Multivariate Statistics

Multivariate measurements of human brain white matter (WM) with diffusion MRI (dMRI) provide information about the role of WM in a variety of cognitive functions and in brain health. Statistical models take advantage of the regularities in these data to make inferences about individual differences. For example, dMRI data provide the basis for accurate brain-age models -models that predict the chronological age of participants from WM tissue properties. Deep learning (DL) models are powerful machine learning models, which have been shown to provide benefits in many multivariate analysis settings. We investigated whether DL would provide substantial improvements for brain-age models based on dMRI measurements of WM in a large sample of children and adolescents. We found that some DL models fit the data better than a linear baseline, but the differences are small. In particular, recurrent neural network architectures provide up to ~6% improvement in accuracy. This suggests that information about WM development is mostly accessible with linear models, and does not require the additional invariance and non-linearity offered by DL models. However, in some applications this incremental improvement may prove critical. We provide open-source software that fits DL models to dMRI data ().

Multivariate measurements of human brain white matter (WM) with diffusion MRI (dMRI) provide information about the role of WM in a variety of cognitive functions and in brain health. Statistical models take advantage of the regularities in these data to make inferences about individual differences. For example, dMRI data provide the basis for accurate brain-age models – models that predict the chronological age of participants from WM tissue properties. Deep learning (DL) models are powerful machine learning models, which have been shown to provide benefits in many multivariate analysis settings. We investigated whether DL would provide substantial improvements for brain-age models based on dMRI measurements of WM in a large sample of children and adolescents. We found that some DL models fit the data better than a linear baseline, but the differences are small. In particular, recurrent neural network architectures provide up to ∼6% improvement in accuracy. This suggests that inform...

Mathematical morphology is a popular framework for non-linear image processing, first introduced for binary and grey-level images, then extended to colour and multivariate images. Various pseudo-morphologies have been proposed as solutions to the problem of ordering multivariate data. Despite the lack of some properties, pseudomorphologies have proved useful in various applications, such as filtering or texture classification. The authors propose to improve the existing colour probabilistic pseudo-morphology by changing the way the local pseudoextrema are chosen. They show the usefulness of the new construction in the context of noise reduction in colour images using the open-close close-open filter, by highlighting the improvement over the original construction and comparing the authors' results with other relevant morphological and pseudo-morphological approaches.

The resolution and quantitation of pure spectra of minority components in measurements of chemical mixtures without prior knowledge of the mixture is a challenging problem. In this work, a combination of band target entropy minimization (BTEM) and target partial least squares (T-PLS) was used to obtain estimates for single pure component spectra and to calibrate those estimates in a true, one-at-a-time fashion. This approach allows for minor components to be targeted and their relative amounts estimated in the presence of other varying components in spectral data. The use of T-PLS estimation is an improvement to the BTEM method because it overcomes the need to identify all of the pure components prior to estimation. Estimated amounts from this combination were found to be similar to those obtained from a standard method, multivariate curve resolution-alternating least squares (MCR-ALS), on a simple, three component mixture dataset. Studies from two experimental datasets demonstrate ...

Grape is one of the nutritious fruits that have commercial value as well, and most farmers try to raise it in their lands. Considering various factors affecting growth and yield of grape, the process of assessing the suitability of land for cultivation in order to spatial planning of this product needs the use of comprehensive and diverse geographic and descriptive information. GIS technology provides the possibility of using this type of data and facilitates spatial analysis of information based on the appropriate models. Therefore, in this study regarding the ecological needs of grape, multi-criteria decision making (MCDM) method based on analytical hierarchy process (AHP) was used for modeling and spatial analysis of information in ARC/GIS 9.3 software environment. Eventually, East Azarbaijan province suitable lands for grape cultivation and production with regard to climatic elements and land physical factors (temperature, precipitation, relative humidity, topography, etc.) were evaluated and zoned. Results of this research showed that, spatially, 10 percent of the province has conditions varying between suitable to very suitable for grape production compared to the rest of province which in terms of spatial zones included Mianeh, Malekan, Shabstar, Jolfa, Bonab and Ajabshir cities and the most suitable areas were presented concerning final layer.

