Outlier detection in spatial error models using modified thresholding-based iterative procedure for outlier detection approach.

BACKGROUND: Outliers, data points that significantly deviate from the norm, can have a substantial impact on statistical inference and provide valuable insights in data analysis. Multiple methods have been developed for outlier detection, however, almost all available approaches fail to consider the spatial dependence and heterogeneity in spatial data. Spatial data has diverse formats and semantics, requiring specialized outlier detection methodology to handle these unique properties. For now, there is limited research exists on robust spatial outlier detection methods designed specifically under the spatial error model (SEM) structure. METHOD: We propose the Spatial-Θ-Iterative Procedure for Outlier Detection (Spatial-Θ-IPOD), which utilizes a mean-shift vector to identify outliers within the SEM. Our method enables an effective detection of spatial outliers while also providing robust coefficient estimates. To assess the performance of our approach, we conducted extensive simulations and applied it to a real-world empirical study using life expectancy data from multiple countries. RESULTS: Simulation results showed that the masking and JD (Joint Detection) indicators of our Spatial-Θ-IPOD method outperformed several commonly used methods, even in high-dimensional scenarios, demonstrating stable performance. Conversely, the Θ-IPOD method proved to be ineffective in detecting outliers when spatial correlation was present. Moreover, our model successfully provided reliable coefficient estimation alongside outlier detection. The proposed method consistently outperformed other models (both robust and non-robust) in most cases. In the empirical study, our proposed model successfully detected outliers and provided valuable insights in the modeling process. CONCLUSIONS: Our proposed Spatial-Θ-IPOD offers an effective solution for detecting spatial outliers for SEM while providing robust coefficient estimates. Notably, our approach showcases its relative superiority even in the presence of high leverage points. By successfully identifying outliers, our method enhances the overall understanding of the data and provides valuable insights for further analysis.

Statistical analysis of ENDOR spectra.

Electron-nuclear double resonance (ENDOR) measures the hyperfine interaction of magnetic nuclei with paramagnetic centers and is hence a powerful tool for spectroscopic investigations extending from biophysics to material science. Progress in microwave technology and the recent availability of commercial electron paramagnetic resonance (EPR) spectrometers up to an electron Larmor frequency of 263 GHz now open the opportunity for a more quantitative spectral analysis. Using representative spectra of a prototype amino acid radical in a biologically relevant enzyme, the [Formula: see text] in Escherichia coli ribonucleotide reductase, we developed a statistical model for ENDOR data and conducted statistical inference on the spectra including uncertainty estimation and hypothesis testing. Our approach in conjunction with 1H/2H isotopic labeling of [Formula: see text] in the protein unambiguously established new unexpected spectral contributions. Density functional theory (DFT) calculations and ENDOR spectral simulations indicated that these features result from the beta-methylene hyperfine coupling and are caused by a distribution of molecular conformations, likely important for the biological function of this essential radical. The results demonstrate that model-based statistical analysis in combination with state-of-the-art spectroscopy accesses information hitherto beyond standard approaches.

Method for Estimating Road Impulse Ahead of Vehicles in Urban Environment with Microelectromechanical System Three-Dimensional Sensor.

Most automated vehicles (AVs) are equipped with abundant sensors, which enable AVs to improve ride comfort by sensing road elevation, such as speed bumps. This paper proposes a method for estimating the road impulse features ahead of vehicles in urban environments with microelectromechanical system (MEMS) light detection and ranging (LiDAR). The proposed method deploys a real-time estimation of the vehicle pose to solve the problem of sparse sampling of the LiDAR. Considering the LiDAR error model, the proposed method builds the grid height measurement model by maximum likelihood estimation. Moreover, it incorporates height measurements with the LiDAR error model by the Kalman filter and introduces motion uncertainty to form an elevation weight method by confidence eclipse. In addition, a gate strategy based on the Mahalanobis distance is integrated to handle the sharp changes in elevation. The proposed method is tested in the urban environment. The results demonstrate the effectiveness of our method.

Measurement Modeling and Performance Analysis of a Bionic Polarimetric Imaging Navigation Sensor Using Rayleigh Scattering to Generate Scattered Sunlight.

