Statistical Estimation Approach Research Articles

IoT and machine learning approach for the determination of optimal freshwater replenishment rate in aquaponics system

IoT and machine learning approach for the determination of optimal freshwater replenishment rate in aquaponics system

Coupled hydrogeophysical inversion of an artificial infiltration experiment monitored with ground-penetrating radar: synthetic demonstration

Abstract. In this study, we investigate the use of ground-penetrating radar (GPR) time-lapse monitoring of artificial soil infiltration experiments. The aim is to evaluate this protocol in the context of estimating the hydrodynamic unsaturated soil parameter values and their associated uncertainties. The originality of this work is to suggest a statistical parameter estimation approach using Markov chain Monte Carlo (MCMC) methods to have direct estimates of the parameter uncertainties. Using the GPR time data from the moving wetting front only does not provide reliable results. Thus, we propose to use additional information from other types of reflectors to optimize the quality of the parameter estimation. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity Ks, the saturated and residual water contents θs and θr, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the MCMC method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the GPR data to the hydrodynamic soil parameters are different between moving and fixed reflectors, whereas fixed reflectors at various depths have similar sensitivities. Ks has a similar and strong influence on the data of both types of reflectors. Concerning the other parameters, for the wetting front, only θs and α have an influence, and only at long time steps since the total variance is zero at the very beginning of the experiment. On the other hand, for the fixed reflectors, the total variance is not zero at the very start and the parameters θs, θr, α and n can have an influence from the very beginning of the infiltration. Results of parameter estimation show that the use of calibration data from the moving or fixed reflectors alone does not enable a good identification of all soil parameters. With the moving reflector, the error between the estimated mean value and the exact target value for θr and α is 9 % and 45 %, respectively, and less than 3 % for the other parameters. The best reduction of the size of the parameter distribution is obtained for n, with a posterior distribution 9 times smaller than the prior one. For the others, this reduction ratio varies between 1 and 5. For the fixed reflectors, the estimated mean values are far from the target values for α, θr and n, representing for a reflector located at 120 cm 15 %, 27 %, and 121 %, respectively. On the other hand, when both data are combined, all soil parameters can be well estimated with narrow confidence intervals. For instance, when using both data from the moving wetting front and a fixed reflector located at 120 cm for calibration, the estimated mean values of the errors of all parameters are less than 5 %. Moreover, all parameter distributions are well reduced, with a maximum reduction for Ks, leading to a posterior distribution being 46 times smaller than the prior one, and the worst but still satisfactory being for θr for which the posterior distribution is 8 times smaller than the prior one. The methodology was applied to fine, medium, and coarse sands with very good results, particularly for the finest soil. The thickness of the unsaturated zone was also tested (0.5, 1, and 2 m) and a better estimation of the hydrodynamic parameters is obtained when the water table is deeper. In addition, the height of water applied in the infiltrometry test influences the speed of the test without affecting the performance of the proposed method.

An efficient approach for statistical moments estimation of structural response based on a novel adaptive hybrid dimension-reduction method

Statistical moments estimation is one of the main topics for the analysis of a stochastic system, but the balance among the accuracy, efficiency, and versatility for different methods of statistical moments estimation still remains a challenge. In this paper, a novel point estimate method (PEM) based on a new adaptive hybrid dimension-reduction method (AH-DRM) is proposed. Firstly, the adaptive cut-high-dimensional model representation (cut-HDMR) is briefly reviewed, and a novel AH-DRM is developed, where the high-order component functions of the adaptive cut-HDMR are further approximated by multiplicative forms of the low-order component functions. Secondly, a new point estimation method (PEM) based on the AH-DRM is proposed for statistical moments estimation. Finally, several examples are investigated to demonstrate the performance of the proposed PEM. The results show the proposed PEM has fairly high accuracy and good versatility for statistical moments estimation.

Advantages of a Statistical Estimation Approach for Clock Frequency Estimation of Heterogeneous and Irregular CGRAs

Estimating the maximum clock frequency of homogeneous Coarse Grained Reconfigurable Arrays/Architectures (CGRAs) with an arbitrary number of Processing Elements (PE) is difficult. Clock frequency estimation of highly heterogeneous CGRAs takes additional factors into account, thus is even more difficult. Main challenges are the heterogeneous set of operators for each Processing Element (PE) and the irregular interconnect (connecting a CGRA’s PEs). Multiple estimation approaches could be reasonable. We propose an optimized statistical estimator, which is based on our prior work. We demonstrate its superiority to state-of-the-art neural networks in terms of accuracy and robustness, especially in situations with a sparse set of training data.

