Graphical Methods in Computational Statistics

Graphical methods have played a central role in the development of statistical theory and practice.This presentation briefly reviews some of the highlights in the historical development of statistical graphics, and gives a simple taxonomy which can be used to characterize the current use of graphical methods.This taxonomy is used to describe the evolution of the use of graphics in some major statistical and related scientific journals.Some recent advances in the use of graphical methods for statistical analysis are reviewed, and several graphical methods for the statistical presentation of data are illustrated, including the use of multi-colored maps.

This chapter focuses on basic graphical and numerical methods for data description and exploration. Data visualization is used to represent the data using graphical methods. It is one of the most effective and intuitive ways to explore the important patterns in the data such as data distribution, relationship among variables, surprising clusters, and outliers. The chapter discusses some of the most basic and useful types of graphical methods or data plots for industrial data analytics applications. It introduces commonly used plots that show some aspects of how multiple variables are related to each other. The pairwise relationship of multiple numerical variables can be visualized simultaneously by using a matrix of scatter plots. Data visualization is an effective and intuitive representation of the qualitative features of the data. The chapter also introduces common summary statistics for univariate and multivariate data.

The graphical display based on a raster scan is widely applied in the technique of CAD, CAM and management, etc. It's advantage are high resolution and good quality in graphic display, low cost, convenience and flexibility in use. Hence it is rapidly developed. This article mainly discusses graphical display method, principles and various software techniques, such as control program, graphical generation software package and command form etc. based on a raster.

CO 2 emissions and heat flow through soil, fumaroles, and steam heated mud pools at the Reykjanes geothermal area, SW Iceland

Urban security is of great importance, especially in public spaces like parks, which are considered a place for relaxation, comfort, and recreation. Various crimes occur in such places due to problems such as lack of supervision, large numbers of people, and reduced lighting, which increase the number of defenseless and private places. To analyze the security status of public parks, this study employed geographic information systems (GIS)‐based spatial analysis of crimes in the Tehran metropolis, the capital of Iran. The study includes twenty-four crimes occurring in forty-one parks in Tehran in 2015. Required information was collected by contacting the police department and the weight of each index was determined using an analytical network process. To rank the parks, the PROMETHEE model was applied and graphical statistical methods were used in a GIS environment to detect and display the spatial pattern of crimes. The results of the analysis show that crime is low in central, northern, and southern parts of the city, whereas it is high in the western and eastern parts of Tehran. In addition, there is a significant positive relationship between two variables such as area and park ranks in terms of security. It is essential to detect the place conditions resulting in crime opportunities or simplify it by relying on geographic science principles. Results of this research are of great importance for several organizations in Tehran, such as the Municipality of Tehran, police department, justice system, and other relevant organizations to increase safety in parks and for the development of GIScience in the context of crime analysis.

The article considers the use of the Python environment Thonny for educational graphic visualization of the double sorting algorithm using the example of working with arrays of numbers. Students were introduced to the sorting algorithm in the 8th grade, where it was studied in text and practical form without graphic display. In the 10th grade, as part of the study of the module "Models and Simulation. Data Analysis and Visualization", it is proposed to demonstrate the operation of the algorithm using the Pygame library, which allows combining mathematical concepts and algorithmic skills in a visual form. Special attention is paid to the development of students' practical programming skills and understanding of the dynamics of the work of algorithms through interactive graphic visualization. The Thonny environment offers students and teachers a convenient integration of code and graphic display, which allows students to gradually master the basics of using the Pygame library and Python programming structures. The proposed visualization illustrates the process of sorting an array of numbers using the double selection method, in which for better clarity, the maximum and minimum elements are highlighted in color, and the current element during the check is marked with a separate color. Such a structured visualization allows students to understand the logic of the algorithm and the order of performing exchange operations. Visualization of sorting results significantly improves students' understanding of the educational material and contributes to a deeper assimilation of theoretical concepts. Students can observe the dynamics of changes in the elements of the array, evaluate the effectiveness of the algorithm, and develop logical and algorithmic thinking. The implementation of such interactive exercises in the Thonny environment creates a modern learning environment that meets the requirements of STEM education and the development of interdisciplinary competencies of students.