The bionic polarimetric imaging navigation sensor (BPINS) is a navigation sensor that provides absolute heading, and it is of practical engineering significance to model the measurement error of BPINS. The existing BPINSs are still modeled using photodiode-based measurements rather than imaging measurements and are not modeled systematically enough. This paper proposes a measurement performance analysis method of BPINS that takes into account the geometric and polarization errors of the optical system. Firstly, the key error factors affecting the overall measurement performance of BPINS are investigated, and the Stokes vector-based measurement error model of BPINS is introduced. Secondly, based on its measurement error model, the effect of the error source on the measurement performance of BPINS is quantitatively analyzed using Rayleigh scattering to generate scattered sunlight as a known incident light source. The numerical results show that in angle of E-vector (AoE) measurement, the coordinate deviation of the principal point has a greater impact, followed by grayscale response inconsistency of CMOS and integration angle error of micro-polarization array, and finally lens attenuation; in degree of linear polarization (DoLP) measurement, the grayscale response inconsistency of CMOS has a more significant impact. This finding can accurately guide the subsequent calibration of BPINS, and the quantitative results provide an important theoretical reference for its optimal design.

Research on High-Precision Measurement Method for Small-Size Gears with Small-Modulus.

Small-modulus gears, which are essential for motion transmission in precision instruments, present a measurement challenge due to their minuscule gear gaps. A high-precision measurement method under the influence of positioning errors is proposed, enabling precise evaluation of the machining quality of small-modulus gears. Firstly, a compound measurement platform for small-modulus gears is developed. Using a 3D model of the measurement system, the mathematical relationships governing motion transmission between various components are analyzed. Secondly, the formation mechanism of gear positioning error is revealed and its important influence on measurement accuracy is discussed. An optimization method for spatial coordinate transformation matrices under positioning errors of gears is proposed. Thirdly, the study focuses on small-sized gears with a modulus of 0.1 mm and a six-level accuracy. Based on the aforementioned measurement system, the tooth profile measurement points are collected in the actual workpiece coordinate system. Then, gear error parameters are extracted based on the established models for tooth profile deviation and pitch deviation. Finally, the accuracy and effectiveness of the proposed measurement method are verified by comparing the measurement results of the P26 gear measuring center.

Spatially adaptive calibrations of airbox PM2.5 data.

The Taiwan air quality monitoring network (TAQMN) and the AirBox network both monitor PM2.5 in Taiwan. The TAQMN, managed by Taiwan's Environmental Protection Administration (EPA), provides high-quality PM2.5 measurements at 77 monitoring stations. The AirBox network launched more recently consists of low-cost, small internet-of-things (IoT) microsensors (i.e., AirBoxes) at thousands of locations. While the AirBox network provides broad spatial coverage, its measurements are unreliable and require calibrations. However, applying a universal calibration procedure to all AirBoxes does not work well because the calibration line varies with local factors, including the chemical compositions of PM2.5 , which are not homogeneous in space. Therefore, different calibrations are needed at different locations to adapt to their local environments. Unfortunately, AirBoxes and EPA locations are misaligned, challenging the calibration task. In this paper, we propose a spatial model with spatially varying coefficients to account for the heterogeneity in the data. Our method gives spatially adaptive calibrations of AirBoxes and produces accurate PM2.5 concentration estimates with their error bars at any location, incorporating two types of measurements. In addition, the proposed method is robust to outliers, requires no colocated data, and provides calibration formulas for new AirBoxes once they are added to the network. We illustrate our approach using hourly PM2.5 data in 2020. After the calibration, the results show that the PM2.5 prediction improves by about 38%-68% in root-mean-squared prediction error. Once the calibration formulas are established, we can obtain reliable PM2.5 values even if we ignore EPA data.

Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty.

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naïve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naïve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Exploration of spatiotemporal heterogeneity and socio-demographic determinants on COVID-19 incidence rates in Sarawak, Malaysia.