Estimation of Parameters and Pooling in Nonlinear Flooding Event Scenarios with Bayesian Model.

Water-related tragedies are the highest common of all proven natural calamities and pose severe attacks on people and on socioeconomic status development. Due to the obvious controversy surrounding, their volume, location and time of incidence, geological swaths, and geophysical interrelations, flood events are difficult to completely control. Hence, complete flood prevention is always considered to be a viable choice. The specialized flood occurrences are investigated by developing a structural measure. In this paper, nonlinear flood event circumstance is determined by using a statistical Bayesian parametric approach for parameter estimation. A popular tool for estimating a flood design is model of nonlinear flood event. Nonlinear flood event models are subjected to a Bayesian technique for estimating parameter. The approach is based on the minimization function of square for models with nonlinear calculated peak discharges in terms of parameters. The observed and calculated peak discharges for numerous storms in the watershed, data on the pattern of error observed, and previous information on values of parameter all influence this objective function. The subsequent matrix for covariance is a measure of the calculated parameters' accuracy. Rainfall and runoff data from a Harvey River sample are used in this study to show the process.

National Governance Index, Corruption Index and Growth Rate—International Evidence from Sub-Saharan and MENA Countries

In an international setting of developing countries, applying advanced statistical estimation approaches such as the system generalized method of moments (GMM), two-stage least square (2SLS) regressions, and cluster analysis, this paper revisits the impact of macro-level governance quality and the corruption index on the economic growth rate. We use cross-country panel data for 40 sub-Saharan and the Middle Eastern and North African (MENA) countries over the period of 2009–2020. The empirical results document the positive and negative effects of the national governance index and the corruption index on the economic growth rate. Additionally, foreign direct investment and population have a positive impact on the economic growth rate and trade openness has a negative impact. The study evaluates the robustness of these associations through a series of tests. These findings have important policy implications for policymakers and regulators in developing countries. In particular, the study recommends the implementation of an anti-corruption campaign and improving country-level governance quality that could encourage increased foreign direct investment for an accelerated economic growth rate. These will further enhance accountability, transparency, the rule of law, social responsibility, the public voice, and government effectiveness.

Non-Euclidean estimation of acoustic cross-spectral density matrices: Evaluation by matched-field localization in an ocean waveguide.

A set of non-Euclidean cross-spectral density matrix (CSDM) estimators based on the Frechet mean and median is applied to spatially localize an acoustic source in a stochastic shallow water environment driven by internal gravity waves. The resulting geometric-based matrix estimates are incorporated into matched-field processors defined through steering matrices using intrinsic distance measures between pairs of CSDMs on a Riemannian manifold for each replica source location. Their performance is evaluated using the probability of correct localization to determine any improvement in source localization over the conventional (maximum likelihood) statistical approach for CSDM estimation.

Anonymization of distribution feeder data using statistical distribution and parameter estimation approach

Distribution networks are undergoing a transition due to the rapid increase in distributed energy resources (DERs). Concerns over revealing critical infrastructure information and breaching consumer privacy have significantly hindered their development. Many applications that require data sharing are still impractical due to the lack of sufficient datasets, privacy concerns, and data access problems. To address these issues, a statistical distribution approach for parameter estimation is proposed. The statistical patterns of real distribution feeders are examined by accessing the confidential database of a local distribution network service provider (DNSP). An algorithm based on the Maximum Likelihood Estimate (MLE) is applied to estimate the statistical distribution parameters that represent the actual data. Then, these statistical distribution parameters are used to generate anonymized datasets that are realistic. A Kolmogorov–Smirnov (K-S) test is conducted to confirm the effectiveness of anonymized datasets, and results are compared with the actual feeder datasets. Validation is carried out with existing methods and comparisons are shown on the different portions of the datasets (25 percent, 50 percent, 75 percent, and 100 percent). The comparison results indicate superior performance over traditional methods, with a performance improvement ranging from 1 to 13 percent. The practical application of the method is demonstrated on the IEEE 123-node test feeder. The method achieves consistent results on voltage profiles, with a maximum difference of 0.420 percent between actual and anonymized datasets.