There is little evidence available on whether external auditors' independence collaborates or mitigates earnings manipulation. Therefore, this study examines the effects of external auditor's independence on earnings management of consumer goods firms in Nigeria. The study relies on secondary data derived from various companies' financial statements to determine and measure the level of earnings manipulations, applying an all-inclusive multivariate analysis. Samples of 20 consumer goods firms quoted in Nigeria Stock Exchange were used for the period of ten years spanning 2010 to 2019. The study employed ex-post facto and longitudinal research design. The secondary sources of data were collected from annual reports of the selected consumer goods companies and three (3) specific objectives and hypotheses were tested and analyzed using descriptive statistics, Pearson correlation analysis, variance inflation factor and panel regression analysis. The empirical analysis using a total of 200 company-year observations, shows that audit tenure exerts positive non-significant effects and exhibit direct relationship with the amount of discretionary accruals of quoted consumer goods companies in Nigeria while a negative and significant effect were documented for firm size and Joint provision of audit and non-audit services at 95% confidence level respectively. Generally, the value of R-squared which is the coefficient of determination stood at 37% which implies that 37% of the systematic variations in individual dependent variables were explained in the model while about 63% were unexplained thereby captured by the stochastic error term. The study concludes that rendering joint services and lengthy auditor tenure are a mechanism through which management influence auditors to compromise their independence and therefore allow unethical practices such as earnings management. In line with the above findings, this study therefore recommends among others that, non-audit services that are likely to increase total audit fees and make the auditors closer to management should be abolished, and where it is deemed necessary, separate audit firm should be employed to provide non-audit services to a client.

Mineral deposits frequently contain several elements of interest that are spatially correlated and require the use of joint geostatistical simulation techniques in order to generate models preserving their spatial relationships. Although joint-simulation methods have long been available, they are impractical when it comes to more than three variables and mid to large size deposits. This paper presents the application of block-support simulation of a multi-element mineral deposit using minimum/maximum autocorrelation factors to facilitate the computationally efficient joint simulation of large, multivariable deposits. The algorithm utilized, termed dbmafsim, transforms point-scale spatial attributes of a mineral deposit into uncorrelated service variables leading to the generation of simulated realizations of block-scale models of the attributes of interest of a deposit. The dbmafsim algorithm is utilized at the Yandi iron ore deposit in Western Australia to simulate five cross-corre...

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Background The coronavirus disease (COVID-19) pandemic has affected more than 200 countries and has infected more than 2,800,000 people as of April 24, 2020. It was first identified in Wuhan City in China in December 2019. Objective The aim of this study is to identify the top 15 countries with spatial mapping of the confirmed cases. A comparison was done between the identified top 15 countries for confirmed cases, deaths, and recoveries, and an advanced autoregressive integrated moving average (ARIMA) model was used for predicting the COVID-19 disease spread trajectories for the next 2 months. Methods The comparison of recent cumulative and predicted cases was done for the top 15 countries with confirmed cases, deaths, and recoveries from COVID-19. The spatial map is useful to identify the intensity of COVID-19 infections in the top 15 countries and the continents. The recent reported data for confirmed cases, deaths, and recoveries for the last 3 months was represented and compare...

The umeta command performs u-statistics-based random-effects meta-analysis on a dataset of univariate, bivariate or trivariate point estimates, sampling variances, and for bivariate or trivariate data, within-study correlations or covariances. The methodology is described in ...

We have previously demonstrated Stata implementation of bivariate ramdom effects meta-analysis of the sensitivity and specificity of a single binary diagnostic test by means of the midas module (Dwamena NASUG2007; Dwamena WCSUG 2007). In this presentation we extend our ...

Lately sociology of education has had to deal with complex challenges and the rise of new social phenomenon: the impact of migration processes and global fluxes in the different contexts of instruction, the strategies for social inclusion, the demand of citizenship expressed by the "new generations". Citizenship is in the current context multiform meaning on the social and individual and is tied both to the matter of the formation of the citizen in the rights and duties, and on the matter of the right to education and of recognizing the full dignity of everyone, the right of difference and diversity. The essential knot of citizenship is given by "equal opportunities". The contribution suggest the results of a research carried out -with the administration of a questionnaire -to Italian preadolescents and foreigners attending secondary schools of first degree in the Abruzzo Region (Italy). Different aspects concerning scholastic success, creation of social relations and building of citizenship and living together were taken into consideration. The data obtained from the answers to the questionnaire are analyzed with the tools of the multivariate statistics in order to have information on the latent sociological trends of the multi-cultural society in Italy.

