Statistical Data Modeling Research Articles

Deep and statistical learning in biomedical imaging: State of the art in 3D MRI brain tumor segmentation

Clinical diagnosis and treatment decisions rely upon the integration of patient-specific data with clinical reasoning. Cancer presents a unique context that influences treatment decisions, given its diverse forms of disease evolution. Biomedical imaging allows non-invasive assessment of diseases based on visual evaluations, leading to better clinical outcome prediction and therapeutic planning. Early methods of brain cancer characterization predominantly relied upon the statistical modeling of neuroimaging data. Driven by breakthroughs in computer vision, deep learning has become the de facto standard in medical imaging. Integrated statistical and deep learning methods have recently emerged as a new direction in the automation of medical practice unifying multi-disciplinary knowledge in medicine, statistics, and artificial intelligence. In this study, we critically review major statistical, deep learning, and probabilistic deep learning models and their applications in brain imaging research with a focus on MRI-based brain tumor segmentation. These results highlight that model-driven classical statistics and data-driven deep learning is a potent combination for developing automated systems in clinical oncology.

Rapid detection of milk adulteration using Raman spectroscopy and statistical modelling

Food adulteration has become a concern for consumers and food safety authorities. Milk is a commune adulterated food product, like melamine adulteration, which resulted in devastating effects, especially on young children. Because of the current fast paste economy, it is essential to develop equally fast analysis methods to ensure reliable and sensitive results quickly with little to no sample preparation. For that purpose, a Raman method was developed and Partial least squares regression (PLS) was applied in order to develop a model for adulterated goat milk detection. Minitab 17 software was used for the statistical modeling of data. Validation matrices were constructed using unadulterated goat milk and goat milk adulterated with cow milk in different proportions (0-50%). The prediction model had a correlation coefficient of 99.8 %.

A pseudo principal component analysis method for multi-dimensional open-high-low-close data in candlestick chart

As the most widely-used data form in the field of finance, the open-high-low-close (OHLC) data is being collected by all kinds of financial trading systems all the time. This paper puts forward a pseudo-principal component analysis (PCA) for multi-dimensional OHLC data, which can extract their useful information in a comprehensible way for visualization and easy interpretation. Firstly, a novel feature-based representation for OHLC data is proposed, which contains fruitful and explicit economic implications. Next, we define a full set of numerical characteristics and variance-covariance structures for the feature-based OHLC data. Then, the pseudo-PCA procedure for OHLC data is deduced based on the proposed algebraic operators. Finally, the effectiveness and interpretability of the proposed pseudo-PCA method are verified through finite simulations and three typical empirical experiments. This paper enriches the application scenarios of classical PCA and contributes to the multivariate statistical modeling of symbolic data. The proposed applications can serve as models for related studies.

Exploring Industry-Level Fairness of Auto Insurance Premiums by Statistical Modeling of Automobile Rate and Classification Data

The study of actuarial fairness in auto insurance has been an important issue in the decision making of rate regulation. Risk classification and estimating risk relativities through statistical modeling become essential to help achieve fairness in premium rates. However, because of minor adjustments to risk relativities allowed by regulation rules, the rates charged eventually may not align with the empirical risk relativities calculated from insurance loss data. Therefore, investigating the relationship between the premium rates and loss costs at different risk factor levels becomes important for studying insurance fairness, particularly from rate regulation perspectives. This work applies statistical models to rate and classification data from the automobile statistical plan to investigate the disparities between insurance premiums and loss costs. The focus is on major risk factors used in the rate regulation, as our goal is to address fairness at the industry level. Various statistical models have been constructed to validate the suitableness of the proposed methods that determine a fixed effect. The fixed effect caused by the disparity of loss cost and premium rates is estimated by those statistical models. Using Canadian data, we found that there are no significant excessive premiums charged at the industry level, but the disparity between loss cost and premiums is high for urban drivers at the industry level. This study will help better understand the extent of auto insurance fairness at the industry level across different insured groups characterized by risk factor levels. The proposed fixed-effect models can also reveal the overall average loss ratio, which can tell us the fairness at the industry level when compared to loss ratios by the regulation rules.

