight cases from two wind fields are used to test and verify the proposed method. The results indicate that the proposed method is a highly qualified method that has a much higher prediction interval coverage probability and narrower prediction interval width.

Bayesian consensus-based sample size criteria for binomial proportions.

Many sample size criteria exist. These include power calculations and methods based on confidence interval widths from a frequentist viewpoint, and Bayesian methods based on credible interval widths or decision theory. Bayesian methods account for the inherent uncertainty of inputs to sample size calculations through the use of prior information rather than the point estimates typically used by frequentist methods. However, the choice of prior density can be problematic because there will almost always be different appreciations of the past evidence. Such differences can be accommodated a priori by robust methods for Bayesian design, for example, using mixtures or ϵ-contaminated priors. This would then ensure that the prior class includes divergent opinions. However, one may prefer to report several posterior densities arising from a "community of priors," which cover the range of plausible prior densities, rather than forming a single class of priors. To date, however, there are no corresponding sample size methods that specifically account for a community of prior densities in the sense of ensuring a large-enough sample size for the data to sufficiently overwhelm the priors to ensure consensus across widely divergent prior views. In this paper, we develop methods that account for the variability in prior opinions by providing the sample size required to induce posterior agreement to a prespecified degree. Prototypic examples to one- and two-sample binomial outcomes are included. We compare sample sizes from criteria that consider a family of priors to those that would result from previous interval-based Bayesian criteria.

Sensitivity of methods for analyzing continuous outcome from stratified cluster randomized trials – an empirical comparison study

The assessment of the sensitivity of statistical methods has received little attention in cluster randomized trials (CRTs), especially for stratified CRT when the outcome of interest is continuous. We empirically examined the sensitivity of five methods for analyzing the continuous outcome from a stratified CRT - aimed to investigate the efficacy of the Classroom Communication Resource (CCR) compared to usual care to improve the peer attitude towards children who stutter among grade 7 students. Schools – the clusters, were divided into quintile based on their socio-political resources, and then stratified by quintile. The schools were then randomized to CCR and usual care groups in each stratum. The primary outcome was Stuttering Resource Outcomes Measure. Five methods, including the primary method, were used in this study to examine the effect of CCR. The individual-level methods were: (i) linear regression; (ii) mixed-effects method; (iii) GEE with exchangeable correlation structure (primary method of analysis). And the cluster-level methods were: (iv) cluster-level linear regression; and (v) meta-regression. These methods were also compared with or without adjustment for stratification. Ten schools were stratified by quintile, and then randomized to CCR (223 students) and usual care (231 students) groups. The direction of the estimated differences was same for all the methods except meta-regression. The widths of the 95% confidence intervals were narrower when adjusted for stratification. The overall conclusion from all the methods was similar but slightly differed in terms of effect estimate and widths of confidence intervals. TrialregistrationClinicaltrials.gov, NCT03111524. Registered on 9 March 2017.

Uncertainty Quantification of Density and Stratification Estimates with Implications for Predicting Ocean Dynamics

AbstractWe present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5% to 4% of the expected values for the linear internal wave phase speed and 15%–40% for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article.

Reconstruction of traffic situations from digital video-recording using method of volumetric kinetic mapping

In the past the traffic accident reconstruction was based in principle only on indirect methods that use accident marks and witness reports. These data were then used within backward reconstruction of event for determination of motion status of accident participants and expression of desirable quantities as are initial velocities, impact velocities, distances travelled or temporal conditions. These methods and their accuracy are dependent on the width of intervals of input quantities or on limited possibilities for motion synchronization between numerable participants of road traffic accidents. Existence of footage from CCTV cameras that captures traffic situations presents very valuable source of information about these accidents. The goal of the article is proposal of a volumetric kinetic mapping (VKM) method of accident reconstruction from CCTV footage. The method is based on synthesis of videoediting, videoanalysis and kinetic simulation using dedicated software for accident reconstruction. The method was furthermore validated for speed-time and distance-time variables by means of experimental test runs and by subsequent application of the method in the reconstruction of these tests using PC-Crash simulation software and two videoediting software packages. Results of the reconstructions of validation runs using VKM method were then verified by comparing them to the measured data from Corrsys Datron Microstar measuring system.