BACKGROUND: In Sarawak, 252 300 coronavirus disease 2019 (COVID-19) cases have been recorded with 1 619 fatalities in 2021, compared to only 1 117 cases in 2020. Since Sarawak is geographically separated from Peninsular Malaysia and half of its population resides in rural districts where medical resources are limited, the analysis of spatiotemporal heterogeneity of disease incidence rates and their relationship with socio-demographic factors are crucial in understanding the spread of the disease in Sarawak. METHODS: The spatial dependence of district-wise incidence rates is investigated using spatial autocorrelation analysis with two orders of contiguity weights for various pandemic waves. Nine determinants are chosen from 14 covariates of socio-demographic factors via elastic net regression and recursive partitioning. The relationships between incidence rates and socio-demographic factors are examined using ordinary least squares, spatial lag and spatial error models, and geographically weighted regression. RESULTS: In the first 8 months of 2021, COVID-19 severely affected Sarawak's central region, which was followed by the southern region in the next 2 months. In the third wave, based on second-order spatial weights, the incidence rate in a district is most strongly influenced by its neighboring districts' rate, although the variance of incidence rates is best explained by local regression coefficient estimates of socio-demographic factors in the first wave. It is discovered that the percentage of households with garbage collection facilities, population density and the proportion of male in the population are positively associated with the increase in COVID-19 incidence rates. CONCLUSION: This research provides useful insights for the State Government and public health authorities to critically incorporate socio-demographic characteristics of local communities into evidence-based decision-making for altering disease monitoring and response plans. Policymakers can make well-informed judgments and implement targeted interventions by having an in-depth understanding of the spatial patterns and relationships between COVID-19 incidence rates and socio-demographic characteristics. This will effectively help in mitigating the spread of the disease.

Performance Enhancement of INS and UWB Fusion Positioning Method Based on Two-Level Error Model.

In GNSS-denied environments, especially when losing measurement sensor data, inertial navigation system (INS) accuracy is critical to the precise positioning of vehicles, and an accurate INS error compensation model is the most effective way to improve INS accuracy. To this end, a two-level error model is proposed, which comprehensively utilizes the mechanism error model and propagation error model. Based on this model, the INS and ultra-wideband (UWB) fusion positioning method is derived relying on the extended Kalman filter (EKF) method. To further improve accuracy, the data prefiltering algorithm of the wavelet shrinkage method based on Stein's unbiased risk estimate-Shrink (SURE-Shrink) threshold is summarized for raw inertial measurement unit (IMU) data. The experimental results show that by employing the SURE-Shrink wavelet denoising method, positioning accuracy is improved by 76.6%; by applying the two-level error model, the accuracy is further improved by 84.3%. More importantly, at the point when the vehicle motion state changes, adopting the two-level error model can provide higher computational stability and less fluctuation in trajectory curves.

An Algorithm for Online Stochastic Error Modeling of Inertial Sensors in Urban Cities.

Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models.

Bias due to Berkson error: issues when using predicted values in place of observed covariates.

Studies often want to test for the association between an unmeasured covariate and an outcome. In the absence of a measurement, the study may substitute values generated from a prediction model. Justification for such methods can be found by noting that, with standard assumptions, this is equivalent to fitting a regression model for an outcome variable when at least one covariate is measured with Berkson error. Under this setting, it is known that consistent or nearly consistent inference can be obtained under many linear and nonlinear outcome models. In this article, we focus on the linear regression outcome model and show that this consistency property does not hold when there is unmeasured confounding in the outcome model, in which case the marginal inference based on a covariate measured with Berkson error differs from the same inference based on observed covariates. Since unmeasured confounding is ubiquitous in applications, this severely limits the practical use of such measurements, and, in particular, the substitution of predicted values for observed covariates. These issues are illustrated using data from the National Health and Nutrition Examination Survey to study the joint association of total percent body fat and body mass index with HbA1c. It is shown that using predicted total percent body fat in place of observed percent body fat yields inferences which often differ significantly, in some cases suggesting opposite relationships among covariates.

The impact of accuracy and precision of analytical test methods on the determination of withdrawal periods.

Treatment of food-producing animals with veterinary medicinal products (VMPs) can result in residues in foodstuffs (e.g. eggs, meat, milk, or honey) representing a potential consumer health risk. To ensure consumer safety, worldwide regulatory concepts for setting safe limits for residues of VMPs e.g. as tolerances (US) or maximum residue limits (MRLs, EU) are used. Based on these limits so-called withdrawal periods (WP) are determined. A WP represents the minimum period of time required between the last administration of the VMP and the marketing of foodstuff. Usually, WPs are estimated using regression analysis based on residue studies. With high statistical confidence (usually 95% in the EU and 99% in the US) the residues in almost all treated animals (usually 95%) have to be below MRL when edible produce is harvested. Here, uncertainties from both sampling and biological variability are taken into account but uncertainties of measurement associated with the analytical test methods are not systematically considered. This paper describes a simulation experiment to investigate the extent to which relevant sources of measurement uncertainty (accuracy and precision) can impact the length of WPs. A set of real residue depletion data was artificially 'contaminated' with measurement uncertainty related to permitted ranges for accuracy and precision. The results show that both accuracy and precision had a noticeable effect on the overall WP. Due consideration of sources of measurement uncertainty may improve the robustness, quality and reliability of calculations upon which regulatory decisions on consumer safety of residues are based.