Comparing groups on the basis of survival is common in medical research. Survival time data require methods that properly account for the situation when the time of death is not observed because some subjects are still alive at the end of the study (censoring). In addition, methods are required that make no assumptions about the shape of the survival time distribution (nonparametric). There are widely used methods for statistical comparison and graphic display of survival of two samples. The log-rank test (1) provides a comparison of the observed number of deaths in each group versus the number that would be expected if the total mortality were distributed according to the proportion in each group. These statistical comparisons are often accompanied by Kaplan–Meier curves that provide a graphic display of the distribution of survivorship over time (2). This estimator, calculated from samples that are partially censored, is a monotonically non-increasing step function with steps at each observed death time. Although calculated separately for each group, these graphs are displayed simultaneously in a single plot to promote a visual comparison of survival over the entire study period. It is often of interest to compare the survival of a single sample to that of a defined reference population. For example, when a series of patients with a rare, life-threatening disease has been collected, it may be of interest to know if the study sample is experiencing the same survival as the demographically matched standard (general) population, according to actuarial tables. This is especially of interest when the disease is curable or not usually lethal and the age of onset is late in life. It is not appropriate to use methods developed for two-sample comparisons to do this analysis, because the variance would be incorrectly calculated and thus the P value would be invalid. It is possible to provide a single summary measure of the relative survival of a sample compared with a standard population by estimating the standardized mortality ratio (3). However, investigators often want to report a P value from a statistical test that compares the two populations—essentially a one-sample log-rank test. Although such tests are published in the statistical literature (4,5), medical investigators do not generally read this literature, and thus these tests are not widely known and used by this community. In fact, these articles (4,5) have been cited fewer than 10 times in the medical literature over the past 20 years. Some ad hoc methods have been devised for a one-sample survival test. For example, one approach is to use the actuarial tables to determine the expected remaining lifetime at the age of study entry for each of the subjects in the sample and then to treat these times as exact death times of a hypothetical sample of the same number of subjects from the reference population. It is possible then to calculate a two-sample log-rank test and report the resulting P value. However, this test is inappropriate because the variance would be incorrectly calculated and thus the P value would be invalid. Similar pitfalls arise in trying to obtain an accompanying graphical display that would appropriately represent the survival of the standard population in the same manner in which the Kaplan–Meier plot represents the sample. Because there are no methods that are widely cited in the medical literature, there is a tendency to develop ad hoc methods. For example, one approach is to calculate the expected remaining lifetime for each subject in the sample by using the actuarial tables matched by age, sex, and/or race. This set of numbers is then treated as exact observed death times, and the Kaplan–Meier estimator is calculated for this hypothetical population. This calculation results in a step function with the number of steps equal to the size of the sample being studied. This is not correct. As an illustration, suppose everyone in the sample began observation at the same age and, thus, would have the same expected remaining lifetime, say s. The survival distribution for the hypothetical matched sample representing the reference group would then have a value of 1 until s, at which point the curve would drop to 0. The correct method must use the entire remaining survival curve (calculated from the reference actuarial tables) for each subject. The purpose of this commentary is to describe both the simple one-sample log-rank test that is equivalent to the standardized mortality ratio and an estimate for survivorship in the matched standard population that allows a visual comparison of survivorship of the sample and standard populations. We will discuss the issues in designing a study that will rely on one-sample methods. The software to perform analyses discussed in this commentary can be found at our Web site: http://biostatistics.mgh.harvard. edu/biostatistics/resources.html (6). As an illustration, we use these methods to compare the survival of a small cohort of patients diagnosed with extra-mammary Paget’s disease at Massachusetts General Hospital with the survival of the general population (7).

Data visualization is one of the techniques to understand the patterns of data in graphical methods. Data visualization is an effective tool for transforming raw data into actionable insights and facilitating data-driven decision-making. High-dimensional synthetic data are datasets created artificially with an abundance of attributes or aspects. This type of synthetic data is particularly helpful for attempting to assess machine learning algorithms and data analysis techniques in scenarios with a large number of factors. The method can be difficult because of the more complicated nature of high-dimensional data, but it is necessary for a variety of applications, such as testing machine learning algorithms, evaluating data analysis techniques, and exploring model behaviour in high-dimensional spaces. These trained high-dimensional synthetic data are given to the visualization techniques to produce graphical representation and better decision-making models. This chapter elaborates on visualizing synthetic high-dimensional data for better understanding by common men.