Diversity and interdisciplinarity: Should variety, balance and disparity be combined as a product or better as a sum? An information-theoretical and statistical estimation approach

Diversity is a central concept not only in ecology, but also in the social sciences and in bibliometrics. The discussion about an adequate measure of diversity is strongly driven by the work of Rao (Sankhyā Indian J Stat Series A 44:1-22, 1982) and Stirling (J R Soc Interface 4:707-719, 2007). It is to the credit of Leydesdorff (Scientometr 116:2113-2121, 2018) to have proposed a decisive improvement with regard to an inconsistency in the Rao-Sterling-diversity indicator that Rousseau (Scientometr 116:645-653, 2018) had pointed out. With recourse to Shannon's probabilistically based entropy concept, in this contribution the three components of diversity “variety”, “balance”, and “disparity” are to be reconceptualized as entropy masses that add up to an overall diversity indicator dive. Diversity can thus be interpreted as the degree of uncertainty or unpredictability. For "disparity", for example, the concept of mutual information is used. However, probabilities must be estimated statistically. A basic estimation strategy (cross tables) and a more sophisticated one (parametric statistical model) are presented. This overall probability-theoretical based concept is applied exemplarily to data on research output types of funded research projects in UK that were the subject of the Metric Tide Report (REF 2014) and ex-ante evaluation data of a research funding organization. As expected, research output types depend on the research area, with journal articles having the strongest individual balance among the output types, i.e., being represented in almost all research areas. For the ex-ante evaluation data of 1,221 funded projects the diversity components were statistically estimated. The overall diversity of the projects in terms of entropy is 55.5% of the maximal possible entropy.

PHEV! The PHysically-based Extreme Value distribution of river flows

Magnitude and frequency are prominent features of river floods informing design of engineering structures, insurance premiums and adaptation strategies. Recent advances yielding a formal characterization of these variables from a joint description of soil moisture and daily runoff dynamics in river basins are here systematized to highlight their chief outcome: the PHysically-based Extreme Value (PHEV) distribution of river flows. This is a physically-based alternative to empirical estimates and purely statistical methods hitherto used to characterize extremes of hydro-meteorological variables. Capabilities of PHEV for predicting flood magnitude and frequency are benchmarked against a standard distribution and the latest statistical approach for extreme estimation, by using both an extensive observational dataset and long synthetic series of streamflow generated for river basins from contrasting hydro-climatic regions. The analyses outline the domain of applicability of PHEV and reveal its fairly unbiased capabilities to estimate flood magnitudes with return periods much longer than the sample size used for calibration in a wide range of case studies. The results also emphasize reduced prediction uncertainty of PHEV for rare floods, notably if the flood magnitude-frequency curve displays an inflection point. These features, arising from the mechanistic understanding embedded in the novel distribution of the largest river flows, are key for a reliable assessment of the actual flooding hazard associated to poorly sampled rare events, especially when lacking long observational records.

A single phantom, a single statistical method for low-contrast detectability assessment.

The assessment of low-contrast-details is a part of the quality control (QC) program in digital radiology. It generally consists of evaluating the threshold contrast (Cth) detectability details for different-sized inserts, appropriately located in dedicated QC test tools. This work aims to propose a simplified method, based on a statistical model approach for threshold contrast estimation, suitable for different modalities in digital radiology. A home-madelow-contrast phantom, made of a central aluminium insert with a step-wedge, was assembled and tested. The reliability and robustness of the method were investigated for Mammography, Digital Radiography, Fluoroscopy and Angiography. Imageswere analysed using our dedicated software developed on Matlab®. TheCth is expressed in the same unit (mmAl) for all studied modalities. This method allows the collection of Cthinformation from different modalities and equipment by different vendors, and it could be used to define typical values. Results are summarized in detail. For 0.5 diameter detail, Cthresults are in the range of: 0.018-0.023mmAl for 2D mammography and 0.26-0.34mmAl DR images. For angiographic images, for 2.5mm diameter detail, the Cths median values are 0.55, 0.4, 0.06, 0.12mmAl for low dose fluoroscopy, coronary fluorography, cerebral and abdominal DSA, respectively. The statistical method proposed in this study gives a simple approach for Low-Contrast-Details assessment, and the typical values proposed can be implemented in a QA program for digital radiology modalities.

Statistical Inversion Approach for Stress Estimation Based on Strain Monitoring in Continuously Pre-Stressed Concrete Beams

Stress is one of the most important physical indexes reflecting the mechanical behavior of concrete structures. In general, stress in structures cannot be directly monitored and can only be estimated through an established model of stress and strain. The accuracy of the estimated stress depends on the rationality of the established model for stress and strain. As the strain measured by sensors contains creep, shrinkage, and elastic strain, it is difficult to establish an analytical model for strain and stress. In this paper, a statistical inverse method was utilized to estimate the stress in continuously pre-stressed concrete beams based on the monitored strain. Stress in the beams and the model uncertainty factors were treated as model parameters. A linear-simplified method was adopted to determine the prior distribution of the stresses. The posterior distribution of the stresses at different locations during bridge construction can be obtained by the proposed method. A continuously pre-stressed concrete beam bridge was taken as the case study to verify the effectiveness of the proposed method. Additionally, the constitution of the total strain in the different construction stages was calculated. It was concluded that the creep strain is the dominant part of the total strain.

