Assumption Of Statistical Independence Research Articles

Dynamics of large oscillator populations with random interactions.

We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions defined via the coupling functions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function.

Quantum Nonlocality: How Does Nature Do It?

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space-time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other's state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell-CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter's freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole.

Integration of Time-Frequency Analysis and Regularization Technique for Improved Identification of Fetal Electrocardiogram

This research article presents a novel methodology for effectively extracting the fetal electrocardiogram (FECG) from a single-channel signal acquired on the maternal abdomen. The signal comprises a mixture of the FECG, maternal electrocardiogram (MECG), and ambient noise. The central concept involves projecting the signal into higher-dimensional spaces and leveraging the assumption of statistical independence among the constituent components to achieve their separation from the mixture. To accomplish this, singular value decomposition (SVD) is initially applied to the spectrogram, followed by an iterative application of independent component analysis (ICA) on the principal components. The SVD technique contributes to the enhanced separability of each individual component, while ICA facilitates the promotion of statistical independence between the fetal and maternal ECGs. Furthermore, we refine and customize the aforementioned approach specifically for ECG signals by incorporating knowledge of the frequency distribution of the MECG and other inherent ECG characteristics. The effectiveness of the proposed methodology is validated through comprehensive experimental studies, demonstrating its superior accuracy and performance compared to existing techniques.

Constrained Decoupled Dictionary Learning of Task fMRI data

AbstractBackgroundDictionary learning techniques have the potential to efficiently detect functional connectivity impairments in distributed brain networks associated with Alzheimer’s Disease (AD) when applied to task functional magnetic resonance imaging (tfMRI) data. However, traditional methods are constrained in what brain networks they can identify due to the statistical independence assumptions they make, and they do not leverage the structure of the tfMRI task when identifying networks. We used a new sparse dictionary learning technique to identify brain functional network correlates of cardiometabolic risk variables in a community‐based cohort.MethodThe Bogalusa Heart Study (BHS) is community‐based cohort study of atherosclerosis and risk factors for cardiovascular disease. fMRI data was collected from 100 participants of BHS during performance of a Stroop task. Spatially concatenated tfMRI data was factorized into a group‐wise temporal dictionary matrix and a set of scan‐level spatial patterns while biasing a subset of learned temporal patterns to be paradigm related. Scan‐level spatial patterns obtained as a result were aggregated and factorized to derive a group‐level spatial dictionary matrix and sparse loading coefficients. The sparse loading coefficients obtained from this Constrained Decoupled Dictionary Learning (CDDL) method were used as descriptive biomarkers, the relevance of which was established by using them to predict cardiometabolic variables including fasting glucose level, homeostatic model assessment for insulin resistance (HOMA‐IR) index and fasting insulin level using support vector regression and a leave‐one out cross‐validation. The performance of the algorithm was calculated in terms of Mean Absolute Percentage Error (MAPE) between actual and predicted cardiometabolic variable valuesResultThe SVM regressor was able to predict the cardiometabolic variables with low MAPE. The prediction of glucose values achieved the least MAPE for all kernel types (Table 1).ConclusionCombining prior knowledge, decoupling of spatial and temporal patterns, and high‐dimensional regression, we generated brain functional network patterns from real‐world tfMRI data that associated with known cardiometabolic indicators of brain health. These brain functional network patterns thus have the potential to serve as indicators of brain health.

The effect of source sparsity on independent vector analysis for blind source separation

In this paper, the effect of source sparsity on the performance of the independent vector analysis (IVA) algorithm for blind source separation is investigated. The IVA algorithm was originally developed under the assumption of statistical independence between the sources and has made great advances in recent years. However, its performance under different sparsity conditions is rarely studied. This study begins by mathematically analyzing the performance of IVA in permutation alignment, which is proved to directly correlate with the degree of frame-level W-disjoint orthogonality (F-WDO) of the sources. We further prove that IVA can theoretically achieve the optimal separation in the cases where the sources are F-WDO. Experimental results show a strong positive correlation between a quantitative measure of F-WDO and the IVA algorithm’s performance under various conditions.

A Multi-Spectral Fractal Image Model and Its Associated Fractal Dimension Estimator

We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral bands. The model is validated mathematically under the assumption of statistical independence of the spectral components. Using this model, we generate several synthetic multi-spectral fractal images of varying complexity, with seven statistically independent spectral bands at specific wavelengths in the visible domain. The fractal dimension estimator is based on the widely used probabilistic box-counting classical approach extended to the multivariate domain of multi-spectral images. We validate the estimator on the previously generated synthetic multi-spectral images having fractal properties. Furthermore, we deploy the proposed multi-spectral fractal image estimator for the complexity assessment of real remotely sensed data sets and show the usefulness of the proposed approach.