Bayesian analysis for partly linear Cox model with measurement error and time-varying covariate effect.

The Cox proportional hazards model is commonly used to estimate the association between time-to-event and covariates. Under the proportional hazards assumption, covariate effects are assumed to be constant in the follow-up period of study. When measurement error presents, common estimation methods that adjust for an error-contaminated covariate in the Cox proportional hazards model assume that the true function on the covariate is parametric and specified. We consider a semiparametric partly linear Cox model that allows the hazard to depend on an unspecified function of an error-contaminated covariate and an error-free covariate with time-varying effect, which simultaneously relaxes the assumption on the functional form of the error-contaminated covariate and allows for nonconstant effect of the error-free covariate. We take a Bayesian approach and approximate the unspecified function by a B-spline. Simulation studies are conducted to assess the finite sample performance of the proposed approach. The results demonstrate that our proposed method has favorable statistical performance. The proposed method is also illustrated by an application to data from the AIDS Clinical Trials Group Protocol 175.

The spatial influences of organic farming and environmental heterogeneity on biodiversity in South Australian landscapes.

The potential link between certified organic farming and biodiversity and conservation remains unexplored in Australia, despite the country having the world's largest amount of certified organic farmland and unprecedented biodiversity loss. This study modelled the spatial effects of organic farming (intensity of local farming systems), environmental heterogeneity, and urbanisation on two widely studied environmental taxa - vascular plant and bird species richness (surrogate measures of biodiversity) - in South Australia, using a unique certified organic farming postcode level dataset from 2001 to 2016 (N = 5440). The spatial Durbin error model results confirmed the positive spatial congruence of organic farming with greater vascular plant species richness, whereas only weak to no significant evidence was found for bird species richness. Landscape features (habitat heterogeneity) and green vegetation (a proxy indicator of resource availability) - rather than organic farming - appeared to be most associated with bird species richness. Both plant and bird species richness were positively associated with habitat heterogeneity (land cover diversity and elevation range), plant productivity and proportion of conservation land and water bodies. Whereas, increased anthropogenic land use for cropping and horticultural farming, soil type diversity and proximity to the coast significantly reduced species richness of both taxa. The results suggest that a multi-scale spatially refined biodiversity conservation strategy, with spatial targeting that promotes low intensive farming systems and increases landscape heterogeneity to provide quality habitat (a whole of landscape approach by incorporating private agricultural landholders), could be beneficial for biodiversity conservation.

Factors Affecting Stunting in Children under 5 Years of Age in Indonesia using Spatial Model.

Background: Stunting in children under 5 years of age is a condition where they have a length or height that is less than -2 standard deviations of the growth standard of Indonesian children. Stunting is caused by chronic malnutrition in the first 1000 days of life. The spatial panel data method was developed to solve problems related to spatial objects that are measured periodically by involving elements of area and time. Objectives: The purpose of this study was to determine the best model and factors that influence stunting in children under 5 years of age in Indonesia using spatial panel data. Methods: The data used were from the website of the Central Statistics Agency and the publications of the Ministry of Health of the Republic of Indonesia in 2015-2019. Determination of the selected model is done by comparing the random effect spatial autoregressive model and spatial error model (SEM) random effect based on the value and Akaike information criterion (AIC). SEM random effect produces the largest value and the smallest AIC. Results: The selected spatial panel data model in determining the factors that influence stunting in children under 5 years of age in Indonesia is the SEM random effect based on the largest and AIC compared to other models. Conclusion: Based on the selected model, children under five with malnutrition and poor nutrition, receiving Vitamin A, and the average monthly per capita expenditure on food have a significant effect on the percentage of stunting in children under five in Indonesia.

Efficient study design to estimate population means with multiple measurement instruments.

Outcomes from studies assessing exposure often use multiple measurements. In previous work, using a model first proposed by Buonoccorsi (1991), we showed that combining direct (eg, biomarkers) and indirect (eg, self-report) measurements provides a more accurate picture of true exposure than estimates obtained when using a single type of measurement. In this article, we propose a tool for efficient design of studies that include both direct and indirect measurements of a relevant outcome. Based on data from a pilot or preliminary study, the tool, which is available online as a shiny app at https://michalbitan.shinyapps.io/shinyApp/, can be used to compute: (1) the sample size required for a statistical power analysis, while optimizing the percent of participants who should provide direct measures of exposure (biomarkers) in addition to the indirect (self-report) measures provided by all participants; (2) the ideal number of replicates; and (3) the allocation of resources to intervention and control arms. In addition we show how to examine the sensitivity of results to underlying assumptions. We illustrate our analysis using studies of tobacco smoke exposure and nutrition. In these examples, a near-optimal allocation of the resources can be found even if the assumptions are not precise.

