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The radar on the Global Precipitation Measurement (GPM) mission observes precipitation at 13.6 GHz (Ku-band) and 35.6 GHz (Ka-band) and also receives echoes from the earth’s surface. Statistics of surface measurements for non-raining conditions are saved in a database for later use in estimating the precipitation path-integrated attenuation. Previous work by Meneghini and Jones (2011) showed that while averaging over larger latitude/longitude bins increase the number of samples, it can also increase sample variance due to spatial inhomogeneity in the data. As a result, Meneghini and Kim (2017) proposed a new, adaptive method of database construction, in which the number of measurements averaged depends on the spatial homogeneity. The purpose of this work is to re-visit previous, single-frequency results using dual-frequency data and optimal interpolation (kriging). Results include that (1) temporal inhomogeneity can create similar results as spatial, (2) Ka-band behavior is similar to Ku-band, (3) the Ku-/Ka-band difference has less spatial inhomogeneity than either band by itself, and (4) kriging and the adaptive method can reduce the sample variance. The author concludes that finer spatial and temporal resolution is necessary in constructing the database for single frequencies but less so for the Ku-/Ka-band difference. The adaptive approach reduces sample standard deviation with a relatively modest computational increase.

Ranked set sampling (RSS) utilizes imprecise rankings on the variable of interest in order to draw an informative sample from the target population. The resulting sample, consisting of independent judgment order statistics, resembles a stratified random sample. Estimating the variances of strata is an important problem in RSS. The standard method is based on the sample variance of units in each stratum. A plug-in estimator is also available in the literature that remedies some shortcomings of the standard estimator. We adjust the latter estimator using kernel estimator of the distribution function. The developed estimator is shown to be consistent, and its performance is investigated by means of simulation. It turns out that our proposal can be considerably more efficient than the existing estimators when perfect or nearly perfect ranking holds.

The standard cosmological model is inherently relativistic, and yet a wide range of cosmological observations can be predicted accurately from essentially Newtonian theory. This is not the case on `ultra-large' distance scales, around the cosmic horizon size, however, where relativistic effects can no longer be neglected. In this paper, we present a novel suite of 53 fully relativistic simulations generated using the gevolution code, each covering the full sky out to $z \approx$ 0.85, and approximately 1930 square degrees out to $z \approx$ 3.55. These include a relativistic treatment of massive neutrinos, as well as the gravitational potential that can be used to exactly calculate observables on the past light cone. The simulations are divided into two sets, the first being a set of 39 simulations of the same fiducial cosmology (based on the Euclid Flagship 2 cosmology) with different realisations of the initial conditions, and the second which fixes the initial conditions, but varies each of seven cosmological parameters in turn. Taken together, these simulations allow us to perform statistical studies and calculate derivatives of any relativistic observable with respect to cosmological parameters. As an example application, we compute the cross-correlation between the Doppler magnification term in the convergence, $\kappa_v$, and the CDM+baryon density contrast, $\delta_{\rm cb}$, which arises only in a (special) relativistic treatment. We are able to accurately recover this term as predicted by relativistic perturbation theory, and study its sample variance and derivatives with respect to cosmological parameters., Comment: 9 pages, 6 figures, corresponds to published version

Context. The analytical procedures used in the audit are currently based on data mining techniques. The work solves the problem of increasing the efficiency and effectiveness of analytical audit procedures by clustering based on spectral decomposition. The object of the research is the process of auditing the compliance of payment and supply sequences for raw materials. Objective. The aim of the work is to increase the effectiveness and efficiency of the audit due to the method of spectral clustering of sequences of payment and supply of raw materials while automating procedures for checking their compliance. Method. The vectors of features are generated for the objects of the sequences of payment and supply of raw materials, which are then used in the proposed method. The created method improves the traditional spectral clustering method by automatically determining the number of clusters based on the explained and sample variance rule; automatic determination of the scale parameter based on local scaling (the rule of K-nearest neighbors is used); resistance to noise and random outliers by replacing the k-means method with a modified PAM method, i.e. replacing centroid clustering with medoid clustering. As in the traditional approach, the data can be sparse, and the clusters can have different shapes and sizes. The characteristics of evaluating the quality of spectral clustering are selected. Results. The proposed spectral clustering method was implemented in the MATLAB package. The results obtained made it possible to study the dependence of the parameter values on the quality of clustering. Conclusions. The experiments carried out have confirmed the efficiency of the proposed method and allow us to recommend it for practical use in solving audit problems. Prospects for further research may lie in the creation of intelligent parallel and distributed computer systems for general and special purposes, which use the proposed method for segmentation, machine learning and pattern recognition tasks.

