Sample Variance Research Articles

Many-body localized to ergodic transitions in a system with correlated disorder

We study the transition from a many-body localized phase to an ergodic phase in spin chain with correlated random magnetic fields. Using multiple statistical measures like gap statistics and extremal entanglement spectrum distributions, we find the phase diagram in the disorder-correlation plane, where the transition happens at progressively larger values of the correlation with increasing values of disorder. We then show that one can use the average of sample variance of magnetic fields as a single parameter which encodes the effects of the correlated disorder. The distributions and averages of various statistics collapse into a single curve as a function of this parameter. This also allows us to analytically calculate the phase diagram in the disorder-correlation plane.

Blockchain solution benefits for controlling pandemics: Bottom-up decentralization, automation with real-time update, and immutability with privacy preservation

The current COVID-19 pandemic has created turmoil around the world. To fight this ongoing global crisis and future ones, all stakeholders must collaborate and share timely and truthful information. This paper proposes a blockchain solution based on its inherent technological advantages. We posit that benefits can be derived from three unique blockchain features: bottom-up decentralization, automation with real-time update, and immutability with privacy preservation. A decentralized common platform provides easy access and increases participation in disease surveillance, which reduces the estimation errors of the compartmental model parameters. Automation with real-time update facilitates prompt detection and diagnosis, accurate contact tracing, and targeted mitigation and containment, achieving faster recovery and slower transmission. Being immutable while preserving privacy, the blockchain solution enhances respondents’ willingness to truthfully report their contact history, avoiding false and erroneous data that will cause wrong estimates on pandemic transmission and recovery. Thus, the blockchain solution mitigates three types of risks: sample variance, delay, and bias. Through simulation, we quantify the value of the blockchain solution in these three aspects. Accordingly, we provide specific action plans based on our research findings: before building blockchain solutions for controlling COVID-19, governments and organizations can calculate the blockchain benefits and decide whether or not they should invest in such blockchain solutions by conducting a cost-benefit analysis.

Estimating Genetic Variance in Life-Span Response to Diet: Insights From Statistical Simulation.

Several studies demonstrate genetic variation in response to dietary restriction (DR) by replicating treatments across isogenic lines/strains from genetic reference panels. These studies typically quantify the response to DR as an effect size, estimated for each strain separately (eg, the difference in mean life span between groups). Such "no-pooling" analyses are expected to systematically overestimate variation in response DR, principally by overlooking sampling variance. In contrast, "partial-pooling" analyses using mixed-effects models are less prone to this bias. I demonstrate these issues using simulations, which also show that partial-pooling analyses can improve replicability among studies. Regardless of the analyses used, estimates of among-strain variation will have low precision when sample sizes are small. A worked example using survival data in mice is given. Life-span studies using genetic reference panels always have to trade-off within- and among-strain replication owing to logistical challenges. The simulation presented can also be used to help design such studies through power analysis.

VARIANCE GAMMA MODEL AND ITS DEVELOPMENT FOR STOCKS CALL OPTION PRICES ESTIMATION

One of the developments in the options market is the formation of various pricing models for an option to help the buyer determine the fairness of the price. Black-Scholes model uses the assumption that the log return price of stocks is normally distributed, while in reality, the real-world price couldn’t fit into that assumption. To be able to obtain an option price calculation that considers skewness and kurtosis in the stock price data, there are many alternative methods, namely Black-Scholes with Gram-Charlier expansion and Variance Gamma models. As a development of the Variance Gamma model, there are also several methods that are able to reduce the simulations variance generated by the Variance Gamma model, namely Antithetic Variate Variance Gamma model and the Importance Sampling Variance Gamma method. For the results, the Importance Sampling Variance Gamma model and the Antithetic Variate Variance Gamma model are really able to reduce the resulting simulations variance so that it can produce more accurate option prices with market prices compared to the Variance Gamma model. In the end, all Variance Gamma models are able to produce a call option price that is more in line with the market price than all Black Scholes models.