Exceptionally Steep Brain-Body Evolutionary Allometry Underlies the Unique Encephalization of Osteoglossiformes.

Brain-body static allometry, which is the relationship between brain size and body size within species, is thought to reflect developmental and genetic constraints. Existing evidence suggests that the evolution of large brain size without accompanying changes in body size (that is, encephalization) may occur when this constraint is relaxed. Teleost fish species are generally characterized by having close-fitting brain-body static allometries, leading to strong allometric constraints and small relative brain sizes. However, one order of teleost, Osteoglossiformes, underwent extreme encephalization, and its mechanistic bases are unknown. Here, I used a dataset and phylogeny encompassing 859 teleost species to demonstrate that the encephalization of Osteoglossiformes occurred through an increase in the slope of evolutionary (among-species) brain-body allometry. The slope is virtually isometric (1.03 ± 0.09 SE), making it one of the steepest evolutionary brain-body allometric slopes reported to date, and it deviates significantly from the evolutionary brain-body allometric slopes of other clades of teleost. Examination of the relationship between static allometric parameters (intercepts and slopes) and evolutionary allometry revealed that the dramatic steepening of the evolutionary allometric slope in Osteoglossiformes was a combined result of evolution in the slopes and intercepts of static allometry. These results suggest that the evolution of static allometry, which likely has been driven by evolutionary changes in the rate and timing of brain development, has facilitated the unique encephalization of Osteoglossiformes.

A Novel Calibration Method for Gyro-Accelerometer Asynchronous Time in Foot-Mounted Pedestrian Navigation System.

Pedestrian Navigation System (PNS) is one of the research focuses of indoor positioning in GNSS-denied environments based on the MEMS Inertial Measurement Unit (MIMU). However, in the foot-mounted pedestrian navigation system with MIMU or mobile phone as the main carrier, it is difficult to make the sampling time of gyros and accelerometers completely synchronous. The gyro-accelerometer asynchronous time affects the positioning of PNS. To solve this problem, a new error model of gyro-accelerometer asynchronous time is built. The effect of gyro-accelerometer asynchronous time on pedestrian navigation is analyzed. A filtering model is designed to calibrate the gyro-accelerometer asynchronous time, and a zero-velocity detection method based on the rate of attitude change is proposed. The indoor experiment shows that the gyro-accelerometer asynchronous time is estimated effectively, and the positioning accuracy of PNS is improved by the proposed method after compensating for the errors caused by gyro-accelerometer asynchronous time.

Introduction to Semi-Classical Analysis for Digital Errors of Qubit in Quantum Processor.

In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has been pointed out that a new type of quantum error, such as nonlinear error, appears. It is not clear how to handle such new effects in information theory. First of all, one should make the characteristics of the error probability of qubits clear as communication channel error models in information theory. The purpose of this paper is to survey the progress for modeling the quantum noise effects that information theorists are likely to face in the future, to cope with such nontrivial errors mentioned above. This paper explains a channel error model to represent strange properties of error probability due to new quantum noise. By this model, specific examples on the features of error probability caused by, for example, quantum recurrence effects, collective relaxation, and external force, are given. As a result, it is possible to understand the meaning of strange features of error probability that do not exist in classical information theory without going through complex physical phenomena.

GIS-based spatial modelling of COVID-19 death incidence in São Paulo, Brazil.

Seeking to understand the socio-spatial behaviour of the COVID-19 virus in the most impacted area in Brazil, five spatial regression models were analysed to assess the disease distribution in the affected territory. Results obtained using the Spearman correlation test provided evidence for the correlation between COVID-19 death incidence and social aspects such as population density, average people per household, and informal urban settlements. More importantly, all analysed models using four selected explanatory variables have proven to represent at least 85 per cent of reported deaths at the district level. Overall, our results have demonstrated that the geographically weighted regression (GWR) model best explains the spatial distribution of COVID-19 in the city of São Paulo, highlighting the spatial aspects of the data. Spatial analysis has shown the spread of COVID-19 in areas with highly vulnerable populations. Our findings corroborate reports from the recent literature, pointing out the need for special attention in peripheral areas and informal settlements.