Some nonparametric tests for randomness in sequences
Some nonparametric tests for randomness in sequences
SEQUENTIAL ANALYSIS↗
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Permutation Testing and Bootstrapping: NonParametric Approaches to Statistical Testing and Estimation
No abstract available
Young, Millennia↗
Are the 1986-1988 changes in solar free-oscillation frequency splitting significant?
The solar normal-mode splitting coefficients deduced from Big Bear Solar Observatory (BBSO) data differ between 1986 and 1988; inversions for equatorial rotation are slower at depth and faster near the surface in 1988 than in 1986. The significance of the change has been disputed. The data sets overlap for five splitting coefficients (a(j))super 5 sub j = 1 associated with 710 multiplets. On the assumption that rotation rate varies smoothly with radius, both data sets are satisfied by the same rotation model at all colatitudes except near 30-40 deg and near 70 deg (and at their southern hemisphere reflections 140-150 deg and 110 deg). The evidence for equatorial change is weak. Nonparametric tests show a significant offset in the magnitudes of a(1), a(2), and a(4), and of linear combinations sensitive to rotation at colatitudes of 60-80 deg (and 120 deg). Nonparametric tests show significant radial trends in the changes to a(2), a(4), and (less significantly) a(5). There is strong anticorrelation between a(2) and a(4), a(1) and a(3), and a(3) and a(5), suggesting that the estimates are not independent. Individual coefficients a(j) show more evidence for change than do 'physical' linear combinations, adding weight to this hypothesis. Some of the changes in splitting might be related to solar activity, which changed most near colatitude 70 deg from 1986 to 1988.
Gough, Douglas↗
Asymptotic Efficiency of New Distribution-Free Tests of Symmetry for Generalized Skew Alternatives
The Bahadur efficiency of new nonparametric tests of symmetry recently proposed by Nikitin and Ahsanullah is calculated. In contrast to this result, where only location alternatives were discussed, in the present paper generalized skew alternatives are of interest. It is shown that the new tests are highly efficient for a large class of skew alternatives. The problem of most favorable alternatives is also studied.
97 MATHEMATICS AND COMPUTING↗
Percent-Level Test of Isotropic Expansion Using Type Ia Supernovae
We propose and implement a novel, robust, and nonparametric test of statistical isotropy of the expansion of the Universe and apply it to around 1000 type Ia supernovae from the Pantheon sample. We calculate the angular clustering of supernova magnitude residuals and compare it to the noise expected under the isotropic assumption. We also test for systematic effects and demonstrate that their effects are negligible or are already accounted for in our procedure. Here, we express our constraints as an upper limit on the rms spatial variation in the Hubble parameter at late times. For the sky smoothed with a Gaussian with FWHM = 60°, less than 1% rms spatial variation in the Hubble parameter is allowed at 99.7% confidence.
79 ASTRONOMY AND ASTROPHYSICS↗
FORTRAN implementation of Friedman's test for several related samples
The FRIEDMAN program is a FORTRAN-coded implementation of Friedman's nonparametric test for several related samples with one observation per treatment/-block combination, or as it is sometimes called, the two-way analysis of variance by ranks. The FRIEDMAN program is described and a test data set and its results are presented to aid potential users of this program.
Davidson, S. A.↗
Dietary B group vitamin intake and the bladder cancer risk: a pooled analysis of prospective cohort studies
Abstract Purpose Diet may play an essential role in the aetiology of bladder cancer (BC). The B group complex vitamins involve diverse biological functions that could be influential in cancer prevention. The aim of the present study was to investigate the association between various components of the B group vitamin complex and BC risk. Methods Dietary data were pooled from four cohort studies. Food item intake was converted to daily intakes of B group vitamins and pooled multivariate hazard ratios (HRs), with corresponding 95% confidence intervals (CIs), were obtained using Cox-regression models. Dose–response relationships were examined using a nonparametric test for trend. Results In total, 2915 BC cases and 530,012 non-cases were included in the analyses. The present study showed an increased BC risk for moderate intake of vitamin B1 (HR B1 : 1.13, 95% CI: 1.00–1.20). In men, moderate intake of the vitamins B1, B2, energy-related vitamins and high intake of vitamin B1 were associated with an increased BC risk (HR (95% CI): 1.13 (1.02–1.26), 1.14 (1.02–1.26), 1.13 (1.02–1.26; 1.13 (1.02–1.26), respectively). In women, high intake of all vitamins and vitamin combinations, except for the entire complex, showed an inverse association (HR (95% CI): 0.80 (0.67–0.97), 0.83 (0.70–1.00); 0.77 (0.63–0.93), 0.73 (0.61–0.88), 0.82 (0.68–0.99), 0.79 (0.66–0.95), 0.80 (0.66–0.96), 0.74 (0.62–0.89), 0.76 (0.63–0.92), respectively). Dose–response analyses showed an increased BC risk for higher intake of vitamin B1 and B12. Conclusion Our findings highlight the importance of future research on the food sources of B group vitamins in the context of the overall and sex-stratified diet.
