is broad consensus among educators, communication scholars, sociologists, and economists that the development and diffusion of information and communication technologies (ICT) are having a profound effect on modern life. This is due to the affordances of new digital media, which bridge the interactive features of speech and the archival characteristics of writing; allow many-to-many communication among people without regard to time and space, including mass collaborative editing of texts; facilitate the creation of a global hyper-indexed multimodal information structure; and enable content production and distribution in both writing and multimedia on a scale previously unimaginable (Jewitt, 2008; Warschauer, 1999). For all these reasons, computer-mediated communication can be considered a new mode of information (Poster, 1990), or a "fourth revolution in the means of production of knowledge" (Harnad, 1991, p. 39), following the three prior revolutions of language, writing, and print. The previous revolution, brought about through the development and diffusion of printing, took centuries to unfold, as its full impact depended on the industrial revolution that Gutenberg's printing press preceded by several centuries (Eisenstein, 1979). Today, though, the development and diffusion of computers and the Internet occur simultaneously with a new economic revolution, based on transition from an industrial to an informational economy (Castells, 1996). This helps explain both why new media have spread so fast and also why they are so crucial to enabling full social and economic participation. As Castells (1998) concludes, based on his exhaustive socioeconomic analysis of this postindustrial stage of capitalism, "information technology,

New Technology and Digital Worlds: Analyzing Evidence of Equity in Access, Use, and Outcomes

We introduce a new Empirical Bayes approach for large-scale hypothesis testing, including estimating false discovery rates (FDRs), and effect sizes. This approach has two key differences from existing approaches to FDR analysis. First, it assumes that the distribution of the actual (unobserved) effects is unimodal, with a mode at 0. This "unimodal assumption" (UA), although natural in many contexts, is not usually incorporated into standard FDR analysis, and we demonstrate how incorporating it brings many benefits. Specifically, the UA facilitates efficient and robust computation-estimating the unimodal distribution involves solving a simple convex optimization problem-and enables more accurate inferences provided that it holds. Second, the method takes as its input two numbers for each test (an effect size estimate and corresponding standard error), rather than the one number usually used ($p$ value or $z$ score). When available, using two numbers instead of one helps account for variation in measurement precision across tests. It also facilitates estimation of effects, and unlike standard FDR methods, our approach provides interval estimates (credible regions) for each effect in addition to measures of significance. To provide a bridge between interval estimates and significance measures, we introduce the term "local false sign rate" to refer to the probability of getting the sign of an effect wrong and argue that it is a superior measure of significance than the local FDR because it is both more generally applicable and can be more robustly estimated. Our methods are implemented in an R package ashr available from http://github.com/stephens999/ashr.

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False discovery rates: a new deal.

Fundamentals of Modern Manufacturing: Materials, Processes and Systems

More than 50 years ago, John Tukey called for a reformation of academic statistics. In “The Future of Data Analysis,” he pointed to the existence of an as-yet unrecognized science, whose subject of...

https://courses.csail.mit.edu/18.337/2015/docs/50YearsDataScience.pdf

50 Years of Data Science

It is well known that when data are nonnormally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson's correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, including Pearson, Spearman's rank-order, transformation, and resampling approaches. With most sample sizes (n ≥ 20), Type I and Type II error rates were minimized by transforming the data to a normal shape prior to assessing the Pearson correlation. Among transformation approaches, a general purpose rank-based inverse normal transformation (i.e., transformation to rankit scores) was most beneficial. However, when samples were both small (n ≤ 10) and extremely nonnormal, the permutation test often outperformed other alternatives, including various bootstrap tests.

Testing the Significance of a Correlation With Nonnormal Data: Comparison of Pearson, Spearman, Transformation, and Resampling Approaches

This contribution is based on a discussion on the future of data analysis which took place on the last day of the symposium IDA 2000. By different discussants the main problems of current data analysis as well as future developments were discussed. Moreover a network for cooperation and continuing education in the field of uncertainty analysis was initiated and the list of scientists who initiated this is given.

