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Energy and agricultural commodities and markets have been examined extensively, albeit separately, for a number of years. In the energy literature, the returns, volatility and volatility spillovers (namely, the delayed effect of a returns shock in one asset on the subsequent volatility or covolatility in another asset), among alternative energy commodities, such as oil, gasoline and ethanol across different markets, have been analysed using a variety of univariate and multivariate models, estimation techniques, data sets, and time frequencies. A similar comment applies to the separate theoretical and empirical analysis of a wide range of agricultural commodities and markets. Given the recent interest and emphasis in bio-fuels and green energy, especially bio-ethanol, which is derived from a range of agricultural products, it is not surprising that there is a topical and developing literature on the spillovers between energy and agricultural markets. Modelling and testing spillovers between the energy and agricultural markets has typically been based on estimating multivariate conditional volatility models, specifically the Baba, Engle, Kraft, and Kroner (BEKK) and dynamic conditional correlation (DCC) models. A serious technical deficiency is that the Quasi-Maximum Likelihood Estimates (QMLE) of a Full BEKK matrix, which is typically estimated in examining volatility spillover effects, has no asymptotic properties, except by assumption, so that no valid statistical test of volatility spillovers is possible. Some papers in the literature have used the DCC model to test for volatility spillovers. However, it is well known in the financial econometrics literature that the DCC model has no regularity conditions, and that the QMLE of the parameters of DCC has no asymptotic properties, so that there is no valid statistical testing of volatility spillovers. The purpose of the paper is to evaluate the theory and practice in testing for volatility spillovers between energy and agricultural markets using the multivariate Full BEKK and DCC models, and to make recommendations as to how such spillovers might be tested using valid statistical techniques. Three new definitions of volatility and covolatility spillovers are given, and the different models used in empirical applications are evaluated in terms of the new definitions and statistical criteria.

•BrainStat is a toolbox for the statistical analysis and context decoding of neuroimaging data.•It implements univariate and multivariate linear models and interfaces with the BigBrain Atlas, Allen Human Brain Atlas and Nimare databases.•BrainStat handles surface, volume, and parcel level data formats, and provides a series of interactive visualization functions.•The toolbox has been implemented in Python and MATLAB.•BrainStat is openly available at https://github.com/MICA-MNI/BrainStat, and documented on https://brainstat.readthedocs.io/. Analysis and interpretation of neuroimaging datasets has become a multidisciplinary endeavor, relying not only on statistical methods, but increasingly on associations with respect to other brain-derived features such as gene expression, histological data, and functional as well as cognitive architectures. Here, we introduce BrainStat - a toolbox for (i) univariate and multivariate linear models in volumetric and surface-based brain imaging datasets, and (ii) multidomain feature association of results with respect to spatial maps of post-mortem gene expression and histology, task-based fMRI meta-analysis, as well as resting-state fMRI motifs across several common surface templates. The combination of statistics and feature associations into a turnkey toolbox streamlines analytical processes and accelerates cross-modal research. The toolbox is implemented in both Python and MATLAB, two widely used programming languages in the neuroimaging and neuroinformatics communities. BrainStat is openly available and complemented by an expandable documentation.

Beyond the challenge of keeping up to date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. Here, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the {performance} package of the easystats ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude by reviewing the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. A preprint of this paper is available at: 10.31234/osf.io/bu6nt.

The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain–computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses. •Backward models cannot be interpreted in terms of the studied brain processes.•This affects common classification and regression techniques like SVM and LASSO.•The problem does not occur for forward models (e.g., GLMs).•We propose a way to transform linear backward models into linear forward models.•This makes backward models interpretable in terms of the studied brain processes.

In air pollution forecasting, handling missing data is a significant challenge and a crucial task. In this study, we aim to forecast air pollutants in Eskişehir, Türkiye, presenting a new stacking-based imputation method (S-UImpute) to address the missing data problem. To this end, we apply three widely used forecasting methods: Autoregressive Integrated Moving Average (ARIMA), Support Vector Regression (SVR), and Long Short-Term Memory (LSTM), and eight commonly used missing data imputation methods (ZeroFill, MeanFill, MedianFill, ForwardFill, BackwardFill, Interpolation, Kalman filtering, and SVR-based imputation) for benchmarking on univariate time series data. We collect comprehensive datasets, which have various proportions of missing data, from five air quality monitoring stations in Eskişehir. To evaluate the performance of the proposed method at high missing data rates, we generated artificial missing data on top of the existing missing data at rates of 10%, 15%, 20%, and 25%. The S-UImpute + LSTM model mostly outperformed the other imputation method and forecasting model combinations in terms of modified symmetric Mean Absolute Percentage Error (msMAPE). Moreover, S-UImpute provided more consistent and generalized performance compared with other imputation methods. As LSTM produced the most accurate forecasting, it is used to statistically compare imputation methods and determine the best-performing one. According to the Friedman statistical test, there is a statistically significant difference between the missing data imputation methods. Following this, the Wilcoxon signed-rank test applied afterwards indicates that the best method is S-UImpute.