On enhanced estimation and monitoring of population variance using robust auxiliary parameters based estimators

SummarySearching for efficient estimators of population variance as compared to sample variance has been the key area of interest of the researchers. Auxiliary variable has helped very much in finding estimators more efficient than sample variance. Auxiliary variable is greatly correlated with main study variable. Many authors including Isaki (J Am Stat Assoc 1983, 78, 117) used positively correlated auxiliary variable in the form of various conventional and non‐conventional auxiliary parameters and suggested different ratio type estimators of population variance. In this article, we have suggested a naïve class of variance estimators based on some robust auxiliary parameters, which deals with the outliers in the data. The properties including bias and Mean Square Error (MSE) of suggested family of estimators are studied up to first order of approximation. The theoretical as well as empirical comparison of introduced family of estimators is carried out with competing variance estimators. The estimator with the least MSE is recommended in different areas of applications. At last, the Shewhart type control charts based on the proposed estimators are also studies for application in quality control.

Forge: the f(R)-gravity cosmic emulator project – I. Introduction and matter power spectrum emulator

ABSTRACT We present a large suite of cosmological simulations, the forge (F-of-R Gravity Emulator) simulation suite, which is designed to build accurate emulators for cosmological observables in galaxy clustering, weak gravitational lensing, and galaxy clusters for the f(R)-gravity model. A total of 200 simulations explore the cosmological parameter space around a standard Planck cosmology with a Latin hypercube, for 50 combinations of $\bar{f}_{R0}$, Ωm, σ8, and h with all other parameters fixed. For each parameter combination, or node, we ran four independent simulations, one pair using 10243 particles in $500\, h^{-1}\, \mathrm{Mpc}$ simulation boxes to cover small scales, and another pair using 5123 simulation particles in $1.5\, h^{-1}\, \mathrm{Gpc}$ boxes for larger scales. Each pair of initial conditions is selected such that sample variance on large scales is minimized on average. In this work we present an accurate emulator for the matter power spectrum in f(R) gravity trained on forge. We have verified, using the cross-validation technique, that the emulator accuracy is better than $2.5{{\, \rm per\, cent}}$ for the majority of nodes, particularly around the centre of the explored parameter space, up to scales of $k = 10\, h \, \mathrm{Mpc}^{-1}$. We have also checked the power spectrum emulator against simulations that are not part of our training set and found excellent agreement. Due to its high accuracy on small scales, the forge matter power spectrum emulator is well suited for weak-lensing analysis and can play a key tool in constraining f(R) gravity using current and future observational data.

AK-HMC-IS: A Novel Importance Sampling Method for Efficient Reliability Analysis Based on Active Kriging and Hybrid Monte Carlo Algorithm

Abstract Sampling methods are powerful tools for structural reliability analysis with complex failure domains due to their stability and accuracy. One of the most frequently used sampling methods is the importance sampling (IS) method, which can markedly reduce the sampling variance and computational costs. The pivotal problem in IS method is the determination of the IS probability density function (ISPDF), which influences the accuracy and efficiency of reliability analysis greatly. This study proposes an effective method for constructing the ISPDF, combining the hybrid Monte Carlo algorithm (HMC) with the Gaussian mixture model. The HMC is superior to the common Markov chain Monte Carlo algorithm in convergence, which is helpful in improving sampling efficiency. Our ISPDF is generated adaptively and does not require the most probable failure point (MPFP); therefore, it can also work well for multiple MPFPs and high-nonlinear problems. To release the computational burden further, the performance function is replaced with the Kriging model, and the well-known U criterion is used for its refinement. In the proposed method, the process of the refinement of the Kriging model is coupled with the HMC sampling for constructing the ISPDF, which is the difference between some common methods; thus, no samples are vain. We verify the proposed method using three classical numerical examples and one practical engineering problem. Results show that the proposed method is accurate and superior to common IS methods in efficiency.

Variance and precision of microplastic sampling in urban rivers

Microplastics (MPs), plastic particles <5 mm in diameter, have become an emerging ubiquitous concern for the environment. Rivers are the primary pathways that transport MPs from the land to the ocean; however, standardized methodologies for in-situ sampling in freshwater environments remain undefined. Notably, uncertainties in MP sampling methods lead to errors in estimating MP discharge through rivers. In the present study, the inter-sample variance of plankton net-obtained MP concentrations for two urban rivers in Japan was investigated. Numerical concentrations, expressed in particles·m−3, revealed that variance s2 was proportional to the mean m of replicated estimates of numerical concentrations. A derived statistical model suggested that river MPs disperse according to purely random processes; that is, Poisson point processes. Accordingly, a method was established to project the “precision,” the ratio of the standard error to m, of numerical concentrations based on the number of net sampling repetitions. It was found that the mean of two replicates maintained sufficient precision of <30% for conditions with high concentrations of ≥3 particles·m−3. Projected precisions under different levels of MP concentrations are also presented to help design future field campaigns.