/pdf/on-the-future-of-data-analysis-4kmdmmyr56.pdf

On the Future of Data Analysis

Non-Precise Data and Their Formal Description Non-Precise Data Non-Precise Numbers and Characterizing Functions Construction of Characterizing Functions Non-Precise Vectors Functions of Non-Precise Quantities and Non-Precise Functions Descriptive Statistics with Non-Precise Data Non-Precise Samples Histograms for Non-Precise Data Cumulative Sums for Non-Precise Data Empirical Distribution Function for Non-Precise Data Empirical Fractiles for Non-Precise Data Foundations for Statistical Inference with Non-Precise Data Combination of Non-Precise Observations Sample Moment for Non-Precise Observations Sequences of Non-Precise Observations Classical Statistical Inference for Non-Precise Data Point Estimators for Parameters Confidence Regions for Parameters Nonparametric Estimation Statistical Tests and Non-Precise Data Bayesian Inference for Non-Precise Data Bayes' Theorem for Non-Precise Data Bayesian Confidence Regions Based on Non-Precise Data Non-Precise Predictive Distributions Non-Precise a priori Distributions Bayes Theorem for Non-Precise a priori Distribution and Non-Precise Data Bayesian Decisions Based on Non-Precise Information Outlook References List of Symbols Index

Statistical Methods for Non-Precise Data

Preface. Part I FUZZY INFORMATION. 1. Fuzzy Data. 1.1 One-dimensional Fuzzy Data. 1.2 Vector-valued Fuzzy Data. 1.3 Fuzziness and Variability. 1.4 Fuzziness and Errors. 1.5 Problems. 2. Fuzzy Numbers and Fuzzy Vectors. 2.1 Fuzzy Numbers and Characterizing Functions. 2.2 Vectors of Fuzzy Numbers and Fuzzy Vectors. 2.3 Triangular Norms. 2.4 Problems. 3. Mathematical Operations for Fuzzy Quantities. 3.1 Functions of Fuzzy Variables. 3.2 Addition of Fuzzy Numbers. 3.3 Multiplication of Fuzzy Numbers. 3.4 Mean Value of Fuzzy Numbers. 3.5 Differences and Quotients. 3.6 Fuzzy Valued Functions. 3.7 Problems. Part II DESCRIPTIVE STATISTICS FOR FUZZY DATA. 4. Fuzzy Samples. 4.1 Minimum of Fuzzy Data. 4.2 Maximum of Fuzzy Data. 4.3 Cumulative Sum for Fuzzy Data. 4.4 Problems. 5. Histograms for Fuzzy Data. 5.1 Fuzzy Frequency of a Fixed Class. 5.2 Fuzzy Frequency Distributions. 5.3 Axonometric Diagram of the Fuzzy Histogram. 5.4 Problems. 6. Empirical Distribution Functions. 6.1 Fuzzy Valued Empirical Distribution Function. 6.2 Fuzzy Empirical Fractiles. 6.3 Smoothed Empirical Distribution Function. 6.4 Problems. 7. Empirical Correlation for Fuzzy Data. 7.1 Fuzzy Empirical Correlation Coefficient. 7.2 Problems. Part III FOUNDATIONS OF STATISTICAL INFERENCE WITH FUZZY DATA. 8. Fuzzy Probability Distributions. 8.1 Fuzzy Probability Densities. 8.2 Probabilities based on Fuzzy Probability Densities. 8.3 General Fuzzy Probability Distributions. 8.4 Problems. 9. A Law of Large Numbers. 9.1 Fuzzy Random Variables. 9.2 Fuzzy Probability Distributions induced by Fuzzy Random Variables. 9.3 Sequences of Fuzzy Random Variables. 9.4 Law of Large Numbers for Fuzzy Random Variables. 9.5 Problems. 10. Combined Fuzzy Samples. 10.1 Observation Space and Sample Space. 10.2 Combination of Fuzzy Samples. 10.3 Statistics of Fuzzy Data. 10.4 Problems. Part IV CLASSICAL STATISTICAL INFERENCE FOR FUZZY DATA. 11. Generalized Point Estimations. 11.1 Estimations based on Fuzzy Samples. 11.2 Sample Moments. 11.3 Problems. 12. Generalized Confidence Regions. 12.1 Confidence Functions. 12.2 Fuzzy Confidence Regions. 12.3 Problems. 13. Statistical Tests for Fuzzy Data. 13.1 Test Statistics and Fuzzy Data. 13.2 Fuzzy p-Values. 13.3 Problems. Part V BAYESIAN INFERENCE AND FUZZY INFORMATION. 