Designing databases and using generalized estimating equations for entheseal datasets: An example from the Tiwanaku culture (AD 500–1100)

AbstractStudying entheseal changes (EC) in human skeletal remains involves questions surrounding how researchers should collect, process, and evaluate these data as there are no set standards. Osteoarcheological research should also be able to answer population‐level queries using entheses, such as if group A was moving their body in different ways from group B? Or are there age‐related tasks or gendered labors? However, not all entheseal data can be easily evaluated in this fashion. If researchers select one area of the body, they may not be able to discuss population‐level differences. In addition, if data are evaluated by each muscle attachment area throughout a body, the results can be overwhelming. Further, grouping EC may produce problems with statistical assumptions of independence. To address these design and scalar issues, we discuss proper database construction, including the importance for consistent data collection strategies and in anchoring individuals under a specimen number. We also show how generalized estimating equations (GEE) can address how individual‐level scores can be collected and population‐level research questions can be answered with entheseal marker data processed in SAS 9.4 or the free alternative, R. We utilize a sample of over 1200 adults from the Tiwanaku culture (AD 500–1100) of Bolivia and Peru. We demonstrate evaluating significant overall differences while also pinpointing specific EC by sex or by age at death to discuss various ways in which bodies moved in the past.

Human genomic data have different statistical properties than the data of randomised controlled trials.

Madole & Harden argue that the Mendelian reshuffling of genes and genomes is analogous to randomised controlled trials. We are not convinced by their arguments. First, their recipe for meeting the demands on randomised experiments is inherently inconsistent. Second, disequilibrium across chromosomes conflicts with their assumption of statistical independence. Third, the genome-wide association study (GWAS) method has many pitfalls, including low repeatability.

On limiting the influence of serial correlation in metocean data for prediction of extreme return levels and environmental contours

Metocean conditions change slowly, over the course of hours, sometimes even days, as storms develop and swells travel across the globe. Thus, measurements of these conditions are often serially correlated. However, many commonly employed methods for predicting metocean conditions for engineering design analyses are built upon an assumption of statistical independence of the data (e.g., hourly significant wave heights). In this brief study, we present an assessment of the serial (temporal) dependence in a selected metocean dataset. A method for processing a dataset that identifies and groups data sequences as “storm” events, and thus reduces serial dependence, is proposed and tested for estimating extreme metocean return levels. The results of this study show that the proposed procedure does indeed limit dependence and that environmental contours produced using this storm grouping procedure are reasonable based on the original dataset and when compared with associated alternative contours that ignore temporal dependence.

Relations Between Statistics of Three-Dimensional Flame Curvature and its Two-Dimensional Counterpart in Turbulent Premixed Flames

The relations between the actual flame curvature probability density function (PDF) evaluated in three-dimensions and its two-dimensional counterpart based on planar measurements have been analytically derived subject to the assumptions of isotropy and statistical independence of various angles and two-dimensional curvature. These relations have been assessed based on Direct Numerical Simulation (DNS) databases of turbulent premixed (a) statistically planar and (b) statistically axisymmetric Bunsen flames. It has been found that the analytically derived relation interlinking the PDFs of actual three-dimensional curvature and its two-dimensional counterpart holds reasonably well for a range of curvatures around the mean value defined by the inverse of the thermal flame thickness for different turbulence intensities across different combustion regimes. The flame surface is shown to exhibit predominantly two-dimensional cylindrical curvature but there is a significant probability of finding saddle type flame topologies and this probability increases with increasing turbulence intensity. The presence of saddle type flame topologies affects the ratios of second and third moments of two-dimensional and three-dimensional curvatures. It has been demonstrated that the ratios of second and third moments of two-dimensional and three-dimensional curvatures cannot be accurately predicted based on two-dimensional measurements. The ratio of the third moments of two-dimensional and three-dimensional curvatures remains positive and thus the qualitative nature of curvature skewness can still be obtained based on two-dimensional curvature measurements. As the curvature skewness is often taken to be a marker of the Darrius-Landau instability, the conclusion regarding the presence of this instability can potentially be taken from the two-dimensional curvature measurements.

Separation of Aortic and Pulmonary Components from Second Heart Sounds without an Assumption of Statistical Independence

Separation of Aortic and Pulmonary Components from Second Heart Sounds without an Assumption of Statistical Independence

Supermeasured: Violating Bell-Statistical Independence Without Violating Physical Statistical Independence

Bell’s theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an assumption called Statistical Independence. Violations of Statistical Independence are commonly interpreted as correlations between the measurement settings and the hidden variables (which determine the measurement outcomes). Such correlations have been discarded as “fine-tuning” or a “conspiracy”. We here point out that the common interpretation is at best physically ambiguous and at worst incorrect. The problem with the common interpretation is that Statistical Independence might be violated because of a non-trivial measure in state space, a possibility we propose to call “supermeasured”. We use Invariant Set Theory as an example of a supermeasured theory that violates the Statistical Independence assumption in Bell’s theorem without requiring correlations between hidden variables and measurement settings (physical statistical independence).