60 APPLIED LIFE SCIENCES↗
Linear clusters of galaxies - A194
New measurements for 160 redshifts and previous measurements for 108 other redshifts are presented for galaxies within 5 deg of A194. The galaxy distribution in A194 is shown to be inconsistent with a spherically symmetric King model. A mass-to-light ratio is derived using the virial theorem which is lower than the mean for the groups in the CfA redshift survey (Huchra and Geller, 1982; Geller, 1984). A nonparametric test for galaxy-cluster alignment and a Chi-squared test are used to search for alignment of galaxy major axes with the axis of A194. Evidence for neither luminosity segregation nor significant differences in the velocity or surface distributions of galaxies as a function of morphological type is found.
Chapman, G. N. F.↗
Influence of tumor location on the intensity-modulated radiation therapy plan of helical tomotherapy
Given the design of the Helical TomoTherapy device, the patient's central axis is routinely aligned with the machine's rotational axis to prevent the patient's body from colliding with the machine walls. However, for treatment of tumors located away from the patient's central axis, this position may not be optimal as the adequate radiation dose may not reach the affected site. Our study aimed to investigate the influence of tumor location on dose quality and delivery efficiency of tomotherapy plans. A phantom and 15 patients were selected for this study. Two plans, A and B, were implemented for each case. In plan A, the patient's central axis was aligned with the machine's rotational axis, whereas in plan B, the center of the planning target volume (PTV) was aligned with the machine's rotational axis. Both plans were optimized with the same planning parameters, and the dose quality of the plans was evaluated using dosimetrics. The delivery efficiency was determined from delivery time and monitor units (MUs). A paired t-test or nonparametric Wilcoxon signed-rank test was performed for statistical comparison. In the phantom study, the median delivery times were 358 and 336 seconds for plans A and B, respectively, and this difference was significant (p = 0.005). In the patient study, the median delivery times were 348 and 317 seconds for plans A and B, respectively, and this difference was also significant (p = 0.001). The dose qualities of both plans for each patient were nearly identical. No significant differences were found in the conformal index, heterogeneity index, and mean dose delivered to normal tissue between the plans. Both phantom and patient studies showed that for normal-sized patients, the delivery time reduced as the distance between the PTV and the patient's central axis increased when the PTV center was aligned with the machine axis. In conclusion, aligning the PTV center with the machine's rotational axis by shifting the patient during tomotherapy reduces the delivery time without compromising the dose quality of intensity-modulated radiation therapy.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
New Approach for Temporal Stability Evaluation of Pseudo-Invariant Calibration Sites (PICS)
Pseudo-Invariant Calibration Sites (PICS) are one of the most popular methods for in-flight vicarious radiometric calibration of Earth remote sensing satellites. The fundamental question of PICS temporal stability has not been adequately addressed. However, the main purpose of this work is to evaluate the temporal stability of a few PICS using a new approach. The analysis was performed over six PICS (Libya 1, Libya 4, Niger 1, Niger 2, Egypt 1 and Sudan 1). The concept of a “Virtual Constellation” was developed to provide greater temporal coverage and also to overcome the dependence limitation of any specific characteristic derived from one particular sensor. TOA reflectance data from four sensors consistently demonstrating “stable” calibration to within 5%—the Landsat 7 ETM+ (Enhanced Thematic Mapper Plus), Landsat 8 OLI (Operational Land Imager), Terra MODIS (Moderate Resolution Imaging Spectroradiometer) and Sentinel-2A MSI (Multispectral Instrument)–were merged into a seamless dataset. Instead of using the traditional method of trend analysis (Student’s T test), a nonparametric Seasonal Mann-Kendall test was used for determining the PICS stability. The analysis results indicate that Libya 4 and Egypt 1 do not exhibit any monotonic trend in six reflective solar bands common to all of the studied sensors, indicating temporal stability. A decreasing monotonic trend was statistically detected in all bands, except SWIR 2, for Sudan 1 and the Green and Red bands for Niger 1. An increasing trend was detected in the Blue band for Niger 2 and the NIR band for Libya 1. These results do not suggest abandoning PICS as a viable calibration source. Rather, they indicate that PICS temporal stability cannot be assumed and should be regularly monitored as part of the sensor calibration process.