The small tributaries to upstream Langat of Peninsular Malaysia play an important role to water quality in downstream. This study was carried out to investigate the indicator pollution and identify the potential sources of pollutants using multivariate chemometric techniques. Sampling campaign was conducted on monthly basis from January-June, 2015, duly interval dry and rainy seasons at six stations. Hierarchical cluster analysis (HACA) was employed on temporal and spatial dataset. Temporal dataset were grouped into two clusters on the basis of rainfall before collecting samples; the months of January, March and June formed one cluster and February, April and May appeared in the other. Spatial dataset were grouped into three clusters namely less polluted, medium polluted and polluted sites. Factor Analysis (FA) and Principal Component Analysis (PCA) were applied to identify the significant sources of pollutants, which resulted in five latent factors amounting to 73.0% of the total variance in data sets. Varifactors obtained from factor analysis indicate that the parameters responsible for water quality variations are related to physicochemical parameters and nutrients from both nonpoint and point sources. The nonpoint sources include plantation area, weathering of sedimentary rock and natural vegetation and point sources include mainly domestic wastewater. Thus, this study illustrates the water quality assessment, identification of pollution factors and temporal/spatial variations in water quality for the surface water of upstream tributaries to implement effective river water quality management with multivariate statistical techniques for analysis and interpretation of complex data sets.

The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for all the available information from multivariate time series. However, the inclusion of non-informative or non-significant variables creates estimation problems related to the 'curse of dimensionality'. To deal with this issue, direct causality measures using variable selection and dimension reduction techniques have been introduced. In this comparative work, the performance of an ensemble of bivariate and multivariate causality measures in the time domain is assessed, focusing on dimension reduction causality measures. In particular, different types of highdimensional coupled discrete systems are used (involving up to 100 variables) and the robustness of the causality measures to time series length and different noise types is examined. The results of the simulation study highlight the superiority of the dimension reduction measures, especially for high-dimensional systems.

In a recent work we proposed the corrected transfer entropy (CTE), which reduces the bias in the estimation of transfer entropy (TE), a measure of Granger causality for bivariate time series making use of the conditional mutual information. An extension of TE to account for the presence of other time series is the partial TE (PTE). Here, we propose the correction of PTE, termed Corrected PTE (CPTE), in a similar way to CTE: time shifted surrogates are used in order to quantify and correct the bias, and the estimation of the involved entropies of high-dimensional variables is made with the method of k-nearest neighbors. CPTE is evaluated on coupled stochastic systems with both linear and nonlinear interactions. Finally, we apply CPTE to economic data and investigate whether we can detect the direct causal effects among economic variables.

Measures of the direction and strength of the interdependence among time series from multivariate systems are evaluated based on their statistical significance and discrimination ability. The best-known measures estimating direct causal effects, both linear and nonlinear, are considered, i.e., conditional Granger causality index (CGCI), partial Granger causality index (PGCI), partial directed coherence (PDC), partial transfer entropy (PTE), partial symbolic transfer entropy (PSTE) and partial mutual information on mixed embedding (PMIME). The performance of the multivariate coupling measures is assessed on stochastic and chaotic simulated uncoupled and coupled dynamical systems for different settings of embedding dimension and time series length. The CGCI, PGCI and PDC seem to outperform the other causality measures in the case of the linearly coupled systems, while the PGCI is the most effective one when latent and exogenous variables are present. The PMIME outweighs all others in the case of nonlinear simulation systems.

In this paper, we introduce the partial symbolic transfer entropy (PSTE), an extension of the symbolic transfer entropy that accounts only for the direct causal effects among the components of a multivariate system. It is an information theoretic measure, and as such does not suffer from model mis-specification bias. The PSTE is defined on the ranks of vectors that are formed from the reconstructed vectors, instead of the original time series values. The statistical significance of * Corresponding author 1 PSTE is assessed by randomization test making use of surrogate time series. The PSTE is evaluated on multivariate time series of different types of coupled and uncoupled systems and compared with conditional Granger causality index (CGCI). It is shown that the PSTE is not affected by the existence of outliers, it is directly applicable to time series that are non-stationary in mean and in variance, and it is also not affected by data filtering. As a real application, the causal effects among three economic indexes are investigated. Computations of PSTE and CGCI on both the initial returns and the VAR filtered returns, and only of PSTE on the original indexes, showed consistency of the PSTE in estimating the causal effect.

The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for all the available information from multivariate time series. However, the inclusion of non-informative or non-significant variables creates estimation problems related to the 'curse of dimensionality'. To deal with this issue, direct causality measures using variable selection and dimension reduction techniques have been introduced. In this comparative work, the performance of an ensemble of bivariate and multivariate causality measures in the time domain is assessed, focusing on dimension reduction causality measures. In particular, different types of highdimensional coupled discrete systems are used (involving up to 100 variables) and the robustness of the causality measures to time series length and different noise types is examined. The results of the simulation study highlight the superiority of the dimension reduction measures, especially for high-dimensional systems.