Statistics-based approach for large-scale group decision-making under incomplete Pythagorean fuzzy information with risk attitude

As loss in decision sample information occurs during large-scale group decision-making (LSGDM), this paper proposes a statistical estimation approach for handling Pythagorean fuzzy information under the risk attitude of decision-makers (DMs). The DMs are partitioned by risk attitudes (hesitancy degrees) into subgroups. A five-number summary for the subgroups from the incomplete decision information given by the DMs is obtained. The Cornish–Fisher expansion is then applied to estimate the mean, standard variance, and skewness of the decision sample information from the five-number summary. The confidence interval constructed by the skewness is used to obtain the interval-valued Pythagorean fuzzy number (IVPFN) evaluation information of the subgroups. An optimization model based on minimizing the conflicts between the subgroups and the overall group is used to derive the weights of the subgroups. A sorting function of the IVPFNs is used to rank the alternatives. A case study on green credit and a comparison analysis are applied to validate the proposed method.

A Review of Voxel-Based Computerized Ionospheric Tomography with GNSS Ground Receivers

Ionized by solar radiation, the ionosphere causes a phase rotation or time delay to trans-ionospheric radio waves. Reconstruction of ionospheric electron density profiles with global navigation satellite system (GNSS) observations has become an indispensable technique for various purposes ranging from space physics studies to radio applications. This paper conducts a comprehensive review on the development of voxel-based computerized ionospheric tomography (CIT) in the last 30 years. A brief introduction is given in chronological order starting from the first report of CIT with simulation to the newly proposed voxel-based algorithms for ionospheric event analysis. The statement of the tomographic geometry and voxel models are outlined with the ill-posed and ill-conditioned nature of CIT addressed. With the additional information from other instrumental observations or initial models supplemented to make the coefficient matrix less ill-conditioned, equation constructions are categorized into constraints, virtual data assimilation and multi-source observation fusion. Then, the paper classifies and assesses the voxel-based CIT algorithms of the algebraic method, statistical approach and artificial neural networks for equation solving or electron density estimation. The advantages and limitations of the algorithms are also pointed out. Moreover, the paper illustrates the representative height profiles and two-dimensional images of ionospheric electron densities from CIT. Ionospheric disturbances studied with CIT are presented. It also demonstrates how the CIT benefits ionospheric correction and ionospheric monitoring. Finally, some suggestions are provided for further research about voxel-based CIT.

Distributed Estimation for Principal Component Analysis: An Enlarged Eigenspace Analysis

The growing size of modern datasets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This article studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-L-dim (L > 1) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-L-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, the traditional Davis–Kahan theorem requires the explicit eigengap assumption to estimate the top-L-dim eigenspace. To abandon this eigengap assumption, we consider a new route in our analysis: instead of exactly identifying the top-L-dim eigenspace, we show that our estimator is able to cover the targeted top-L-dim population eigenspace. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA, such as principal component regression and single index model. Finally, we provide simulation studies to demonstrate the performance of the proposed distributed estimator.

Estimating the Probable Maximum Precipitation by Physical Methods Using Satellite and Radiolocation Observation Data: Case Study of the Middle Urals

The study considers the methods for evaluating the maximal possible daily storm rainfall (MPR) in the Middle Ural based on a combination of ground, aerological, satellite, and radiolocation data. The methods under consideration represent an alternative to statistical estimation approaches. MPR is evaluated using the total moisture content of cloud systems, described in terms of their stationarity or dynamics over time. The considered methods include evaluating moisture content based on the characteristics of vertical temperature distribution in the troposphere, convection rate, and the height of the upper cloud boundary. The estimates of the probable maximum precipitation, made for the conditions of stable or cloud-dependent moisture content, are comparable with the maximums evaluated by Hershfield statistical method. The probable maximums determined by physical methods are close to the values with exceedance probability of 0.01–0.001%, evaluated with the use of lognormal distribution. The method for evaluating the probable maximum precipitation can be used in engineering practice.