To exploit the power of next-generation large-scale structure surveys, ensembles of numerical simulations are necessary to give accurate theoretical predictions of the statistics of observables. High-fidelity simulations come at a towering computational cost. Therefore, approximate but fast simulations, surrogates, are widely used to gain speed at the price of introducing model error. We propose a general method that exploits the correlation between simulations and surrogates to compute fast, reduced-variance statistics of large-scale structure observables without model error at the cost of only a few simulations. We call this approach Convergence Acceleration by Regression and Pooling (CARPool). In numerical experiments with intentionally minimal tuning, we apply CARPool to a handful of GADGET-III $N$-body simulations paired with surrogates computed using COmoving Lagrangian Acceleration (COLA). We find $\sim 100$-fold variance reduction even in the non-linear regime, up to $k_\mathrm{max} \approx 1.2$ $h {\rm Mpc^{-1}}$ for the matter power spectrum. CARPool realises similar improvements for the matter bispectrum. In the nearly linear regime CARPool attains far larger sample variance reductions. By comparing to the 15,000 simulations from the Quijote suite, we verify that the CARPool estimates are unbiased, as guaranteed by construction, even though the surrogate misses the simulation truth by up to $60\%$ at high $k$. Furthermore, even with a fully configuration-space statistic like the non-linear matter density probability density function, CARPool achieves unbiased variance reduction factors of up to $\sim 10$, without any further tuning. Conversely, CARPool can be used to remove model error from ensembles of fast surrogates by combining them with a few high-accuracy simulations., Comment: 18 pages, 18 figures. v2: Improved and published version; references and discussions added, typos fixed, slight visual modifications of some figures

The classical multi-armed bandit (MAB) framework studies the exploration-exploitation dilemma of the decision-making problem and always treats the arm with the highest expected reward as the optimal choice. However, in some applications, an arm with a high expected reward can be risky to play if the variance is high. Hence, the variation of the reward should be considered to make the arm-selection process risk-aware. In this letter, the mean-variance metric is investigated to measure the uncertainty of the received rewards. We first study a risk-aware MAB problem when the reward follows a Gaussian distribution, and a concentration inequality on the variance is developed to design a Gaussian risk aware-upper confidence bound algorithm. Furthermore, we extend this algorithm to a novel asymptotic risk aware-upper confidence bound algorithm by developing an upper confidence bound of the variance based on the asymptotic distribution of the sample variance. Theoretical analysis proves that both proposed algorithms achieve the $\mathcal {O}(\log (T))$ regret. Finally, numerical results demonstrate that our algorithms outperform several risk-aware MAB algorithms.

As an emerging measure of data freshness, the age of information (AoI) is receiving extensive attention. Many methods using AoI have been proposed for communication scheduling in the Internet of Things (IoT). However, most of them are aimed at constant channel conditions in the ideal state, and the utilization of link resources is not sufficient. In addition, only the optimization of AoI is considered, without considering whether the sample is extruded. Sample extrusion refers to the scenario in which the transmission of the remaining untransmitted sample of the source node cannot be completed within the transmission time interval (TTI) before the arrival of the new sampling period of the source node. Thus, sample extrusion is a phenomenon that occurs when the new sample arrives while the old sample has not yet been completely transmitted. This scenario has a serious impact on delay-sensitive IoT applications. Therefore, under dynamic channel conditions and limited link resources, this paper establishes two mathematical models for AoI and sample extrusion. The influence of the scheduling algorithm on these two target values is analyzed and proven. Based on a greedy strategy, we propose a preemptive online algorithm for link resource allocation that considers two objectives: to give full play to the value of link resources and to minimize sample extrusion. The simulation results show that the proposed strategy can achieve better comprehensive performance in both scenarios where the sample variance between source nodes is small or large.