In a recent work we proposed the corrected transfer entropy (CTE), which reduces the bias in the estimation of transfer entropy (TE), a measure of Granger causality for bivariate time series making use of the conditional mutual information. An extension of TE to account for the presence of other time series is the partial TE (PTE). Here, we propose the correction of PTE, termed Corrected PTE (CPTE), in a similar way to CTE: time shifted surrogates are used in order to quantify and correct the bias, and the estimation of the involved entropies of high-dimensional variables is made with the method of k-nearest neighbors. CPTE is evaluated on coupled stochastic systems with both linear and nonlinear interactions. Finally, we apply CPTE to economic data and investigate whether we can detect the direct causal effects among economic variables.

We propose an extension to multiple dimensions of the univariate index of agreement between PDFs used in climate studies. We also provide a set of high-performance programs targeted both to single and multi-core processors. They compute multivariate PDFs by means of kernels, the optimal bandwidth using smoothed bootstrap and the index of agreement between multidimensional PDFs. Their use is illustrated with two case-studies. The first one assesses the ability of seven global climate models to reproduce the seasonal cycle of zonally averaged temperature. The second case study analyzes the ability of an oceanic reanalysis to reproduce global sea surface temperature and sea surface height. Results show that the proposed methodology is robust to variations in the optimal bandwidth used. The technique is able to process multivariate datasets corresponding to different physical dimensions. The methodology is very sensitive to the existence of a bias in the model with respect to observations.

The present study deals with the assessment of surface water quality from an industrial-urban region located in northern Poland near to the city of Gdansk. Concentrations of thirteen chemicals including total polycyclic aromatic hydrocarbons (PAHs), halogenated volatile organic compounds (HVOCs) and major ions in the samples collected at five sampling points during six campaigns were used as variables throughout the study. The originality in the monitoring data treatment and interpretation was the combination of a traditional classification approach (self-organizing maps of Kohonen) with PAH diagnostic ratios expertise to achieve a reliable pollution source identification. Thus, sampling points affected by pollution from traffic (petroleum combustion products), from crude oil processing (petroleum release related compounds), and from phosphogypsum disposal site were properly discriminated. Additionally, it is shown that this original assessment approach can be useful in finding specific pollution source tracers.

Abstract: The present study deals with the application of self-organizing maps (SOM) of Kohonen for the classification of aerosol monitoring data sets from two sampling points (Arnoldstein and Unterloibach) located close to the border between Austria and Slovenia. ...

Abstract. The present communication deals with the application of several chemometrical methods (cluster and principal components analysis, source apportioning on absolute principal components scores) to an aerosol data collection from Arnoldstein, Austria. It is convincingly shown ...

The present communication deals with the application of several chemometrical methods (cluster and principal components analysis, source apportioning on absolute principal components scores) to an aerosol data collection from Arnoldstein, Austria. It is convincingly shown that six latent factors explaining almost 80 % of the total variance are responsible for the data structure and are conditionally identified as "fertilizer", secondary emission", "lead smelter", "traffic", "salt" and "soil dust". Further more, the contribution of each identified source to the formation of the particle total mass and chemical compounds total concentration is calculated. Thus, a reliable assessment of the air quality in the region of observation is achieved. The apportioning models obtained are checked for adequateness and validated. It is explained why for sodium and magnesium non-adequate models are obtained. The latent factor contribution models can be further used for risk assessment and respective decision making. Additionally, it is commented why chemometrics could be successfully applied as sustainability metrics in various aspects of interpretation of the state of "sustainable development"

Let (X 1 , . . . , Xn) be a multivariate normal random vector with any mean vector, variances equal to 1 and covariances equal and positive. Turner and Whitehead established that the largest order statistic max{X 1 , . . . , Xn} is less than the standard normal random variable in the dispersive order. In this paper, we give a new and straightforward proof for this result. Several possible extensions of this result are also discussed.

The purpose of this paper is to investigate conditions on the underlying distributions and the parameters, on which generalized order statistics are based, to establish the Shaked-Shanthikumar multivariate dispersive ordering of normalized and unnormalized spacings of generalized order statistics from one sample and two samples. Several probability inequalities concerning spacings of generalized order statistics are also given.

The authors provide sufficient and/or necessary conditions for classifying multivariate elliptical random vectors according to the convex ordering and the increasing convex ordering. Their results generalize the corresponding ones for multivariate normal random vectors in the literature.