14. Bayes' Theorem and Fuzzy Information. 14.1 Fuzzy a-priori Distributions. 14.2 Updating Fuzzy a-priori Distributions. 14.3 Problems. 15. Generalized Bayes' Theorem. 15.1 Likelihood Function for Fuzzy Data. 15.2 Bayes' Theorem for Fuzzy a-priori Distribution and Fuzzy Data. 15.3 Problems. 16. Bayesian Confidence Regions. 16.1 Confidence Regions based on Fuzzy Data. 16.2 Fuzzy HPD-Regions. 16.3 Problems. 17. Fuzzy Predictive Distributions. 17.1 Discrete Case. 17.2 Discrete Models with Continuous Parameter Space. 17.3 Continuous Case. 17.4 Problems. 18. Bayesian Decisions and Fuzzy Information. 18.1 Bayesian Decisions. 18.2 Fuzzy Utility. 18.3 Discrete State Space. 18.4 Continuous State Space. 18.5 Problems. References. Part VI REGRESSION ANALYSIS AND FUZZYINFORMATION. 19 Classical regression analysis. 19.1 Regression models. 19.2 Linear regression models with Gaussian dependent variables. 19.3 General linear models. 19.4 Nonidentical variances. 19.5 Problems. 20 Regression models and fuzzy data. 20.1 Generalized estimators for linear regression models based on the extension principle. 20.2 Generalized confidence regions for parameters. 20.3 Prediction in fuzzy regression models. 20.4 Problems. 21 Bayesian regression analysis. 21.1 Calculation of a posteriori distributions. 21.2 Bayesian confidence regions. 21.3 Probabilities of hypotheses. 21.4 Predictive distributions. 21.5 A posteriori Bayes estimators for regression parameters. 21.6 Bayesian regression with Gaussian distributions. 21.7 Problems. 22 Bayesian regression analysis and fuzzy information. 22.1 Fuzzy estimators of regression parameters. 22.2 Generalized Bayesian confidence regions. 22.3 Fuzzy predictive distributions. 22.4 Problems. Part VII FUZZY TIME SERIES. 23 Mathematical concepts. 23.1 Support functions of fuzzy quantities. 23.2 Distances of fuzzy quantities. 23.3 Generalized Hukuhara difference. 24 Descriptive methods for fuzzy time series. 24.1 Moving averages. 24.2 Filtering. 24.2.1 Linear filtering. 24.2.2 Nonlinear filters. 24.3 Exponential smoothing. 24.4 Components model. 24.4.1 Model without seasonal component. 24.4.2 Model with seasonal component. 24.5 Difference filters. 24.6 Generalized Holt-Winter method. 24.7 Presentation in the frequency domain. 25 More on fuzzy random variables and fuzzy random vectors. 25.1 Basics. 25.2 Expectation and variance of fuzzy random variables. 25.3 Covariance and correlation. 25.4 Further results. 26 Stochastic methods in fuzzy time series analysis. 26.1 Linear approximation and prediction. 26.2 Remarks concerning Kalman filtering. Part VIII APPENDICES. A1 List of symbols and abbreviations. A2 Solutions to the problems. A3 Glossary. A4 Related literature. References. Index.

Statistical Methods for Fuzzy Data

Statistical hypothesis testing is very important for finding decisions in practical problems. Usually, the underlying data are assumed to be precise numbers, but it is much more realistic in general to consider fuzzy values which are non-precise numbers. In this case the test statistic will also yield a non-precise number. This article presents an approach for statistical testing at the basis of fuzzy values by introducing the fuzzy p-value. It turns out that clear decisions can be made outside a certain interval which is determined by the characterizing function of the fuzzy p-values.

Reinhard Viertl

Papers

On the Future of Data Analysis

Statistical Methods for Non-Precise Data

Statistical Methods for Fuzzy Data

Testing hypotheses with fuzzy data: The fuzzy p-value

Univariate statistical analysis with fuzzy data