This paper presents a pioneer study of identifying the wind turbine blade condition based on its vibration pattern. The study used variational mode decomposition (VMD) for signal pre-processing. VMD is an adaptive signal decomposition technique, which can non-recursively decompose a multi-component signal into a number of quasi-orthogonal intrinsic mode functions. This new tool is based on a solid mathematical foundation and can obtain a well-defined time–frequency representation. The main advantage of VMD is, there is no residual noise in the modes and it can avoid redundant modes. Thus, VMD provides a noise-free fault signal for classification. Initially, the obtained vibration data are pre-processed using VMD and then the descriptive statistical features like mean, standard deviation, sample variance, and kurtosis were extracted. After the feature extraction, the dominant features were selected using the C4.5 decision tree algorithm. In this study, multilayer perceptron (MLP) was used for fault classification (blade bend, blade crack, erosion, hub-blade loose connection, and pitch angle twist). Then a comparative study was made with MLP without VMD and MLP with VMD to suggest a better model. From the results, the maximum classification accuracy of 87% was obtained for MLP with VMD when compared to MLP without VMD (76.83%).

This research aimed to investigate the soil moisture retention of some selected organic media for growing cucumber plant. The experiment was conducted in a greenhouse structure and moisture content of each of the organic media was determined by a calibrated moisture meter, which was taken before and after the irrigation. The water application was uniform, using a drip irrigation kit for potted system with a capacity of 75cl storage each for the treatments. The pH values of each of the organic media used shows moderate alkalinity. The mean and sample variance of the moisture retention pattern for each of the media gave; saw dust (3.61, 0.073), maize husk (3.41, 0.044), rice husk (3.92, 0.034), eucalyptus leaves (3.27, 0.021), sawdust + soil (2.76, 0.0416), maize husk + soil (2.94, 0.153), rice husk + soil (3.88, 0.069), eucalyptus leaves + soil (2.76, 0.041), eucalyptus leaves + soil unsterilized (3.77, 0.074), and sandy loamy (23.345, 0.009). Moisture retention pattern of the selected media show high moisture retention in sandy loam while other media show a low moisture retention in approximately ratio 6:1, the sample variance shows small variance indicating how the data point spread out. It can be assumed that low retention could be as a result of the presence of fibre or coarse particles given room for large pore spaces that allows easy moisture drain from the organic media. It can also be deduced from the results that maize husk is least suitable for growing purposes because of unsteady moisture retention pattern.

Deriving valid confidence intervals for complex estimators is a challenging task in practice. Estimators of dynamic weighted survival modeling (DWSurv), a method to estimate an optimal dynamic treatment regime of censored outcomes, are asymptotically normal and consistent for their target parameters when at least a subset of the nuisance models is correctly specified. However, their behavior in finite samples and the impact of model misspecification on inferences remain unclear. In addition, the estimators' nonregularity may negatively affect the inferences under some specific data generating mechanisms. Our objective was to compare five methods, two asymptotic variance formulas (adjusting or not for the estimation of nuisance parameters) to three bootstrap approaches, to construct confidence intervals for the DWSurv parameters in finite samples. Via simulations, we considered practical scenarios, for example, when some nuisance models are misspecified or when nonregularity is problematic. We also compared the five methods in an application about the treatment of rheumatoid arthritis. We found that the bootstrap approaches performed consistently well at the cost of longer computational times. The asymptotic variance with adjustments generally yielded conservative confidence intervals. The asymptotic variance without adjustments yielded nominal coverages for large sample sizes. We recommend using the asymptotic variance with adjustments in small samples and the bootstrap if computationally feasible. Caution should be taken when nonregularity may be an issue.

Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalog of the resulting resamplings of the COSMOS2015 galaxies., Comment: 18 pages, 16 figures. Comments welcome

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow’s Opportunity for Selection (I), which is the variance in relative fitness . Crow’s I has been widely used but remains controversial because it depends on mean offspring number in a sample . Here I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow’s I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance to its expected value at a fixed removes dependence of I on mean offspring number, but the result still depends on choice of . A new index is introduced, , which makes Î independent of sample without the need for variance rescaling. ΔI has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. ΔI can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.

This manuscript introduces the idea of using Distributionally Robust Optimization (DRO) for the Counterfactual Risk Minimization (CRM) problem. Tapping into a rich existing literature, we show that DRO is a principled tool for counterfactual decision making. We also show that well-established solutions to the CRM problem like sample variance penalization schemes are special instances of a more general DRO problem. In this unifying framework, a variety of distributionally robust counterfactual risk estimators can be constructed using various probability distances and divergences as uncertainty measures. We propose the use of Kullback-Leibler divergence as an alternative way to model uncertainty in CRM and derive a new robust counterfactual objective. In our experiments, we show that this approach outperforms the state-of-the-art on four benchmark datasets, validating the relevance of using other uncertainty measures in practical applications., Comment: Accepted at AAAI20

The Karst aquifers are usually characterized by high spatial heterogeneity in the humid tropics and subtropics, evidenced by specific landforms features (e.g., heavily fractured outcrops, sinkholes, etc.) and complex subterranean conduit networks. The marked high heterogeneity leads to the temporal–spatial variability of hydrological and hydro-chemical processes, making its environments extremely vulnerable to natural and anthropogenic hazards. The complicated temporal–spatial variability of hydrochemistry in karst systems depends on several underlying factors which influence the hydro-chemical processes. Investigating the factors of the karst water hydrochemistry variability is necessary to understand the hydro-chemical processes and mitigate natural and anthropogenic hazards for ensuring the sustainability of karst water resources. In this paper, an attempt is made to couple geostatistical and geochemical analysis to extract the underlying controlling factors and effective information about the geochemical evolution behave of karst water in Houzhai karst area, southwestern China. Factor analysis was performed to obtain significant statistical relationship of the hydrochemistry variation in the Houzhai karst basin. The ordinary kriging method was applied to the factor scores to investigate the contributions of factors on different regions. The results of the factor analysis indicated four principal factors which explained > 81.678% of the total sample variance: (1) the dilution effect by rainfall; (2) the dissolution effect dominated by calcite; (3) the human agricultural activities effect; (4) the migration of dissolved components under the control of alkaline environments in karst water. It revealed that the dilution effect was more significant (36.579%) than the dissolution effect (22.036%) and human agricultural activities effect (14.596%). These factors made more significant difference of contributions on the karst area in the dry periods than in the rainy periods. The dilution process by rainfall and the dissolution process of carbonate rock had a great influence on the upstream area whereas the human agricultural activities played important roles in the middle-stream area, especially in the dry periods. This integrated approach which combine factor analysis with kriging method is effective in the identification and interpretation of factors related to the variability of hydrochemistry, as well as the contributions of these factors on space and time.