The widely distributed pollutant tributyltin (TBT) was analyzed in different environmental samples (waters and sediments) combining preconcentration on a nylon membrane, excitation-emission fluorescence matrices directly measured over the membrane and second-order multivariate calibration. The latter was implemented using unfolded partial least-squares with residual bilinearization (U-PLS/RBL), a flexible algorithm achieving second-order advantage, even under severe spectral overlapping among sample components. Matrix-specific calibrations were required to overcome matrix effects, resulting in good analytical performance. TBT was determined in the concentration ranges 0.043-1.42 ng Sn mL -1 in water and 24-400 μg Sn kg -1 in sediments, with adequate detection limits in the range 0.03-0.15 ng Sn mL -1 .

The widely distributed pollutant tributyltin (TBT) was analyzed in different environmental samples (waters and sediments) combining preconcentration on a nylon membrane, excitation-emission fluorescence matrices directly measured over the membrane and second-order multivariate calibration. The latter was implemented using unfolded partial least-squares with residual bilinearization (U-PLS/RBL), a flexible algorithm achieving second-order advantage, even under severe spectral overlapping among sample components. Matrix-specific calibrations were required to overcome matrix effects, resulting in good analytical performance. TBT was determined in the concentration ranges 0.043-1.42 ng Sn mL -1 in water and 24-400 μg Sn kg -1 in sediments, with adequate detection limits in the range 0.03-0.15 ng Sn mL -1 .

This work presents a non-sophisticated approach for the trace determination of tributyltin, the most toxic organotin species, in very interfering environments, combining fluorescence measurements of its morin complex and the selectivity of second-order chemometric algorithms. The power of MCR-ALS (multivariate curve resolution/alternating leastsquares) to quantify tributyltin through fluorescence excitation-emission matrices in the presence of its main degradation products and of a pool of additional twenty-three metal ions is demonstrated. The applied algorithm successfully faces the challenge of solving the strong overlapping among the spectra of the several sample components. The proposed methodology was applied to tap, river, lagoon and seawater spiked samples, obtaining satisfactory results at ng L -1 levels, after a pre-concentration step on a C18 membrane, demonstrating the analytical potential of the proposed methodology.

Drinking water quality is a major concern, especially in African countries. This manuscript aims to analyze the chemical composition of Lioua’s groundwater in order to determine the geological processes influencing the chemical elements' composition and origin. Therefore, chemometrics techniques such as multivariate statistical analysis (MSA) and time series methods (TSM) are used. Indeed, MSA includes a component analysis (PCA) and a cluster analysis (CA), while au-tocorrelation analysis (AA) supplemented by simple spectral density analysis (SDA) is used for TMS. PCA displays three main factors explaining a total variance (TV) of 85.01 %. Factors 1, 2, and 3 are 68.72%, 11.96%, and 8.89 % of TV, respectively. In the CA, three groups were controlled by TDS and EC. G1 reveals a close association between SO42−, K+, Ca2+, and TDS; G2 reveals a close association between Na+, Cl−, Mg2+, and EC; G3 shows the dissociation of bicarbonates HCO3− and NO3− from other chemical elements. AA ...

The aim of this study was to quantify genetic divergence among cowpea bean genotypes by means of Integrated Multivariate Analysis, with the purpose of assisting selection of parents for development of new cultivars. A randomized block experimental design was used with 32 treatments and 4 replications. There is agreement among the multivariate techniques applied in clustering of the genotypes. The genotypes show genetic variability, exhibiting potential for use in breeding programs. The crosses carried out between the genotypes MNC02-675F-9-3 and MNC03-737F-5-10 with the genotypes MNC03-737F-5-11, MNC03-737F-5-1, MNC03-725F-3 and MNC03-737F-5-9 may lead to obtaining segregating progenies with high yield potential and an increase in the probability of select superior genotypes in the segregating generations.

This study aimed to evaluate the adaptability and phenotypic stability of cowpea genotypes using a nonlinear regression analysis and multivariate analysis. Experiments were performed at four sites in Brazil using a randomized blocks design with 20 treatments and four replications. The adaptability and stability of genotypes were evaluated by Toler nonlinear regression and genotype plus genotype × environment (GGE) biplot methodologies. Most of the genotypes revealed linear response patterns, with no differences regarding the favorable and unfavorable environments. Regarding the genotype classification for stability and adaptability, the Toler and GGE biplot methodologies are congruent. Genotypes MNC99-537F-4, MNC00-561G-6, MNC99542F-5, and Patativa have high overall adaptability and adequate yield. Therefore, they should be recommended for cultivation in the tested environments. Genotypes closer to the ideotype by the GGE biplot method are considered doubly desirable by the nonlinea...

Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of these problems is high dimensions. We present here a survey on classical methods developed in multivariate approximation theory, which are known to work very well for moderate dimensions and which have potential for applications in really high dimensions. The theory of hyperbolic cross approximation and related theory of functions with mixed smoothness are under detailed study for more than 50 years. It is now well understood that this theory is important both for theoretical study and for practical applications. It is also understood that both theoretical analysis and construction of practical algorithms are very difficult problems. This explains why many fundamental problems in this area are still unsolved. Only a few survey papers and monographs on the topic are published. This and recently discovered deep connections between the hyperbolic cross approximation (and related sparse grids) and other areas of mathematics such as probability, discrepancy, and numerical integration motivated us to write this survey. We try to put emphases on the development of ideas and methods rather than list all the known results in the area. We formulate many problems, which, to our knowledge, are open problems. We also include some very recent results on the topic, which sometimes highlight new interesting directions of research. We hope that this survey will stimulate further active research in this fascinating and challenging area of approximation theory and numerical analysis.

RESUMEN: El pronóstico de la demanda energética diaria tiene gran importancia para las entidades reguladoras de la energía en Colombia. Es cada vez más necesario usar técnicas innovadoras para pronosticar este tipo de variables. En este trabajo se presenta una aproximación a un pronóstico bayesiano, basado en una técnica de elicitación que permite obtener información de expertos y su integración a una única distribución de probabilidad, midiendo el indicador de error absoluto medio porcentual (MAPE) sobre los pronósticos realizados. Se encontró que el uso del método puede ser enriquecedor para innovar frente a la manera de hacer el pronóstico energético y lograr niveles de acierto adecuados, sin contar con ningún dato histórico.

This study evaluates the effectiveness of machine learning-based time series models as alternatives to short-term traditional decline curve models for estimating hydrocarbon reserves. To accurately estimate the hydrocarbons that can be economically recovered from a field, area, or region, the predicted quantities should closely match the actual observed quantities within the same period. In this study, two models were compared based on their Root Mean Square Deviation (RMSE) to solve the decline curve technique of reserve estimation – the traditional exponential model and the time series ML-based Recurrent Neural Network's Long Short-Term Memory (LSTM) model. The study results showed that the LSTM model outperformed the traditional exponential model, with an RMSE of 80.12 compared to 107.41 for reservoir K3, 30.24 to 141.52 for reservoir VII, and 80.56 to 169.81 for reservoir K5. These RMSE values indicate that the LSTM model had a better fit to observed data and thus had better goodness. Therefore, LSTMs serve as improved alternatives to short-term traditional decline curve models.

Periodic (covariance) Stationarity conditions for multivariate periodic autoregressive moving average (PARMA) processes are investigated. It follows from a previous work that a necessary and sufficient condition for the periodic Stationarity of a multivariate periodic process is the (covariance) Stationarity of the “lumped” vector process which contains the periodic vectors as its elements. It is shown that for univariate and multivariate PARMA processes, even with periodically varying orders, the lumped process is a multivariate autoregressive moving average ARMA process, the Stationarity conditions of which are readily available. Periodic Stationarity conditions for the multivariate PARMA (1, 1) process are explicitly obtained, which apply for all PARMA (1, q) processes. It is shown that the periodic Stationarity of a periodic process always implies the Stationarity of the aggregated process, the sum of the periodic vectors. The reverse is yet to be proved or disproved. However, i...

Certain aspects of data generation are studied through multivariate autoregressive (AR) models. The main emphasis is on the preservation of certain desired moments and the effect of initial values on these moments. The problem of preservation of moments is approached in a nontraditional way by starting with the initial values. For this purpose, general AR processes with a random start and with time-varying parameters are introduced to lay a foundation for the analysis of all types of AR processes, including the periodic cases. It is shown that an AR process with a random start and with parameters obtained from the moment equations is capable of generating jointly multivariate normal vectors with any specified means and covariance matrices, and with any specified autocovariance matrices up to a given lag. With a random start, there is no transition period involved for achieving these moments. A simple solution is proposed for matrix equations of the form BB T = A which appear in the moment equations. The aggregation properties of general AR process are also studied. A more detailed analysis is given for the two-period first-order periodic autoregressive model, PAR 2 ( 1 ). For the PAR2(I) process with a random start and with parameters obtained from the moment equations, it is shown that the autocovariance function depends only on the period and the lag, and therefore the process is periodic (covariance) stationary. The PAR2(I) process with a fixed start is also studied. It is shown that the moments of this process depend on the absolute time, in addition to the period and the lag, and therefore the process is not periodic stationary. This dependence diminishes with time, and periodic stationarity is realized if the AR parameters satisfy certain conditions. In that case, the PARt(I) process with a fixed start converges to that with a random start, but only after a certain transition period. This proves the superiority of a random start over a fixed start.