An Adaptive Bilevel Programming Model for Nonparametric Prediction Intervals of Wind Power Generation

It is hard to obtain precise wind power forecasting due to the chaotic nature of weather systems. Prediction intervals become an efficient tool to quantify the uncertainty involved in wind power forecasting. Traditional central prediction intervals are widely produced by forecasters, however, which might be conservative with respect to interval width and not well fit the practical conditions. This paper develops a novel adaptive bilevel programming (ABP) model, with extreme learning machine based quantile regression as the follower's problem and tuning hyperparameters of quantile proportions as the leader's problem. The proposed ABP model aims at minimizing the average interval width subject to well calibration. In order to overcome the difficulties in disposing of the intractable nested structure of bilevel programming, the ABP model is equivalently transformed into a single-level nonlinear programming problem with bilinear terms. An improved spatial branch-and-bound (ISBB) algorithm is proposed to efficiently solve the reformulated bilinear programming problem. In the ISBB algorithm, an innovative bounds tightening method is developed to tighten the convex relaxation of the bilinear constraint and enhance the convergence. Experimental studies based on actual wind farm of USA under four seasons show the significant effectiveness and high robustness of the developed ABP model, as well as the excellent global optimum attainment and convergence performance of the proposed ISBB algorithm. Moreover, the widely used traditional interval scores are first verified to be prejudiced in probabilistic wind power forecasting evaluation.

Evanescent and propagating electromagnetic waves in Bi-isotropic layers

This paper presents a theoretical study of evanescent and propagating electromagnetic waves in bi-isotropic layers. The dispersion relation, guided mode condition, and evanescent wave coupling and tunneling in a bi-isotropic slab placed in a contrast bi-isotropic ambient medium are derived. A transfer matrix model is developed to acquire the transmission and reflection coefficients across the bi-isotropic layers. The creation of discrete guided modes and the continuous interval where the discrete guided modes are conceived are determined. Additionally, the effects of the Tellegen and chirality parameters on the width of the continuous interval are explained. The field distribution reformed by evanescent wave coupling and tunneling through the bi-isotropic slab is presented. The contrast bi-isotropic structure displays an evident high-pass frequency response that is controlled by the chirality of the slab. The behavior of the transmittance response with the material parameters and the incidence angle can facilitate the possible design of future electromagnetic and optical devices.

Impact of missing data on bias and precision when estimating change in patient-reported outcomes from a clinical registry

BackgroundClinical registries, which capture information about the health and healthcare use of patients with a health condition or treatment, often contain patient-reported outcomes (PROs) that provide insights about the patient’s perspectives on their health. Missing data can affect the value of PRO data for healthcare decision-making. We compared the precision and bias of several missing data methods when estimating longitudinal change in PRO scores.MethodsThis research conducted analyses of clinical registry data and simulated data. Registry data were from a population-based regional joint replacement registry for Manitoba, Canada; the study cohort consisted of 5631 patients having total knee arthroplasty between 2009 and 2015. PROs were measured using the 12-item Short Form Survey, version 2 (SF-12v2) at pre- and post-operative occasions. The simulation cohort was a subset of 3000 patients from the study cohort with complete PRO information at both pre- and post-operative occasions. Linear mixed-effects models based on complete case analysis (CCA), maximum likelihood (ML) and multiple imputation (MI) without and with an auxiliary variable (MI-Aux) were used to estimate longitudinal change in PRO scores. In the simulated data, bias, root mean squared error (RMSE), and 95% confidence interval (CI) coverage and width were estimated under varying amounts and types of missing data.ResultsThree thousand two hundred thirty (57.4%) patients in the study cohort had complete data on the SF-12v2 at both occasions. In this cohort, mixed-effects models based on CCA resulted in substantially wider 95% CIs than models based on ML and MI methods. The latter two methods produced similar estimates and 95% CI widths. In the simulation cohort, when 50% of the data were missing, the MI-Aux method, in which a single hypothetical auxiliary variable was strongly correlated (i.e., 0.8) with the outcome, reduced the 95% CI width by up to 14% and bias and RMSE by up to 50 and 45%, respectively, when compared with the MI method.ConclusionsMissing data can substantially affect the precision of estimated change in PRO scores from clinical registry data. Inclusion of auxiliary information in MI models can increase precision and reduce bias, but identifying the optimal auxiliary variable(s) may be challenging.