Box-Behnken design optimization of sulfate reduction from natural water by electrocoagulation process

The purpose of this work is to investigate sulfate removal from aqueous solutions by electrocoagulation (EC). The influence of electrolysis time, initial pH, and current density was carried out. The interaction of the several effects on removal efficiency was also studied. The Box-Behnken experimental design (BBD) in Response Surface Methodology (RSM) was applied in the development of statistical analysis, modeling, and interpretation of the resultant treatment data of sulfate removal by EC. The optimum conditions for highest removal ratio of sulfate from aqueous solution were: current density of 10 mA/cm2, initial pH equal 5 and electrolysis time of 60 min. Sulfate removal efficiency reach a maximum value of 98.76% and the predicted value is 100%. According to ANOVA results, the correlation coefficient (R2) value of 98% proved that experimental data and model predictions agreed well. The R2 adj and R2 pred were also in a reasonable agreement (98% and 95% respectively). The mathematical model that describes the EC process was determined and proved that all variable had linear and quadratic significant effect on sulfate removal efficiency. The optimum conditions founded using BBD conducted to 60 and 90% of sulfate removal respectively from seawater and brackish water.

Mechanistic spatial models for heavy metal pollution

AbstractMining operations can contribute substantial amounts of pollution in the form of atmospheric dust. Statistical models predicting the spread of pollutants from these sources are useful for evaluating the environmental impacts of mines. Our study develops a mechanistic spatial model for heavy metal concentrations in Cape Krusenstern National Monument (CAKR), Alaska, USA. We characterize the spatial structure in our statistical model using a spatio‐temporal process for atmospheric dispersion. Mathematically, this is modeled using an advection‐diffusion partial differential equation that incorporates information about pollutant sources, diffusion, duration of spread, and advection (i.e., prevailing winds). Our approach improves upon previous statistical methods by including a temporally varying advection component and linking indirect concentration measurements to the spatio‐temporal dynamics in the model. We estimated concentrations of three heavy metals jointly using a Bayesian hierarchical model to account for the similarity in processes across chemicals. Our mechanistic statistical model is beneficial because it can predict chemical concentrations for scenarios where mining activities change. Additionally, our analysis provides an example of how using spatio‐temporal processes in statistical models for spatial data can incorporate understanding of mechanisms governing the spread of pollution and provide inferences for parameters associated with these processes.

LESA: Longitudinal Elastic Shape Analysis of Brain Subcortical Structures

Over the past 30 years, magnetic resonance imaging has become a ubiquitous tool for accurately visualizing the change and development of the brain’s subcortical structures (e.g., hippocampus). Although subcortical structures act as information hubs of the nervous system, their quantification is still in its infancy due to many challenges in shape extraction, representation, and modeling. Here, we develop a simple and efficient framework of longitudinal elastic shape analysis (LESA) for subcortical structures. Integrating ideas from elastic shape analysis of static surfaces and statistical modeling of sparse longitudinal data, LESA provides a set of tools for systematically quantifying changes of longitudinal subcortical surface shapes from raw structure MRI data. The key novelties of LESA include: (i) it can efficiently represent complex subcortical structures using a small number of basis functions and (ii) it can accurately delineate the spatiotemporal shape changes of the human subcortical structures. We applied LESA to analyze three longitudinal neuroimaging datasets and showcase its wide applications in estimating continuous shape trajectories, building life-span growth patterns, and comparing shape differences among different groups. In particular, with the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data, we found that Alzheimer’s Disease (AD) can significantly speed the shape change of the lateral ventricle and the hippocampus from 60 to 75 years olds compared with normal aging. Supplementary materials for this article are available online.

Statistical modeling and monitoring of image data in the presence of temporal and spatial correlations

In this paper, the regression-based approach was developed to monitor image data under two-scale analysis. In the first scale, wavelet transformation was used to extract the main features of geometric profile created from the images. The next scale was to monitor the small-scale components which could be expressed by correlation in error terms. To monitor correlation in error terms, one parametric and one non-parametric methods were developed. Parameters of the parametric model including spatial correlation coefficient and error term variance were estimated using Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators, respectively. In non-parametric method, no assumption was made about the structure of correlation in error terms. To extract useful information about the nature of correlation in error terms, Functional Principal Component Analysis (FPCA) was used. After extracting features for both scales, some appropriate test statistics were computed. Then, monitoring the process was performed by plotting these test statistics on corresponding control charts. Simulation and industrial case studies were also performed to evaluate the proposed method’s performance in detecting different shifts. The results indicated the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identify the source of variability.