Metabolomics is a dynamic tool for elucidating biochemical changes in human health and disease. Metabolic profiles provide a close insight into physiological states and are highly volatile to genetic and environmental perturbations. Variation in metabolic profiles can inform mechanisms of pathology, providing potential biomarkers for diagnosis and assessment of the risk of contracting a disease. With the advancement of high-throughput technologies, large-scale metabolomics data sources have become abundant. As such, careful statistical analysis of intricate metabolomics data is essential for deriving relevant and robust results that can be deployed in real-life clinical settings. Multiple tools have been developed for both data analysis and interpretations. In this review, we survey statistical approaches and corresponding statistical tools that are available for discovery of biomarkers using metabolomics.

Metabolomics experiments usually result in a large quantity of data. Univariate and multivariate analysis techniques are routinely used to extract relevant information from the data with the aim of providing biological knowledge on the problem studied. Despite the fact that statistical tools like the t test, analysis of variance, principal component analysis, and partial least squares discriminant analysis constitute the backbone of the statistical part of the vast majority of metabolomics papers, it seems that many basic but rather fundamental questions are still often asked, like: Why do the results of univariate and multivariate analyses differ? Why apply univariate methods if you have already applied a multivariate method? Why if I do not see something univariately I see something multivariately? In the present paper we address some aspects of univariate and multivariate analysis, with the scope of clarifying in simple terms the main differences between the two approaches. Applications of the t test, analysis of variance, principal component analysis and partial least squares discriminant analysis will be shown on both real and simulated metabolomics data examples to provide an overview on fundamental aspects of univariate and multivariate methods.

Data in the Internet of Things (IoT) domain may be missing due to connectivity errors, environmental extremes, sensor malfunctions, and human errors. Despite the many approaches for imputing missing values, the most significant difficulty in terms of imputation precision or compute complexity for larger missing sub-sequences in uni-variate series is still being explored. This work introduced IMD-MP (Imputation of Missing Data using Matrix Profile), a new technique that improves imputation accuracy for big data analysis in IoT applications based on spatial-temporal correlations using a novel distance metric Matrix Profile Distance (MPD). Our method preserves spatial correlation by grouping the sensors present in the network (using grouping algorithm-GA) to impute the missing data of the failed sensor node. After grouping, similar sensor nodes to the failed sensor node are identified using the Node Similarity Algorithm (NSF). From its similar sensor data, a certain number of sub-sequences that are most similar to the one preceding the failed node's missing values are gathered. These sub-sequences heights are optimized to ensure temporal correlation in the imputed data. To find the optimal imputation sequence, the current research uses MPD and similarity scores. Numerical findings using sensor data from real-time environmental mon-itoring and Intel data sets demonstrate the algorithm's effectiveness compared to other benchmarks.

Neuroscience has a long history of inferring brain function by examining the relationship between brain injury and subsequent behavioral impairments. The primary advantage of this method over correlative methods is that it can tell us if a certain brain region is necessary for a given cognitive function. In addition, lesion-based analyses provide unique insights into clinical deficits. In the last decade, statistical voxel-based lesion behavior mapping (VLBM) emerged as a powerful method for understanding the architecture of the human brain. This review illustrates how VLBM improves our knowledge of functional brain architecture, as well as how it is inherently limited by its mass-univariate approach. A wide array of recently developed methods appear to supplement traditional VLBM. This paper provides an overview of these new methods, including the use of specialized imaging modalities, the combination of structural imaging with normative connectome data, as well as multivariate analyses of structural imaging data. We see these new methods as complementing rather than replacing traditional VLBM, providing synergistic tools to answer related questions. Finally, we discuss the potential for these methods to become established in cognitive neuroscience and in clinical applications.

Background: This study intends to identify the best model for predicting the incidence of hand, foot and mouth disease (HFMD) in Ningbo by comparing Autoregressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM) models combined and uncombined with exogenous meteorological variables. Methods: The data of daily HFMD incidence in Ningbo from January 2014 to November 2017 were set as the training set, and the data of December 2017 were set as the test set. ARIMA and LSTM models combined and uncombined with exogenous meteorological variables were adopted to fit the daily incidence of HFMD by using the data of the training set. The forecasting performances of the four fitted models were verified by using the data of the test set. Root mean square error (RMSE) was selected as the main measure to evaluate the performance of the models. Results: The RMSE for multivariate LSTM, univariate LSTM, ARIMA and ARIMAX (Autoregressive Integrated Moving Average Model with Exogenous Input Variables) was 10.78, 11.20, 12.43 and 14.73, respectively. The LSTM model with exogenous meteorological variables has the best performance among the four models and meteorological variables can increase the prediction accuracy of LSTM model. For the ARIMA model, exogenous meteorological variables did not increase the prediction accuracy but became the interference factor of the model. Conclusions: Multivariate LSTM is the best among the four models to fit the daily incidence of HFMD in Ningbo. It can provide a scientific method to build the HFMD early warning system and the methodology can also be applied to other communicable diseases.