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Karl Pearson, founder of modern statistics, came to this field by way of passionate early studies of philosophy and cultural history as well as ether physics and graphical geometry. His faith in science grew out of a deeply moral quest, reflected also in his socialism and his efforts to find a new basis for relations between men and women. This biography recounts Pearson's extraordinary intellectual adventure and sheds new light on the inner life of science. Theodore Porter's intensely personal portrait of Pearson extends from religious crisis and sexual tensions to metaphysical and even mathematical anxieties. Pearson sought to reconcile reason with enthusiasm and to achieve the impersonal perspective of science without sacrificing complex individuality. Even as he longed to experience nature directly and intimately, he identified science with renunciation and positivistic detachment. Porter finds a turning point in Pearson's career, where his humanistic interests gave way to statistical ones, in hisGrammar of Science(1892), in which he attempted to establish scientific method as the moral educational basis for a refashioned culture. In this original and engaging book, a leading historian of modern science investigates the interior experience of one man's scientific life while placing it in a rich tapestry of social, political, and intellectual movements.

Photovoltaic power has great volatility and intermittency due to environmental factors. Forecasting photovoltaic power is of great significance to ensure the safe and economical operation of distribution network. This paper proposes a novel approach to forecast short-term photovoltaic power based on a gated recurrent unit (GRU) network. Firstly, the Pearson coefficient is used to extract the main features that affect photovoltaic power output at the next moment, and qualitatively analyze the relationship between the historical photovoltaic power and the future photovoltaic power output. Secondly, the K-means method is utilized to divide training sets into several groups based on the similarities of each feature, and then GRU network training is applied to each group. The output of each GRU network is averaged to obtain the photovoltaic power output at the next moment. The case study shows that the proposed approach can effectively consider the influence of features and historical photovoltaic power on the future photovoltaic power output, and has higher accuracy than the traditional methods.

Internet of Things (IoT) integration in healthcare improves patient care while also making healthcare delivery systems more effective and economical. To fully realize the advantages of IoT in healthcare, it is imperative to overcome issues with data security, interoperability, and ethical considerations. IoT sensors periodically measure the health-related data of the patients and share it with a server for further evaluation. At the server, different machine learning algorithms are applied which help in early diagnosis of diseases and issue alerts in case vital signs are out of the normal range. Different cyber attacks can be launched on IoT devices which can result in compromised security and privacy of applications such as health care. In this paper, we utilize the publicly available Canadian Institute for Cybersecurity (CIC) IoT dataset to model machine learning techniques for efficient detection of anomalous network traffic. The dataset consists of 33 types of IoT attacks which are divided into 7 main categories. In the current study, the dataset is pre-processed, and a balanced representation of classes is used in generating a non-biased supervised (Random Forest, Adaptive Boosting, Logistic Regression, Perceptron, Deep Neural Network) machine learning models. These models are analyzed further by eliminating highly correlated features, reducing dimensionality, minimizing overfitting, and speeding up training times. Random Forest was found to perform optimally across binary and multiclass classification of IoT Attacks with an approximate accuracy of 99.55% under both reduced and all feature space. This improvement was complimented by a reduction in computational response time which is essential for real-time attack detection and response.

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson′s correlation coefficient (r). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman′s rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation (y = a + bx), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.

In the case of a smart home, the ability to recognize daily activities depends primarily on the strategy used for selecting the appropriate features related to these activities. To achieve the goal, this paper presents a daily activity feature selection strategy based on the Pearson Correlation Coefficient. Firstly, a daily activity feature is viewed as a vector in Pearson Correlation Coefficient formula. Secondly, the relation degree between daily activity features is obtained according to weighted Pearson Correlation Coefficient formula. At last, redundant features are removed by the relation degree between daily activity features. Two distinct datasets are adopted to mitigate the effects of the coupling of the dataset used and the sensor configuration. Three different machine learning techniques are employed to evaluate the performance of the proposed approach in activity recognition. The experiment results show that the proposed approach yields higher recognition rates and achieves average improvement F-measures of 1.56% and 2.7%, respectively.

The correlation coefficient is a statistical measure often used in studies to show an association between variables or to look at the agreement between two methods. In this paper, we will discuss not only the basics of the correlation coefficient, such as its assumptions and how it is interpreted, but also important limitations when using the correlation coefficient, such as its assumption of a linear association and its sensitivity to the range of observations. We will also discuss why the coefficient is invalid when used to assess agreement of two methods aiming to measure a certain value, and discuss better alternatives, such as the intraclass coefficient and Bland–Altman’s limits of agreement. The concepts discussed in this paper are supported with examples from literature in the field of nephrology.

The classical Pearson-Fisher chi-square test is a general approach to testing goodness-of-fit for univariate data. There is a considerable amount of discussion on how to effectively apply this test to practical goodness-of-fit problems in the literature. However, the choice of optimal grouping intervals in constructing the chi-square statistic still remains arguable and uncertain. Based on the statistical principle of defining the mean-square-error representative points, we propose to employ the statistical representative points to construct the Pearson-Fisher chi-square test. We carry out an extensive Monte Carlo study on the performance of the new-type of chi-square test by focusing on some location-scale distributions. It shows that our construction of the chi-square test outperforms the traditional construction of the same test by using equiprobable points for the grouping intervals in the sense of type I error control and power against some general alternative distributions.

The current era is the era of big data and 5G. The network security data in the network is different from the past, and the network security data is growing exponentially. As an important line of defense for network security, intrusion detection technology can efficiently detect and process massive amounts of security data has become an important factor restricting its development. The feature selection method of intrusion detection data directly affects the efficiency of intrusion detection. Therefore, this paper proposes a feature selection algorithm based on pearson correlation coefficient, which performs feature specification on many features, which greatly reduces the amount of security data that needs to be processed, and effectively reduces the dimensionality of the data to increase the intrusion. Detection efficiency.

In the background of all human thinking—acting and reacting are sets of connections between different neurons or groups of neurons. We studied and evaluated these connections using electroencephalography (EEG) brain signals. In this paper, we propose the use of the complex Pearson correlation coefficient (CPCC), which provides information on connectivity with and without consideration of the volume conduction effect. Although the Pearson correlation coefficient is a widely accepted measure of the statistical relationships between random variables and the relationships between signals, it is not being used for EEG data analysis. Its meaning for EEG is not straightforward and rarely well understood. In this work, we compare it to the most commonly used undirected connectivity analysis methods, which are phase locking value (PLV) and weighted phase lag index (wPLI). First, the relationship between the measures is shown analytically. Then, it is illustrated by a practical comparison using synthetic and real EEG data. The relationships between the observed connectivity measures are described in terms of the correlation values between them, which are, for the absolute values of CPCC and PLV, not lower that 0.97, and for the imaginary component of CPCC and wPLI—not lower than 0.92, for all observed frequency bands. Results show that the CPCC includes information of both other measures balanced in a single complex-numbered index.