COLUMN STUDY FOR THE CU(II) REMOVAL BY THE COCONUT SHELL FROM AQUEOUS SOLUTION – MLR AND GA MODELING

Adsorption characteristics of locally available inexpensive natural adsorbent coconut shells were studied for Cu(II) removal. The present study adsorption process was carried through a fixed bed column to find out the breakthrough characteristics. The variation of operating variables is investigated, pH 6, influence Cu(II) concentration (10–30 mg·L–1), bed height (5–15 cm), the flow rate (10–30 ml·min–1). The suitability of various kinetic models has been tested. Maximum adsorption capacity, qe according to Thomas model, was 30.09 mg·g–1obtained at 20 ml/min, flow rate, 30 mg·L–1 metal solution, and 15 cm bed height. The correlation coefficient of the Thomas model ranges from 0.8260 to 0.9839. Besides this, according to the statistical parameters of the Yoon-Nelson and Yan et al. models, proving that the experimental data are suitable for this model. The statistical and GA modeling of the experimental data has also been performed successfully.

Objective Methods for Thinning the Frequency of Reforecasts while Meeting Postprocessing and Model Validation Needs

Abstract This paper utilizes statistical and statistical–dynamical methodologies to select, from the full observational record, a minimal subset of dates that would provide representative sampling of local precipitation distributions across the contiguous United States (CONUS). The CONUS region is characterized by a great diversity of precipitation-producing systems, mechanisms, and large-scale meteorological patterns (LSMPs), which can provide favorable environment for local precipitation extremes. This diversity is unlikely to be adequately captured in methodologies that rely on grossly reducing the dimensionality of the data—by representing it in terms of a few patterns evolving in time—and thus requires data thinning techniques based on high-dimensional dynamical or statistical data modeling. We have built a novel high-dimensional empirical model of temperature and precipitation capable of producing statistically accurate surrogate realizations of the observed 1979–99 (training period) evolution of these fields. This model also provides skillful hindcasts of precipitation over the 2000–20 (validation) period. We devised a subsampling strategy based on the relative entropy of the empirical model’s precipitation (ensemble) forecasts over CONUS and demonstrated that it generates a set of dates that captures a majority of high-impact precipitation events, while substantially reducing a heavy-precipitation bias inherent in an alternative methodology based on the direct identification of large precipitation events in the Global Ensemble Forecast System (GEFS), version 12 reforecasts. The impacts of data thinning on the accuracy of precipitation statistical postprocessing, as well as on the calibration and validation of the Hydrologic Ensemble Forecast Service (HEFS) reforecasts are yet to be established. Significance Statement High-impact weather events are usually associated with extreme precipitation, which is notoriously difficult to predict even using highly resolved state-of-the-art numerical weather prediction models based on first physical principles. The same is true for statistical models that use past data to anticipate the future behavior likely to stem from an observed initial state. Here we use both types of models to identify the occurrences of the states, over the historical climate record, which are likely to lead to extreme precipitation events. We show that the overall statistics of precipitation over the contiguous United States is encapsulated in a greatly reduced set of such states, which could substantially alleviate the computational burden associated with testing of hydrological forecast models used for decision support.

Integrative Modeling, Molecular Mechanics, and Molecular Dynamics Evaluation of Genomics Variants in KMT2C (MLL3), a Gene Involved in Kleefstra Syndrome Type 2