Cross-correlating cosmic microwave background (CMB) lensing and galaxy clustering has been shown to greatly improve the constraints on the local primordial non-Gaussianity (PNG) parameter $f_{\rm NL}$ by reducing sample variance and also parameter degeneracies. To model the full use of the 3D information of galaxy clustering, we forecast $f_{\rm NL}$ measurements using the decomposition in the spherical Fourier-Bessel (SFB) basis, which can be naturally cross-correlated with 2D CMB lensing in spherical harmonics. In the meantime, such a decomposition would also enable us to constrain the growth rate of structure, a probe of gravity, through the redshift-space distortion (RSD). As a comparison, we also consider the tomographic spherical harmonic (TSH) analysis of galaxy samples with different bin sizes. Assuming galaxy samples that mimic a few future surveys, we perform Fisher forecasts using linear modes for $f_{\rm NL}$ and the growth rate exponent $\gamma$, marginalized over standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological parameters and two nuisance parameters that account for clustering bias and magnification bias. Compared to TSH analysis using only one bin, SFB analysis could improve $\sigma(f_{\rm NL})$ by factors 3 to 12 thanks to large radial modes. With future wide-field and high-redshift photometric surveys like the LSST, the constraint $\sigma(f_{\rm NL}) < 1$ could be achieved using linear angular multipoles up to $\ell_{\rm min}\simeq 20$. Compared to using galaxy auto-power spectra only, joint analyses with CMB lensing could improve $\sigma(\gamma)$ by factors 2 to 5 by reducing degeneracies with other parameters, especially the clustering bias. For future spectroscopic surveys like the DESI or $\textit{Euclid}$, using linear scales, $\gamma$ could be constrained to $3\,\%$ precision assuming the GR fiducial value., Comment: 21 pages, 14 figures, 3 tables; references added, published in PRD

Although deep networks have been shown to perform very well on a variety of medical imaging tasks, inference in the presence of pathology presents several challenges to common models. These challenges impede the integration of deep learning models into real clinical workflows, where the customary process of cascading deterministic outputs from a sequence of image-based inference steps (e.g. registration, segmentation) generally leads to an accumulation of errors that impacts the accuracy of downstream inference tasks. In this paper, we propose that by embedding uncertainty estimates across cascaded inference tasks, performance on the downstream inference tasks should be improved. We demonstrate the effectiveness of the proposed approach in three different clinical contexts: (i) We demonstrate that by propagating T2 weighted lesion segmentation results and their associated uncertainties, subsequent T2 lesion detection performance is improved when evaluated on a proprietary large-scale, multi-site, clinical trial dataset acquired from patients with Multiple Sclerosis. (ii) We show an improvement in brain tumour segmentation performance when the uncertainty map associated with a synthesised missing MR volume is provided as an additional input to a follow-up brain tumour segmentation network, when evaluated on the publicly available BraTS-2018 dataset. (iii) We show that by propagating uncertainties from a voxel-level hippocampus segmentation task, the subsequent regression of the Alzheimer's disease clinical score is improved.

Space shift keying antenna sequence modulation (SSK-ASM) is proposed for conveying information bits through unique antenna sequence patterns. The information is conveyed in spatial domain only via mixed Gaussian channel such Rayleigh Flat Fading. In this paper we, present analytical formulation of bit error rate performance of SSK-ASM, by utilizing Sample variance (SV) and Mutual information (MI) criterion in single input Multiple output (SIMO) configuration. Moreover, the exact Average bit error probability (ABEP) over Rayleigh Flat fading channel is developed in close-form. Monte Carlo simulations is shown to be tightly bound to the theoretical framework for SV criterion method.

Intensity mapping of the 21cm signal of neutral hydrogen will yield exciting insights into the Epoch of Reionisation and the nature of the first galaxies. However, the large amount of data that will be generated by the next generation of radio telescopes, such as the Square Kilometre Array (SKA), as well as the numerous observational obstacles to overcome, require analysis techniques tuned to extract the reionisation history and morphology. In this context, we introduce a one-point statistic, to which we refer as the local variance, $\sigma_\mathrm{loc}$, that describes the distribution of the mean differential 21cm brightness temperatures measured in two-dimensional maps along the frequency direction of a light-cone. The local variance takes advantage of what is usually considered an observational bias, the sample variance. We find the redshift-evolution of the local variance to not only probe the reionisation history of the observed patches of the sky, but also trace the ionisation morphology. This estimator provides a promising tool to constrain the midpoint of reionisation as well as gaining insight into the ionising properties of early galaxies., Comment: 14 pages, 14 figures, published in A&A

For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.