Context-independent mapping and free choice are equivalent: a general proof

Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in an HVM means that the results of a measurement do not depend on settings for other measurements. If the measurements are spacelike separated, this assumption is known as local causality. Both free choice and CI mapping assumptions are considered necessary for derivation of the Bell-type criteria of contextuality/nonlocality. It is known, however, for a variety of special cases, that the two assumptions are not logically independent. We show here, in complete generality, for any system of random variables with or without disturbance/signaling, that an HVM that postulates CI mapping is equivalent to an HVM that postulates free choice. If one denies the possibility that a given empirical scenario can be described by an HVM in which measurements depend on other measurements’ settings, free choice violations should be denied too, and vice versa.

What factors drive state firearm law adoption? An application of exponential-family random graph models

Guns are a ubiquitous feature of contemporary US culture, driven, at least partly, by firearms' constitutional enshrinement. However, the majority of laws intended to restrict or expand firearm access and use are formulated and passed in the states, leading to 50 different firearm-related legal environments. To date, little is known about why some states pass more restrictive or permissive firearm laws than others. In this article, we identify patterns of firearm law adoption across states, by framing the problem as a bipartite network (states connected to laws and laws connected to states) that is the result of a complex, and interconnected system of unobserved forces. We employ Exponential-family Random Graph Models (ERGMs), a class of statistical network models that allow for the dispensing of the assumptions of statistical independence, to identify factors that increase or decrease the likelihood of states adopting permissive or restrictive firearms laws over the period 1979 to 2020. Results show that more progressive state governments are associated with a higher chance of enacting restrictive firearm laws, and a lower chance of enacting permissive ones. Conservative state governments are associated with the analogous reversed association. States are more likely to adopt laws if bordering states have also adopted that law. For both restrictive and permissive laws the presence of a law in a neighboring state increased the conditional likelihood of a state having that law, that is laws diffuse across state borders. High levels of homicides are associated with a state having adopted more permissive, but not more restrictive, firearm laws. In summary, these results point to a complex interplay of state internal and external factors that seem to drive different patterns of firearm law adoption Based on these results, future work using related classes of models that take into account the time evolution of the network structure may provide a means to predict the likelihood of future law adoption.

Robust Copula-Based Detection of Shallow-Buried Landmines With Forward-Looking Radar

We propose a technique for landmine detection using forward-looking ground-penetrating radar. The detector is applied to radar images obtained from multiple viewpoints of the region of interest and is based on a robust version of the likelihood ratio test (LRT). We incorporate the statistical dependence between multiview images into the test via copula-based model. The test is designed to maximize the worst-case performance over all feasible pairs of target and clutter distributions, thereby eliminating the need for strong assumptions about the image statistics. We evaluate the detection performance of the proposed technique for different copula functions representing the dependence structure. Using electromagnetic modeled data of shallow-buried targets under varying ground surface roughness profiles, we demonstrate the superiority of the robust copula-based detector over existing parametric and robust LRT approaches designed under the assumption of statistical independence of multiview images.

A statistical reanalysis of morphological differentiation among island night lizards (Xantusia riversiana) from the California Channel Islands

This study re-analyzes morphometric and meristic data among island night lizards, Xantusia riversiana, from the California Channel Islands of San Clemente, Santa Barbara, and San Nicolas in order to ascertain whether the implementation of different statistical methods can recover different results that could potentially alter biological interpretations. Our results concur with a recent previous study demonstrating that the three island populations differ morphologically from one another and that the San Nicolas Island population is the most divergent. Several important aspects, however, of the previous study depart significantly from those recovered here. Our analyses found sexual dimorphism within each population for both morphometric and meristic characters to be relatively uncommon whereas the previous study found nearly all characters to be sexually dimorphic for all island populations. The previous study also recovered significant differences among the three island populations for all morphometric characters whereas far fewer differences were recovered in the present study. Both studies found few significant inter-island differences among the meristic characters. The discordances between these two studies stem from differences in the a priori treatment of the raw character data and the different downstream statistical analyses and visualization techniques used on those data. This was particularly relevant with the use here of an allometric growth algorithm for size-correcting the morphometric data not used in the previous study and by treating all three populations as independently evolving groups. We did not conduct analyses where data from the San Clemente and Santa Barbara island populations were conflated based on their subspecific designation (X. r. reticulata) and then compared to data from the independently evolving San Nicolas Island population. This imprudent use of taxonomy violates the assumptions of statistical independence. We emphasize that explicit justification for the use of particular statistical analyses should occur in all studies—especially if the results bear on the implementation of effective and efficient resource management programs.