Kleefstra Syndrome (KS) is a genetic, neurodevelopmental disorder characterized by intellectual disability, infantile hypotonia, severe expressive language delay, and characteristic facial appearance, with a spectrum of other distinct clinical manifestations. Pathogenic mutations in the epigenetic modifier, type 2 lysine methyltransferase (KMT2C), are attributed to cause KS core features in individuals who are Euchromatic Histone Lysine Methyltransferase 1, EHMT1, mutation negative. These individuals are designated as having KS type 2. In this study, we made use of multidimensional approaches, including conventional genomic bioinformatics, molecular modeling, molecular mechanics, and molecular dynamics simulations, to understand and enhance the annotation and potential mechanisms by which disease‐associated missense variants affect KMT2C function. In addition, we report a scoring system based on statistical integration and modeling of data derived from the structure and dynamics of KMT2C, which allows us to classify germline variants into SV (Structural Variants), DV (Dynamic Variants), SDV (Structural and Dynamic Variant), and VUS (Variant of Uncertain Significance). Moreover, these scores of disease‐associated variants reflect alterations in molecular fitness when compared with tolerated, benign variants, used as controls. Thus, these studies provide data that is more refined, both structurally and functionally for each variant, compared to current annotation tools used in human genomics databases and reveal mechanisms for their dysfunction not predictable from clinical genomic methods alone. This new knowledge extends our understanding of molecular mechanisms underlying the dysfunction of KS type 2‐associated genomic mutations. Lastly, by identifying KMT2C mutation‐specific druggable conformations, this study builds the trajectory toward the future development of small molecules to ameliorate the symptoms of this disease.

Statistical and Machine Learning Models for Remote Sensing Data Mining—Recent Advancements

During the last few decades, the remarkable progress in the field of satellite remote sensing (RS) technology has enabled us to capture coarse, moderate to high-resolution earth imagery on weekly, daily, and even hourly intervals [...]

New aspects in deriving health-based guidance values for bromate in swimming pool water

Bromate, classified as a EU CLP 1B carcinogen, is a typical by-product of the disinfection of drinking and swimming pool water. The aim of this study was (a) to provide data on the occurrence of bromate in pool water, (b) to re-evaluate the carcinogenic MOA of bromate in the light of existing data, (c) to assess the possible exposure to bromate via swimming pool water and (d) to inform the derivation of cancer risk-related bromate concentrations in swimming pool water. Measurements from monitoring analysis of 229 samples showed bromate concentrations in seawater pools up to 34 mg/L. A comprehensive non-systematic literature search was done and the quality of the studies on genotoxicity and carcinogenicity was assessed by Klimisch criteria (Klimisch et al., Regul Toxicol Pharmacol 25:1–5, 1997) and SciRAP tool (Beronius et al., J Appl Toxicol, 38:1460–1470, 2018) respectively. Benchmark dose (BMD) modeling was performed using the modeling average mode in BMDS 3.1 and PROAST 66.40, 67 and 69 (human cancer BMDL10; EFSA 2017). For exposure assessment, data from a wide range of sources were evaluated for their reliability. Different target groups (infants/toddlers, children and adults) and exposure scenarios (recreational, sport-active swimmers, top athletes) were considered for oral, inhalation and dermal exposure. Exposure was calculated according to the frequency of swimming events and duration in water. For illustration, cancer risk-related bromate concentrations in pool water were calculated for different target groups, taking into account their exposure using the hBMDL10 and a cancer risk of 1 in 100,000. Convincing evidence was obtained from a multitude of studies that bromate induces oxidative DNA damage and acts as a clastogen in vitro and in vivo. Since statistical modeling of the available genotoxicity data is compatible with both linear as well as non-linear dose–response relationships, bromate should be conservatively considered to be a non-threshold carcinogen. BMD modeling with model averaging for renal cancer studies (Kurokawa et al., J Natl. Cancer Inst, 1983 and 1986a; DeAngelo et al., Toxicol Pathol 26:587–594, 1998) resulted in a median hBMDL10 of 0.65 mg bromate/kg body weight (bw) per day. Evaluation of different age and activity groups revealed that top athletes had the highest exposure, followed by sport-active children, sport-active adults, infants and toddlers, children and adults. The predominant route of exposure was oral (73–98%) by swallowing water, followed by the dermal route (2–27%), while the inhalation route was insignificant (< 0.5%). Accepting the same risk level for all population groups resulted in different guidance values due to the large variation in exposure. For example, for an additional risk of 1 in 100,000, the bromate concentrations would range between 0.011 for top athletes, 0.015 for sport-active children and 2.1 mg/L for adults. In conclusion, the present study shows that health risks due to bromate exposure by swimming pool water cannot be excluded and that large differences in risk exist depending on the individual swimming habits and water concentrations.