The need to visualize data has emerged from the research field, it has been a useful tool to the study of scientific problems. However the truth is that data visualization is a great way to present data for any area dealing with information, because visually presented information is not only more appealing due to its use of pictograms and colours, but also more efficient in conveying large amounts of information. Throughout the years there have been efforts to develop a classification for these visualizations, in order to provide a better understanding of this way to present data. There are many different classifications but none of them is fully complete. In this paper it is discussed and developed a typology for online data visualization and info graphics. Such a typology will be relevant for a better understanding of what kinds of visualizations exist and in further research to better identify which elements compose a good visualization that is pleasing to the public.

BackgroundCurrently no study has investigated whether Web-based interactive technology can influence females to adopt healthy behaviors. We investigated how and under what conditions do Web-based interactivity influence vaccination intentions among young females.MethodsIn this randomized controlled trail, we conduct a 2 (mode of information presentation: narrative vs. data visualization) × 2 (interactivity: interactive information vs. noninteractive information) between-groups design. A total of 180 Chinese female undergraduate students who had never received HPV vaccination were randomly allocated to 4 experimental groups. Each participant was assessed for their information avoidance behavior and vaccination intention. The hypotheses were tested using a moderated mediation model. All analyses were performed using SPSS version 22.0 with probability set at 0.05 alpha level.ResultsThe indirect relationship between interactivity and behavioral intention though information avoidance was moderated by the mode of presentation. Under the narrative condition, interactivity (vs. non-interactivity) decreased information avoidance and increased the intention to receive HPV vaccination (B = -.23, SE = 0.10, P < 0.05). However, under data visualization condition, no significant difference was observed between the effects of interactivity and non-interactivity on intention.ConclusionThe findings suggest that when young females experience difficulties in manipulating or understanding HPV-related information, their information-avoidance behavior is likely to increase. Rather than use interactive statistical or graphical information, young females are more likely to be persuaded by interactive narratives.

In visualization, the way of data display in physical is different from information graphics or data visualization. By adding interactive technology, physical visualization entered a new dimension. These additions are dramatically changing the creation of art. I try to classify the physical visualization by whether it is interactive or it is programming or not, and analyze how these changes affect to artistic creation.

Generating a blocky rock mass

Today, the paper document is fast becoming a thing of the past. With the rapid development of fast, inexpensive computing and storage devices, many government and private organizations are archiving their documents in electronic form (e.g., personnel records, medical records, patents, etc.). Many of these organizations are converting their paper archives to electronic images, which are then stored in a computer database. Because of this, there is a need to efficiently organize this data into comprehensive and accessible information resources and provide for rapid access to the information contained within these imaged documents. To meet this need, Litton PRC and Litton Data Systems Division are developing a system, the Imaged Document Optical Correlation and Conversion System (IDOCCS), to provide a total solution to the problem of managing and retrieving textual and graphic information from imaged document archives. At the heart of IDOCCS, optical correlation technology provide a means for the search and retrieval of information from imaged documents. IDOCCS can be used to rapidly search for key words or phrases within the imaged document archives and has the potential to determine the types of languages contained within a document. In addition, IDOCCS can automatically compare an input document with the archived database to determine if it is a duplicate, thereby reducing the overall resources required to maintain and access the document database. Embedded graphics on imaged pages can also be exploited, e.g., imaged documents containing an agency's seal or logo can be singled out. In this paper, we present a description of IDOCCS as well as preliminary performance results and theoretical projections.

A real-time LPC-based vocal tract area display for voice development

Wireless sensor network (WSN) is a distributed sensor network. The main research direction of wireless sensor network is the distribution method of its channel. With the development of information technology, the contradiction that between scarce wireless resources and high-density AP points will adversely affect people’s daily life. In this paper, we design a heuristic algorithm based on the channel assignment method by comparing the similarity of the network graphic topology. By calculating the pre-allocation scheme, the optimal throughput of the new topology is compared with the optimal throughput of the genetic algorithm to verify the superiority in the new algorithm. The network model is constructed by three graphical methods: scatter plot, density map and thermal graph. Finally determine the heat map-based channel allocation algorithm as the optimal solution.