Stochastic Method to Predict Effects of Roll Grinding Deviations on Sheet Flatness in Cold Rolling

Abstract Industrial measurements of the diameter profiles of work-rolls used in cold sheet rolling are applied with a stochastic roll-stack model to better understand how residual error from the roll grinding process affects the rolled sheet flatness quality. Roll diameter measurements taken via a noncontact, optical device on new, warm, and worn work-rolls show that the diameter deviations vary along the roll lengths, across roll samples, and at different operational states, suggesting a multidimensional random field problem. Studies are conducted for a 4-high rolling mill with 301 stainless steel sheet to investigate the reliability in achieving target flatness considering the work-roll diameter random field. Also investigated is the sensitivity of the flatness reliability to roll diameter deviations at different locations along the roll lengths and for the three operational states (newly machined, warm, and worn following several passes). The results lead to several key findings. Foremost, it is shown that an assumption of statistical independence among the residual grinding errors at different roll axis locations is improper. Furthermore, it is demonstrated that, for the measured grinding error correlation patterns, the roll diameter deviations external to the roll/sheet contact region play an important role in contributing to flatness defects within the sheet and that these influences vary according to the roll operational state (new, warm, worn). The presented stochastic model and applied measurement data thus provide for a new understanding into how roll grinding performance influences dimensional quality in the sheet rolling process.

Investigation into the foundations of the track-event theory of cell survival and the radiation action model based on nanodosimetry

This work aims at elaborating the basic assumptions behind the “track-event theory” (TET) and its derivate “radiation action model based on nanodosimetry” (RAMN) by clearly distinguishing between effects of tracks at the cellular level and the induction of lesions in subcellular targets. It is demonstrated that the model assumptions of Poisson distribution and statistical independence of the frequency of single and clustered DNA lesions are dispensable for multi-event distributions because they follow from the Poisson distribution of the number of tracks affecting the considered target volume. It is also shown that making these assumptions for the single-event distributions of the number of lethal and sublethal lesions within a cell would lead to an essentially exponential dose dependence of survival for practically relevant values of the absorbed dose. Furthermore, it is elucidated that the model equation used for consideration of repair within the TET is based on the assumption that DNA lesions induced by different tracks are repaired independently. Consequently, the model equation is presumably inconsistent with the model assumptions and requires an additional model parameter. Furthermore, the methodology for deriving model parameters from nanodosimetric properties of particle track structure is critically assessed. Based on data from proton track simulations it is shown that the assumption of statistically independent targets leads to the prediction of negligible frequency of clustered DNA damage. An approach is outlined how track structure could be considered in determining the model parameters, and the implications for TET and RAMN are discussed.

Transported and presumed probability density function modeling of the Sandia flames with flamelet generated manifold chemistry

The first modeling results for Sandia flames D, E, and F using the flamelet generated manifold reduced chemistry model with a transported probability density function (TPDF) closure model are presented. The micro-mixing is modeled with the simple “interaction by exchange with the mean” model and mean molecular diffusion is accounted for through a mean drift term. By accounting for mean molecular diffusion, stable burning flames D, E, and F could be predicted using the standard value for the mixing rate constant Cϕ=2. The TPDF results are used in an a priori analysis of the main simplifying assumptions typically used in presumed PDF (PPDF) models. A new PPDF model that accounts for the correlation between mixture fraction and progress variable in the joint PDF through a Gaussian copula is presented and included in the analysis. The analysis reaffirmed earlier findings: the marginal PDF of the progress variable is not well approximated by a β-PDF and the mixture fraction and progress variable are not statistically independent. The Gaussian copula PPDF model did show a qualitative improvement over the models that invoke the statistical independence assumption. Quantitative analysis showed that the mean progress variable source term could not be predicted accurately by any of the PPDF models. The PPDF models were then applied in actual simulations of flames D and E. The erroneous predictions of the mean progress variable source term cause relative errors in the PPDF simulation results for the conditional mean temperature exceeding 20%.

Improve the performance of independent component analysis by mapping the spectrum to an orthogonal space

Independent Component Analysis (ICA) has attracted chemists recently, for its charm can separate the independent signals from a mixed system and does not need prior knowledge. However, its dissatisfactory performance for the chemical measured signal is still blocking the practicability. Thus, this paper summarized the ICA processing path from the establishment of rectangular coordinates in linear space to the determination of the corresponding relation between the coordinate system and real components. The primary cause of the deviation between the ICA results and the chemical measurements is that the measuring signal was subject to uncertainty. Besides, uncertainty made the deviation of source signal from the statistical independence assumption, or in other words, it appeared to be nonorthogonal. For this key, it proposed to map the measured value to the high-order derivative space, use the derivative to narrow the peak width, reduce the influence of uncertainty, and improve the separation performance of ICA to chemical measurement signal, such as the spectrum. Actual cases of this paper showed that when up to 6th order, the separating results had been perfect for IR spectra, and even for homologs isomers.