Statistical modeling of complex health outcomes and air pollution data: Application of air quality health indexing for asthma risk assessment

&#x0D; Background: Statistical models for complex health outcome data analyses with; zero inflation, autocorrelation, confounding, seasonality and delayed exposures, play an important role in accurately assessing air pollution risk, especially in public health warning using national air quality health indices (NAQHI). NAQHI assessment generalizes model estimates across all geographies and seasons and neglects area and season specific variations. The aim is to develop complex statistical models, specific to the complex data structures and to demonstrate effectiveness of the model estimates in public health massage delivery.&#x0D; Methods: A time series model was fitted to asthma hospital admissions and ambient air pollution data from two sites, Halifax, an urban, traffic and industry polluted site and Sydney, a rural waste disposal polluted site, in the province of Nova Scotia, Canada. I fitted zero inflated, auto regressive, Poisson and Negative Binomial models with lagged effects for sparse asthma admissions and air pollution data and compared the model risk estimates with that of the NAQHI.&#x0D; Results: NAQHI used three pollutants, Nitrogen Dioxide, Ozone and particulate matter. I found Carbon monoxide in the urban site and lead in the waste disposal site as prominent pollutants and there were seasonal differences. The findings demonstrated severe under-assessment of asthma relative risk by NAQHI, when prominent pollutants are neglected and also when auto correlation and zero inflation are ignored. &#x0D; Conclusion: This study demonstrated the importance of complex statistical model use and the consequences of lack of such modelling that accounted for data structures in public health risk assessments.

FUNCTIONAL MODELLING OF TELECOMMUNICATIONS DATA

This work deals with statistical modeling and forecasting of telecommunications data. Main mobile traffic events (SMS, Voice calls, Mobile data) are smoothed using B-spline functions and later analyzed in a functional framework. Functional linear auto-regression models are fitted using both bottom-up and topdown design methodologies. The advantages and disadvantages of both approaches for the prediction of mobile telephone users’ habits are discussed.

Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data

SummaryBinary regression models are ubiquitous in virtually every scientific field. Frequently, traditional generalised linear models fail to capture the variability in the probability surface that gives rise to the binary observations, and remedial methods are required. This has generated a substantial literature composed of binary regression models motivated by various applications. We describe an organisation of generalisations to traditional binary regression methods based on the familiar three‐part structure of generalised linear models (random component, systematic component and link function). This perspective facilitates both the comparison of existing approaches and the development of flexible models with interpretable parameters that capture application‐specific data‐generating mechanisms. We use our proposed organisational structure to discuss concerns with certain existing models for binary data based on quantile regression. We then use the framework to develop and compare several binary regression models tailored to occupancy data for European red squirrels (Sciurus vulgaris).

Considering the effect of dustiness of a photovoltaic module surfaces on solar power generation by matlab software

Purpose. Improving the simulation model of a solar power plant by creating a block model for accounting for dustiness of the surface of photovoltaic modules when calculating the efficiency of electric power generation by a solar power plant. &#x0D; Methodology. Use of statistical data processing methods and modeling in the structure of Matlab tools.&#x0D; Findings. A mathematical model was created, which made it possible to take into account the influence of dustiness of the surface of photovoltaic modules on the efficiency of electric power generation by a solar power station. The model was tested on the real object and the accuracy of modeling was proved. &#x0D; Originality. The scientific novelty is to create mathematical models that describe the effect of dust on the surface of photovoltaic modules on the efficiency of solar station generation based on the Bouguer-Lambert-Behr law, the blocks of precipitation influence on dust were developed, and the rate of dust accumulation was corrected by taking into account the air humidity. &#x0D; Practical value. The obtained results will help to improve the accuracy of modeling of all types of photovoltaic systems. These models can be used as the formation of commercial proposals with more accurate schedules of electric power generation, which can significantly increase the accuracy of the choice of rated capacity of equipment.

