Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet ...actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code.
Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this ...maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters.The handbook begins with a historical intro
Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data ...sets, this book features an operational perspective, practical relevance, and applicability—keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics: Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence. Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law. Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context. Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information—scientific evidence—ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty. This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes. This book is Open Access.
This open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an ...alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.
Data Analysis Huber, Peter J
2011, 2011-04-19T00:00:00, 2011-04-27, 2012-01-09, c2011, Letnik:
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eBook
This book explores the many provocative questions concerning the fundamentals of data analysis. It is based on the time-tested experience of one of the gurus of the subject matter. Why should one ...study data analysis? How should it be taught? What techniques work best, and for whom? How valid are the results? How much data should be tested? Which machine languages should be used, if used at all? Emphasis on apprenticeship (through hands-on case studies) and anecdotes (through real-life applications) are the tools that Peter J. Huber uses in this volume. Concern with specific statistical techniques is not of immediate value; rather, questions of strategy – when to use which technique – are employed. Central to the discussion is an understanding of the significance of massive (or robust) data sets, the implementation of languages, and the use of models. Each is sprinkled with an ample number of examples and case studies. Personal practices, various pitfalls, and existing controversies are presented when applicable. The book serves as an excellent philosophical and historical companion to any present-day text in data analysis, robust statistics, data mining, statistical learning, or computational statistics.
This text shows how to compute statistics under such interval and fuzzy uncertainty. The resulting methods are applied to computer science (optimal scheduling of different processors), to information ...technology, to computer engineering, and to data processing in geosciences, radar imaging, and structural mechanics.
An essential work on the origins of statistics The Rise of Statistical Thinking, 1820–1900 explores the history of statistics from the field's origins in the nineteenth century through to the factors ...that produced the burst of modern statistical innovation in the early twentieth century. Theodore Porter shows that statistics was not developed by mathematicians and then applied to the sciences and social sciences. Rather, the field came into being through the efforts of social scientists, who saw a need for statistical tools in their examination of society. Pioneering statistical physicists and biologists James Clerk Maxwell, Ludwig Boltzmann, and Francis Galton introduced statistical models to the sciences by pointing to analogies between their disciplines and the social sciences. A new preface by the author looks at how the book has remained relevant since its initial publication, and considers the current place of statistics in scientific research.
What is the impact of the COVID-19 on China’s economy? After using the linear regression to analyze the data of GDP, national fiscal revenue and the added value of nine major industries, we find that ...the COVID-19 had a great impact on China’s economy in 2020 but not in 2021. Then, we use the principal component analysis to reduce the dimension of data and define a new variable to represent China’s economy, which is called “Chinese economic quantity”. It can well describe China’s economy, which has the same function as GDP. By comparing its changes in different years, it can verify the influence on China’s economy. Finally, some suggestions and advices will be given.
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