An empirical model for prediction of microalgal growth in outdoor photobioreactors cultivation, using Principal Component Analysis (PCA) and Partial Least Squares (PLS) regression method, is implemented. Experimental data of biomass production were collected over 1 year of operation of a bubble column prototype, monitoring light and temperature and changing cultivation's conditions. PCA isolates 2 Principal Components that explain 80% of the variance and are associated with Environmental Conditions and Cultivation Conditions. Moreover, the PLS regression model showed positive results in term of responses (R 2 =0.84) and residuals, following the experimental trends of outputs as specific growth rate (μ(d -1 )) and productivity calculated at C max (P max (gL -1 d -1 )), giving also good prediction results in its validation test. This method could be easily used for other purpose, by changing the input values of the specific cultivation used (including CO 2 uptake or wastewater dilution ratio in the culture medium), obtaining as outputs the desired variables (lipid production rate, etc.).

A train derailment on February 3, 2023, in East Palestine, Ohio, USA, spilled hazardous industrial organic chemicals (vinyl chloride, 2-butoxyethanol, 2-ethylhexyl acrylate, isobutylene, butyl acrylate, and benzene) into a small stream (Sulfur Run) in a sub-watershed of the Ohio River, killing thousands of fish and other aquatic organisms. Benthic diatoms were sampled 92 days after the spill, on May 17, as a surrogate to assess water quality and evaluate the ecological resilience of diatoms to an episodic organic chemical spill. Diatom community metrics included NMS ordination, MNPP statistics, predominant diatoms, diatom water quality indices, trophic state, and diversity. Despite 92 days of recovery and “stream clean-up” measures, all metrics of diatom community structure in Sulfur Run, the polluted stream, and Leslie Run downstream from the Sulfur Run confluence remained statistically significantly different than in Leslie Run above Sulfur Run. Although the differences were relatively subtle, their high significance and range across a spectrum of community metrics lend credence to the chemical spill causing alterations in diatom community structure. The study demonstrates the value of diatoms in assessing pollution impact and confirms their potential for monitoring water quality restoration from episodic hazardous organic chemical spills. 

The purpose of this study is to simulate the behavior of households in choosing their homes. A two-phase model is proposed. During the first phase, the housing preferences of the locating family are determined. In the second phase, the search process by which the household picks a location possessing these characteristics is simulated. A number of multivariate statistical techniques are employed in the partial calibration of the model.

A reliable and realistic subsurface resource spatial modeling is a common and critical task for geosciences projects (mining, petroleum and environmental) because the models are then integrated with downstream processes to evaluate process performance. Coregionalized variables considered in resource modeling are often related through compositional constraints and complex dependence relationships. Satisfying these constraints and relationships in spatial modeling is a practical requirement to obtain accurate predictions of mineral resources in the subsurface. This paper presents a multistage method that addresses these issues and allows the multivariate simulation of cross-correlated variables with complex features directly on block-support, conditionally to the information of drill hole data at a quasi-point support. At a first stage, a chained transformation is used for removal multivariate complexities and decorrelation of the variables. Then, this chained transformation is adapted within the direct block-support sequential Gaussian simulation algorithm. The back-transformation of the chained transformation reintroduces complex features and correlations. A proof of the concept using a data set from the Gole-Gohar iron ore deposit in Iran demonstrates the performance of the proposed approach, the results of which are then compared against a common modeling approach.

Identifying and quantifying grade uncertainty is important in mineral resource classification from an economic perspective. Conditional simulation techniques can be used to this end. In multi-element deposits, for which spatial correlations are important, techniques such as principal component analysis and minimum/maximum auto-correlation factors can be used to transform the multivariate simulation problem into a series of univariate problems. In this study, a methodology is presented for classifying mineral resources and for assessing the uncertainty in grade-tonnage curves, with an application to a porphyry copper deposit located in the central part of Iran with three correlated variables (grades of Cu, Mo, and Ag). The resources are classified based on the simulated copper grades, considering the so-called 15 % rule. This means that the estimated grade, tonnage, and metal content in a production period will have at most 15 % error at 90 % confidence level.