Tuli, Fatima Tuz Zafrin↗
Asymptotic efficiency of two nonparametric competitors of Wilcoxon's two sample test
Asymptotic efficiency of two nonparametric competitors of Mann-Whitney-Wilcoxon U test
MANN-WHITNEY-WILCOXON U TEST↗
Model-based approach to investigate equipment-induced error in pressure-waveform derived hemodynamic measurements
Advanced hemodynamic monitoring systems have provided less invasive methods for estimating pressure-derived measurements such as pressure-derived cardiac output (CO) measurements. These devices apply algorithms to arterial pressure waveforms recorded via pressure recording components that transmit the pressure signal to a pressure monitor. While standards have been developed for pressure monitoring equipment, it is unclear how the equipment-induced error can affect secondary measurements from pressure waveforms. We propose an approach for modelling different components of a pressure monitoring system and use this model-based approach to investigate the effect of different pressure recording configurations on pressure-derived hemodynamic measurements. The proposed model-based approach is a three-step process. (1) Modelling the response of pressure recording components using bench tests; (2) verifying the identified models through nonparametric equivalence tests; and (3) assessing the effects of pressure recording components on pressure-derived measurements. To delineate the application of this approach, we performed a series of model-based analyses to quantify the combined effect of a wide range of tubing configurations with various damping ratios and natural frequencies and monitors with different bandwidths on pressure waveforms and CO measurements by six pulse contour algorithms. Model-based results show the error in pressure-derived CO measurements because of tubing configurations with different natural frequencies and damping ratios. Tubing configurations with low natural frequencies (<23 Hz) altered characteristics of pressure waveforms in a way that affected the CO measurement, some by as much as 20%. Our method can serve as a tool to quantify the performance of pressure recording systems with different dynamic properties. In conclusion, this approach can be applied to investigate the effects of physiologic signal recording configurations on various pressure-derived hemodynamic measurements.
42 ENGINEERING↗
Contrasting Perspectives Of Junior versus Senior NASA ISS Flight Controllers On Leadership And Cultural Issues
NASA flight controllers have always worked in a very demanding environment, but the International Space Station (ISS) poses even more challenges than prior missions. A recent NASA/Ames survey by Parke and Orasanu of NASA/Johnson flight controllers uncovered concerns about communications problems between American personnel and their international counterparts. To better understand these problems, we interviewed 14 senior and 12 junior ISS flight controllers at NASA/Johnson about leadership and cultural challenges they face and strategies for addressing these challenges. The qualitative interview data were coded and tabulated. Here we present quantitative analyses testing for differences between junior and senior controllers. Based on nonparametric statistical tests comparing responses across groups, the senior controllers were significantly more aware of the impact of working in dispersed teams, the context of constant change, and the upcoming multilateral challenges, while junior controllers were more aware of language and cultural issues. We consider our findings in light of other studies of controllers and other known differences between senior and junior controllers. For example, the fact that senior controllers had their formative early experience controlling pre-ISS short-duration Shuttle missions seems to have both positive and negative aspects, which are supported by our data. Our findings may also reflect gender differences, but we cannot unconfound this effect in our data because all the senior respondents were males. Many of the junior-senior differences are not only due to elapsed time on the job, but also due to a cohort effect. The findings of this study should be used for training curricula tailored differently for junior and senior controllers.
Clement, James L.↗
Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases
We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.
79 ASTRONOMY AND ASTROPHYSICS↗
Probing parity violation with the four-point correlation function of BOSS galaxies
Parity-violating physics in the early universe can leave detectable traces in late-time observables. While vector- and tensor-type parity violation can be observed in the B -modes of the cosmic microwave background, scalar-type signatures are visible only in the four-point correlation function (4PCF) and beyond. This work presents a blind test for parity violation in the 4PCF of the baryon oscillation spectroscopic survey (BOSS) CMASS sample, considering galaxy separations in the range [20; 160]h -1 Mpc The parity-odd 4PCF contains no contributions from standard Λ CDM physics and can be efficiently measured using recently developed estimators. Data are analyzed using both a nonparametric rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a compressed χ 2 analysis, with the former avoiding the assumption of a Gaussian likelihood. These find similar results, with the rank test giving a detection probability of 99.6% (2.9 σ). This provides significant evidence for parity violation, from either cosmological sources or systematics. We perform a number of systematic tests: although these do not reveal any observational artifacts, we cannot exclude the possibility that our detection is caused by the simulations not faithfully representing the statistical properties of the BOSS data. Our measurements can be used to constrain physical models of parity violation. As an example, we consider a coupling between the inflaton and a U (1) gauge field and place bounds on the latter’s energy density, which are several orders of magnitude stronger than those previously reported. Upcoming probes such as DESI and Euclid will reveal whether our detection of parity violation is due to new physics, and strengthen the bounds on a variety of models.
79 ASTRONOMY AND ASTROPHYSICS↗
A comparative study of nonparametric methods for pattern recognition
The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal.