Concentrations, Loads, and Associated Trends of Nutrients Entering the Sacramento–San Joaquin Delta, California

Statistical modeling of water-quality data collected at the Sacramento River at Freeport and San Joaquin River near Vernalis, California, USA, was used to examine trends in concentrations and loads of various forms of dissolved and particulate nitrogen and phosphorus that entered the Sacramento–San Joaquin River Delta (Delta) from upstream sources between 1970 and 2019. Ammonium concentrations and loads decreased at the Sacramento River site from the mid-1970s through 1990 because of the consolidation of wastewater treatment and continuously reduced from the mid-1970s to 2019 at the San Joaquin River site. Current ammonium concentrations are mostly below 4 µM (0.056 mg N L–1) at both sites, a concentration above which reductions in phytoplankton productivity or changes in algal species composition may occur. The Sacramento River at Freeport site is located upstream of the Sacramento Regional County Sanitation District’s treatment facility’s discharge point; nutrient water quality there is representative of upstream sources. Inorganic nitrogen (nitrate plus ammonium) concentrations and loading differed at both sites. At the Sacramento River location, concentrations decrease in the summer agricultural season, reducing the molar ratios of nitrogen to phosphorus. In contrast, inorganic nitrogen concentrations increase in the San Joaquin River during the agricultural season as a result of irrigation runoff, increasing the molar ratio of nitrogen to phosphorus. This increase suggests a possible nitrogen limitation in the northern Delta and a phosphorus limitation in the southern Delta, as indicated by the molar ratios of bioavailable nitrogen to bioavailable phosphorus. Planned upgrades to the Sacramento Regional Wastewater Treatment Plant (SRWTP) will reduce inorganic nitrogen inputs to the northern Delta. Consequently, the supply of bioavailable nitrogen throughout the upper estuary should diminish. Source modeling of nitrogen and phosphorus identifies agriculture, atmospheric deposition, and wastewater effluent as sources of total nitrogen in the Central Valley. In contrast, geologic sources, agriculture, and wastewater discharge are the primary sources of phosphorus.

Analyzing the Best Fitted Probabilistic Model for the Seasonal Rainfall Data in Khulna Region of Bangladesh

There are several pieces of research on the statistical modeling of rainfall data in Bangladesh. Since all the seasons of a year do not receive a similar amount of rainfall, hence one single statistical model might not be able to explain the pattern of rainfall at any season of a year. According to the climatologists, Bangladesh has four seasons which are Monsoon, Post-monsoon, Summer, and Winter based on the geographical characteristics of this country. This paper aims to determine the best-fitted probability distribution model for the monthly rainfall data of each particular season in the Khulna district of Bangladesh using the rainfall data of the Khulna region from 1951 to 2018. Very commonly used seven continuous distributions- Normal, Weibull, Gamma, Log-normal, Exponential, Cauchy, and Logistic distributions were used to model the data and to evaluate the performances of the distributions, three non-parametric goodness-of-fit tests were conducted, and AIC, BIC values were calculated. Parameters of the distributions were estimated by the maximum likelihood method. The best-fit result of each season was taken as the distribution with the lowest AIC and BIC values. Among the seven distributions, the Gamma distribution showed the best-fit results of the monthly rainfall data for the Monsoon, Post-Monsoon, and Winter Season, and the Weibull distribution showed the best-fit result for Summer Season.

TascCODA: Bayesian Tree-Aggregated Analysis of Compositional Amplicon and Single-Cell Data.

Accurate generative statistical modeling of count data is of critical relevance for the analysis of biological datasets from high-throughput sequencing technologies. Important instances include the modeling of microbiome compositions from amplicon sequencing surveys and the analysis of cell type compositions derived from single-cell RNA sequencing. Microbial and cell type abundance data share remarkably similar statistical features, including their inherent compositionality and a natural hierarchical ordering of the individual components from taxonomic or cell lineage tree information, respectively. To this end, we introduce a Bayesian model for tree-aggregated amplicon and single-cell compositional data analysis (tascCODA) that seamlessly integrates hierarchical information and experimental covariate data into the generative modeling of compositional count data. By combining latent parameters based on the tree structure with spike-and-slab Lasso penalization, tascCODA can determine covariate effects across different levels of the population hierarchy in a data-driven parsimonious way. In the context of differential abundance testing, we validate tascCODA’s excellent performance on a comprehensive set of synthetic benchmark scenarios. Our analyses on human single-cell RNA-seq data from ulcerative colitis patients and amplicon data from patients with irritable bowel syndrome, respectively, identified aggregated cell type and taxon compositional changes that were more predictive and parsimonious than those proposed by other schemes. We posit that tascCODA 1 constitutes a valuable addition to the growing statistical toolbox for generative modeling and analysis of compositional changes in microbial or cell population data.