Developing an Improved Statistical Approach for Survival Estimation in Bone Metastases Management: The Bone Metastases Ensemble Trees for Survival (BMETS) Model

To determine whether a machine learning approach optimizes survival estimation for patients with symptomatic bone metastases (SBM), we developed the Bone Metastases Ensemble Trees for Survival (BMETS) to predict survival using 27 prognostic covariates. To establish its relative clinical utility, we compared BMETS with 2 simpler Cox regression models used in this setting. For 492 bone sites in 397 patients evaluated for palliative radiation therapy (RT) for SBM from January 2007 to January 2013, data for 27 clinical variables were collected. These covariates and the primary outcome of time from consultation to death were used to build BMETS using random survival forests. We then performed Cox regressions as per 2 validated models: Chow's 3-item (C-3) and Westhoff's 2-item (W-2) tools. Model performance was assessed using cross-validation procedures and measured by time-dependent area under the curve (tAUC) for all 3 models. For temporal validation, a separate data set comprised of 104 bone sites treated in 85 patients in 2018 was used to estimate tAUC from BMETS. Median survival was 6.4 months. Variable importance was greatest for performance status, blood cell counts, recent systemic therapy type, and receipt of concurrent nonbone palliative RT. tAUC at 3, 6, and 12 months was 0.83, 0.81, and 0.81, respectively, suggesting excellent discrimination of BMETS across postconsultation time points. BMETS outperformed simpler models at each time, with respective tAUC at each time of 0.78, 0.76, and 0.74 for the C-3 model and 0.80, 0.78, and 0.77 for the W-2 model. For the temporal validation set, respective tAUC was similarly high at 0.86, 0.82, and 0.78. For patients with SBM, BMETS improved survival predictions versus simpler traditional models. Model performance was maintained when applied to a temporal validation set. To facilitate clinical use, we developed a web platform for data entry and display of BMETS-predicted survival probabilities.

Gradients in richness and turnover of a forest passerine's diet prior to breeding: A mixed model approach applied to faecal metabarcoding data.

Rather little is known about the dietary richness and variation of generalist insectivorous species, including birds, due primarily to difficulties in prey identification. Using faecal metabarcoding, we provide the most comprehensive analysis of a passerine's diet to date, identifying the relative magnitudes of biogeographic, habitat and temporal trends in the richness and turnover in diet of Cyanistes caeruleus (blue tit) along a 39 site and 2° latitudinal transect in Scotland. Faecal samples were collected in 2014-2015 from adult birds roosting in nestboxes prior to nest building. DNA was extracted from 793 samples and we amplified COI and 16S minibarcodes. We identified 432 molecular operational taxonomic units that correspond to putative dietary items. Most dietary items were rare, with Lepidoptera being the most abundant and taxon-rich prey order. Here, we present a statistical approach for estimation of gradients and intersample variation in taxonomic richness and turnover using a generalised linear mixed model. We discuss the merits of this approach over existing tools and present methods for model-based estimation of repeatability, taxon richness and Jaccard indices. We found that dietary richness increases significantly as spring advances, but changes little with elevation, latitude or local tree composition. In comparison, dietary composition exhibits significant turnover along temporal and spatial gradients and among sites. Our study shows the promise of faecal metabarcoding for inferring the macroecology of food webs, but we also highlight the challenge posed by contamination and make recommendations of laboratory and statistical practices to minimise its impact on inference.

Predicting the Incident Cases of Emerging Infectious Disease Using a Bayesian Probability Model - China, February 2020.

What is already known about this topic?The exact number of incident cases of emerging infectious diseases on a daily basis is of great importance to the disease control and prevention, but it is not directly available from the current surveillance system in time.What is added by this report?In this study, a Bayesian statistical method was proposed to estimate the posterior parameters of the gamma probability distribution of the lag time between the onset date and the reporting time based on the surveillance data. And then the posterior parameters and corresponding cumulative gamma probability distribution were used to predict the actual number of new incident cases and the number of unreported cases per day. The proposed method was used for predicting COVID-19 incident cases from February 5 to February 26, 2020. The final results show that Bayesian probability model predictions based on data reported by February 28, 2020 are very close to those actually reported a month later.What are the implications for public health practice?This research provides a Bayesian statistical approach for early estimation of the actual number of cases of incidence based on surveillance data, which is of great value in the prevention and control practice of epidemics.

Dependability considerations of redundant sensor systems

Integrated sensor systems, which are produced in high volume for safety-critical applications such as automotive, require careful design and optimization strategies. To increase their reliability, such systems are often used in redundant configurations. However, this is in many cases not sufficient: requirements of high production yield, reliability in operation, low probabilities for non-detected system faults, in combination with fast development speed and low production costs require more detailed and careful design approaches. We consequently suggest statistical design, estimation and optimization approaches for efficient product definition and design. This methodology is summarized in a general way for redundant sensor systems. In a first step, the individual sensing channel performance is optimized statistically. In a second step, the dependability figures are optimized dependent on the redundant sensor output function and its diagnostic mechanism parameters based on statistical considerations of faults. The suggested methodology is shown exemplary for a redundant integrated linear Hall magnetic field sensor system for safety-critical automotive applications.