Hahn, S. F.↗
A Nonparametric Method for the Inference of Halo Occupation Distributions
The galaxy–halo connection traces processes by which galaxies form and evolve. The halo occupation distribution (HOD) describes the relationship between galaxies and their host dark matter haloes. Measurements of the galaxy two-point correlation function (2PCF) allow us to extract information about the HODs of observed galaxy samples. Several parametric HOD models have been proposed in the literature, but the choice of parameterization restricts the space of possible HODs. To resolve this issue, we introduce a nonparametric HOD fitting method in which we train an emulator to learn the mappings among the galaxy 2PCF, physical properties used to select galaxy samples, and the HOD, all obtained from simulated past light cones constructed with the Santa Cruz semianalytic model. Implementing this emulator within a likelihood analysis framework, we derive constraints on the HOD of a galaxy sample when provided with a measurement of its 2PCF. Using the emulator to accelerate likelihood evaluations, we test the nonparametric HOD approach on a set of 2PCFs for mock galaxy samples drawn from the TNG100-1 simulation and selected above threshold values of stellar mass and star formation rate. Our framework is able to recover TNG100-1 HODs within 0.2 dex. We use the TNG100-1 mocks to tune the reported uncertainties to estimate those expected in the analysis of observations. Comparing to parametric HOD modelling routines applied to the same mock galaxy samples, our approach consistently infers the HOD with comparable or greater precision and accuracy.
Kennedy, Jacob [Rutgers Univ., Piscataway, NJ (Uni↗
Diffusion and perfusion MR parameters to assess preoperative short-course radiotherapy response in locally advanced rectal cancer: a comparative explorative study among Standardized Index of Shape by DCE-MRI, intravoxel incoherent motion- and diffusion kurtosis imaging-derived parameters
Purpose: To assess preoperative short-course radiotherapy (SCR) tumor response in locally advanced rectal cancer (LARC) by means of Standardized Index of Shape (SIS) by dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), apparent diffusion coefficient (ADC), intravoxel incoherent motion (IVIM) and diffusion kurtosis imaging (DKI) parameters derived from diffusion-weighted MRI (DW-MRI). Materials and methods: Thirty-four patients with LARC who underwent MRI scans before and after SCR followed by delayed surgery, retrospectively, were enrolled. SIS, ADC, IVIM parameters [tissue diffusion (D{sub t}), pseudo-diffusion (D{sub p}), perfusion fraction (f{sub p})] and DKI parameters [mean diffusivity (MD), mean of diffusional kurtosis (MK)] were calculated for each patient. IVIM parameters were estimated using two methods, namely conventional biexponential fitting (CBFM) and variable projection (VARPRO). After surgery, the pathological TNM and tumor regression grade (TRG) were estimated. For each parameter, percentage changes between before and after SCR were evaluated. Furthermore, an artificial neural network was trained for outcome prediction. Nonparametric sample tests and receiver operating characteristic curve (ROC) analysis were performed. Results: Fifteen patients were classified as responders (TRG ≤ 2) and 19 as not responders (TRG > 3). Seven patients had TRG 1 (pathological complete response, pCR). Mean and standard deviation values of pre-treatment CBFM D{sub p} and mean value of VARPRO D{sub p} pre-treatment showed statistically significant differences to predict pCR. (p value at Mann–Whitney test was 0.05, 0.03 and 0.008, respectively.) Exclusively SIS percentage change showed significant differences between responder and non-responder patients after SCR (p value << 0.001) and to assess pCR after SCR (p value << 0.001). The best results to predict pCR were obtained by VARPRO Fp mean value pre-treatment with area under ROC of 0.84, a sensitivity of 96.4%, a specificity of 71.4%, a positive predictive value (PPV) of 92.9%, a negative predictive value (NPV) of 83.3% and an accuracy of 91.2%. The best results to assess after treatment complete pathological response were obtained by SIS with an area under ROC of 0.89, a sensitivity of 85.7%, a specificity of 92.6%, a PPV of 75.0%, a NPV of 96.1% and an accuracy of 91.2%. Moreover, the best results to differentiate after treatment responders vs. non-responders were obtained by SIS with an area under ROC of 0.94, a sensitivity of 93.3%, a specificity of 84.2%, a PPV of 82.4%, a NPV of 94.1% and an accuracy of 88.2%. Promising initial results were obtained using a decision tree tested with all ADC, IVIM and DKI extracted parameter: we reached high accuracy to assess pathological complete response after SCR in LARC (an accuracy of 85.3% to assess pathological complete response after SCR using VARPRO D{sub p} mean value post-treatment, ADC standard deviation value pre-treatment, MD standard deviation value post-treatment). Conclusion: SIS is a hopeful DCE-MRI angiogenic biomarker to assess preoperative treatment response after SCR with delayed surgery. Furthermore, an important prognostic role was obtained by VARPRO F{sub p} mean value pre-treatment and by a decision tree composed by diffusion parameters derived by DWI and DKI to assess pathological complete response.
62 RADIOLOGY AND NUCLEAR MEDICINE↗