Alternative Ways for the Covariance Between Sample Mean and Variance

Alternative Ways for the Covariance Between Sample Mean and Variance

A Study on the Relationship Between Secondary School Students' Digital Game Addiction Awareness and Participation Motivation to Physical Activity

This study is conducted so as to investigate the relationship between secondary school students` digital game awarenees(SDGA) and participation motivation to physical activity (PMPA). 456 female and 241 male secondary school students studying in the Keçiören district of Ankara participated voluntarily. Personel information form, Digital Game Addiction Awareness Scale(DGAAS) developed by Tekkurşun-Demir ve Cicioğlu (2020) and Participation motivation to physical activity Scale(PMPAS) developed by Tekkurşun-Demir ve Cicioğlu (2018) are employed as data collection set. In the analysis of the data obtained, mean( ), standart deviation(sd), percentage(%) and frequency(n) values are utiSecondary Schoold. The pearson product-moment correlation coefficient in pearson correlation analysis, ANOVA in one-way analysis of variance and T-Test in unrelated samples were used. While statistically significant differences were found the relationship between secondary school students' PMPA, SDGA and gender, educational level of father and daily technology usage(p<0,05), the relationship with gender and educational level of mother was trivial (p<0,05); In sum, study results demonstrate that there is a positive and significant relationship between PMPA of secondary school students and the SDGA. In other words, as students' awareness of digital game addiction increases, participation motivation to physical activity increase.

Physical Fitness Profile of Students in terms of Student Activities in Sports

The fatigue experienced by junior high school (SMP) students while doing activities for a moment indicates that the students are not fit. Therefore, improving fitness to do more activities at a productive age is necessary. The purpose of this research was to determine the physical fitness profile of students in terms of sports activities. The quantitative description was the method of this research. The data collection technique used was the Indonesian Physical Fitness Test. The results showed that the fitness level of SMP Sekolah Alam Indonesia students was 0% in the excellent and good category, 31% in the medium category, 36% in the low category, and 33% in the poor category. The calculation obtained a significance value of more than 0.05, meaning the sample variance was normal. Thus, the hypothesis that the variance of the existing variables was the same was accepted. To determine whether there was a difference between sports activities and the fitness profile of SMP SAI students, the researchers performed the independent sample t-test on the data taken from the Indonesian Physical Fitness Test. The obtained significance value was 0.000 (less than 0.05). Therefore, it can be interpreted that there was a significant difference between the Fitness Profile of SMP SAI students and sports activities. In conclusion, the 8th-grade students of the school have not yet reached the good and excellent categories. The more active students are in exercising, the better their physical fitness level will be.

Determination of the Application Rate of Conventional Compost Integrated with Chemical Fertilizer on Maize (Zia Maize) Yield in Dugda District of East Shoa Zone, Oromia

Integrated soil fertility management is the application of inorganic in combination with organic fertilizer to maintain soil fertility and improve crop yield. A study was conducted in East Shoa Zone, Dugda District on farmers' fields to determine the combined effects of conventional compost as organic fertilizer and NPS as inorganic fertilizer on soil chemical properties and maize production. There were five treatments: Recommended rate of inorganic fertilizer, 100, 75, 50 and 25% equivalent level of compost for nitrogen fertilizer. Recommended level of 69 P2O5/ha were equally applied at all treatments. The experiment was laid out in RCBD design with three replications. The analysis of variance showed no significant differences (P &gt; 0.05) in maize grain yield response. However, the highest maize grain yield (8728.20 kg ha-1) was obtained from treatment two that received 100% equivalent compost for nitrogen fertilizer and the lowest (8325 kg ha-1) was obtained from treatment one where recommended chemical fertilizer alone was applied. Composite Soil samples were also collected before compost application and after harvesting to evaluate the residual effect of compost on soil physiochemical properties. Accordingly, laboratory analysis showed no significance differences (P &gt; 0.05) in total N, available P, soil organic carbon and CEC. However, analysis of variance of post-harvest composite soil samples indicated significant differences on soil available P, OC, TN and CEC as compared to initial soil sample. On the other hand, partial budget analysis was done to determine economically optimum rate of compost integrated with chemical fertilizer. Accordingly, the highest net benefit (126527 Eth. Birr ha-1) was recorded for treatment two where 100% compost (4.6t/ha) plus 150kg/ha NPS fertilizers were applied. The highest marginal rate of return (146) was also obtained from the same treatment. Therefore, the present study showed that combined application of organic and NPS fertilizer enhanced maize productivity and soil fertility status in the study area. Hence combined fertilizer application of 4.6 t ha1 conventional compost integrated with 150 kg ha-1 NPS improved maize productivity and soil chemical properties, and recommended for the study area and similar agro-ecology.