This paper describes a general framework of incorporating magnetic data as prior information in the modeling of an iron deposit based on sparse drilling boreholes. Since multivariate kriging of a sparse pattern of drilling yields lower uncertainty in mineral deposit modeling, a model of magnetic susceptibility as a second variable which has an acceptable level of correlation with the first variable, iron, is used to make a model of iron grade. Before applying an inversion technique to recover a 3D model of magnetic susceptibility, the normalized full gradient (NFG) approach is used to generate an approximate visualization of probable magnetic anomaly. Based on the NFG result, we have acquired appropriate dimensions of composites to apply the geophysical inversion method. The subsurface of the desired area of the magnetic anomaly is divided into a mesh with a large number of rectangular prisms (composites) with unknown susceptibilities. The recovered magnetic susceptibility model which has a correlation equal to 0.543 with the iron grade is used as a second variable in order to apply a multivariate set of kriging equations. The collocated cokriging method as a modified version of the cokriging system is used to interpolate the iron grade based on a model of magnetic susceptibility. This method has been applied to a real case study in Zanjan Province of Iran, showing its effectiveness when we encounter with such lack of drilled boreholes in the study area.

The present study aims to enhance the morpho-phsyiological traits, effective utilization of phosphorus and potassium, nutritional quality, and maize productivity using combinations of inorganic and organic amendments in alkaline calcareous soil. The inorganic fertilizers were applied as control (PK 0 ), recommended PK (PK R ), and 75% of PK R (PK R75 ) either alone or in combination with different composts; university compost (UC), NIAB compost (NC) and vermicompost (VC), and organic acids; citric acid (CA) and oxalic acid (OA). The results indicated a significant effect of treatments on morpho-physiological and biochemical attributes of maize during crop growth. Stomatal conductance (g s ) and transpiration rate (E) increased up to 93% and 139%, respectively, over control when PK R75 was applied with NC + CA. While, photosynthesis and chlorophyll contents were maximum at PK R75 along with UC + CA. The PK R along with UC + CA increased grain yield (108%) and biological yield (98%) over control. Moreover, the respective treatment increased P content in straw and grain up to 100% and 122% over control (P content: 0.08 and 0.18%), respectively, while 14.3 and 21.2% higher over PK R treatment (0.14 and 0.33%), respectively. The maximum K accumulation in maize grains was noted with PK R combined with NC + CA which was further confirmed with principle component analysis. The results clearly suggest integrated use of mineral PK fertilizers along with composts and organic acids could be an effective strategy to increase P and K supply, and enhance qualitative and quantitative parameters of maize grown on calcareous soil.

The multivariate estimation problems arise if the observations are available for several related variables of interest. The multivariate time series may be found in many fields of application such as economics, meteorology and utilities. The current study has three main objectives. The first one is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average processes. The second objective is to investigate the numerical efficiency of the proposed technique in solving the estimation problems by conducting a wide simulation study. The last objective is to study the sensitivity of the numerical efficiency with respect to the parameters values and time series length. The results show that the proposed technique succeeded in estimating the parameters of the multivariate moving average processes. The results are not sensitive to the changes in parameter values or in time series length. INDEX TERMS Multivariate time series, multivariate (vector) moving average processes, Bayesian estimation, matrix normal-Wishart prior, Jeffreys' prior.

ABSTRACT: This study measured the effect of the association between agronomic traits related to the yield of canola grains grown at different sowing dates through path analysis. Another objective was to obtain a method to predict the oil content in the grains, fitting a multivariate model through near-infrared (NIR) spectroscopy analysis. The experiment was conducted in the field using a randomized block design in plots subdivided by time, with four plots (sowing dates), six subplots (canola hybrids), and four replicates. In each hybrid, phenological observations were performed, and the grain yield was determined. The data were subjected to analysis of variance in the R environment using the F test at 5% probability. The oil content in the grains was determined by the traditional chemical method, and based on the NIR spectral signature of the grain samples, partial least squares regression (PLS-R) was established to estimate the oil content in the canola grains. The sowing dates inf...

The effect of sample movement on spectral response during fiber probe diffuse reflectance near-infrared spectrometry (NIR) sampling was characterized. This is of central importance in Process Analytical Chemistry (PAC) and Process Analytical Technology (PAT). The incitement to this study was the observation of spectral artifacts during measurements of powder samples in process streams when using a mechanically scanning spectrometer. Artifacts appeared as momentary changes in the spectral response during acquisition of a scan. These transitions emanate from continuous replacement of the sample subfraction seen by the probe and are typical for turbid media where sample properties may vary locally with respect to scattering and/or absorption. The impact on qualitative and quantitative analysis using chemometric methods such as principal component analysis (PCA) and partial least squares (PLS) regression was evaluated through experimental and theoretical simulations. It was generally found that spectra with the smallest residuals after projection onto the models came from non-moving samples or samples moving only slowly. It is shown that the magnitude of the spectral residuals is directly connected to the effective sample size, which relates both to sample speed as well as to the sample area presented to the probe. Implications for in-line/on-line process analysis of solids are discussed.