A new criterion based on estimator variance for model sampling in precision agriculture

Model sampling has proven to be an interesting approach to optimize the sampling of an agronomic variable of interest at the field level. The use of a model improves the quality of the estimates by making it possible to integrate the information provided by one or more auxiliary data. It has been shown that such an approach gives better estimations compared to more traditional approaches.Through a statistical work describing the properties of model sampling variance, this paper details how the different factors either related to sample characteristics or to the correlation between the auxiliary data and the variable of interest, affect estimation error. The resulting equations show that the use of samples with a mean close to the field mean and with a substantial dispersion reduces the estimation variance. On the basis of these statistical considerations, a variance criterion is defined to compare sample properties. The lower the value of the criterion of a sample, the lower the variance of the estimate and the expected errors. These theoretical insights were applied to real commercial vine fields in order to validate the demonstration.Nine vine fields were considered with the objective to provide the best yield estimation. High resolution vegetative index derived from airborne multispectral image was used to drive the sampling and the estimation. The theoretical considerations were verified on the nine fields; as the observed estimation errors correspond quite well to the values predicted by the equations. The selection of a large number of random samples from these fields confirms that samples associated with higher values of the chosen criterion result, on average, in larger yield estimation errors. Samples with the highest criterion values are associated with mean estimation errors up to two times larger than those of average samples. Random sampling is also compared to two target sampling approaches (Clustering based on quantiles or on k-means algorithm) commonly considered in the literature, whose characteristics improve the value of the proposed criterion. It is shown that these sampling strategies produce samples associated with criterion values up to 100 times smaller than random sampling. The use of these easy-to-implement methods thus guarantees to reduce the variance of the estimation and the estimation errors.

Seroprevalence of COVID-19 in Blood Donors: A Systematic Review and Meta-Analysis.

Introduction Determining the prevalence of SARS-CoV-2 in blood donors makes the control of virus circulation possible in healthy people and helps implement strategies to reduce virus transmission. The purpose of the study was to examine the seroprevalence of COVID-19 in blood donors using systematic review and meta-analysis. Materials and Methods The electronic databases PubMed, Scopus, Web of Science, and the Google Scholar search engine were searched using standard keywords up to 2022-04-26. The variance of each study was calculated according to the binomial distribution. Studies were combined according to the sample size and variance. Q Cochrane test and I2 index were used to examine the heterogeneity of the studies. Data analysis was performed in STATA 14 software, and the significance level of the tests was P < 0.05. Results In the 28 papers examined with 227894 samples, the seroprevalence of COVID-19 in blood donors was 10% (95% CI: 9%, 11%), estimated 5% (95% CI: 4%, 7%) among men and 6% (95% CI: 4%, 7%) among women. This rate in different blood groups was as follows: A 12% (95% CI: 10%–14%), B 12% (95% CI: 10%–15%), AB 9% (95% CI: 7%–12%), and O 13% (95% CI: 11%–16%). The seroprevalence of COVID-19 in blood donors in North America 10%, Europe 7%, Asia 23%, South America 5%, and Africa was 4%; Moreover, the seroprevalence of IgG antibodies was estimated to be 23% (95% CI: 18%–29%) and IgM 29% (95% CI: 9%–49%). Conclusion The highest prevalence of COVID-19 serum in women blood donors was among blood group O and Asia. The seroprevalence of IgG and IgM antibodies was high too.

Quantifying Long‐Term Reproducibility of Zircon Reference Materials by U‐Pb LA‐ICP‐MS Dating

Inter‐session excess variance of U/Pb and Pb/Pb ratios in LA‐ICP‐MS zircon dating is the largest contributor to systematic errors, which in turn limit the accuracy of age determinations. Quantifying long‐term excess variance of reference materials allows for the estimation of excess variance in samples, but such compilations are not available in the literature. Here, we present the results of over 100 measurement sessions over 6 years for seven common zircon reference materials and calculate a characteristic excess variance for each. For 206Pb/238U ages, these values (2s) are as follows: AusZ7‐1 = 1.7% (115 sessions), AusZ7‐5 = 0% (74), OD‐3 = 0.6% (19), Temora2 = 1.2% (86), Plešovice = 1.1% (100), 91500 = 1.0% (146) and Mud Tank = 3.0% (12). For 207Pb/206Pb ages, smaller excess variances are observed: Temora2 = 0.3%, Plešovice = 0.4%, Mud Tank = 1.7% and 91500 = 0.4%. These values are well‐constrained estimates of inter‐session excess variance for the ETH Zürich LA‐ICP‐MS laboratory using a sector‐field ICP‐MS, and may provide either a first‐order estimate for other laboratories or a value to compare against their own reference material compilations.

Additive Seasonality in Time Series using Row and Overall Sample Variances of the Buys-Ballot Table

This study considers test for seasonality in the additive model using the Buys-Ballot table and the nature of trending curves (linear, quadratic and exponential). The test is applied to the periodic and overall sample variances of the Buys-Ballot table to detect the presence and absence of seasonal indices in time series.

On Some Characteristics of the Joint Distribution of Sample Variances

The joint distribution of correlated sample variances and their product moments have been derived. Finite expressions have been derived for product moments of sample variances of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution of a sample variance given the other variance have also been discussed. Shannon entropy of the distribution is also derived. When the variables are uncorrelated, the resulting characteristics match with the independent case of sample variances.

Stringent σ8 constraints from small-scale galaxy clustering using a hybrid MCMC + emulator framework

ABSTRACT We present a novel simulation-based hybrid emulator approach that maximally derives cosmological and Halo Occupation Distribution (HOD) information from non-linear galaxy clustering, with sufficient precision for DESI Year 1 (Y1) analysis. Our hybrid approach first samples the HOD space on a fixed cosmological simulation grid to constrain the high-likelihood region of cosmology + HOD parameter space, and then constructs the emulator within this constrained region. This approach significantly reduces the parameter volume emulated over, thus achieving much smaller emulator errors with fixed number of training points. We demonstrate that this combined with state-of-the-art simulations result in tight emulator errors comparable to expected DESI Y1 LRG sample variance. We leverage the new abacussummit simulations and apply our hybrid approach to CMASS non-linear galaxy clustering data. We infer constraints on σ8 = 0.762 ± 0.024 and fσ8(zeff = 0.52) = 0.444 ± 0.016, the tightest among contemporary galaxy clustering studies. We also demonstrate that our fσ8 constraint is robust against secondary biases and other HOD model choices, a critical first step towards showcasing the robust cosmology information accessible in non-linear scales. We speculate that the additional statistical power of DESI Y1 should tighten the growth rate constraints by at least another 50–60 ${{\ \rm per\ cent}}$, significantly elucidating any potential tension with Planck. We also address the ‘lensing is low’ tension, which we find to be in the same direction as a potential tension in fσ8. We show that the combined effect of a lower fσ8 and environment-based bias accounts for approximately $50{{\ \rm per\ cent}}$ of the discrepancy.

An exploration of how training set composition bias in machine learning affects identifying rare objects

When training a machine learning classifier on data where one of the classes is intrinsically rare, the classifier will often assign too few sources to the rare class. To address this, it is common to up-weight the examples of the rare class to ensure it is not ignored. It is also a frequent practice to train on restricted data where the balance of source types is closer to equal for the same reason. Here we show that these practices can bias the model toward over-assigning sources to the rare class. We also explore how to detect when training data bias has had a statistically significant impact on the trained model’s predictions, and how to reduce the bias’s impact. While the magnitude of the impact of the techniques developed here will vary with the details of the application, for most cases it should be modest. They are, however, universally applicable to every time a machine learning classification model is used, making them analogous to Bessel’s correction to the sample variance.

DIFFERENCE-CUM-EXPONENTIAL EFFICIENT ESTIMATOR OF POPULATION VARIANCE

In the current investigation, we have suggested a Difference Cum-Exponential Type Efficient Estimator of Population variance of the study variable using information on the auxiliary variable. Up to the first order of approximation, the proposed estimator's bias and mean square error (MSE) expressions are derived and suggested optimum estimator is also found, with its optimal qualities are investigated. The suggested estimator is proven to be more competent than sample variance, classic ratio estimators based on Isaki , Singh et al. and Kadilar and Cingi estimators in [1-3]. Numerical study is also carried out by using real data sets.