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.
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.
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.
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its ...asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.
Technological advances have enabled the profiling of multiple molecular layers at single-cell resolution, assaying cells from multiple samples or conditions. Consequently, there is a growing need for ...computational strategies to analyze data from complex experimental designs that include multiple data modalities and multiple groups of samples. We present Multi-Omics Factor Analysis v2 (MOFA+), a statistical framework for the comprehensive and scalable integration of single-cell multi-modal data. MOFA+ reconstructs a low-dimensional representation of the data using computationally efficient variational inference and supports flexible sparsity constraints, allowing to jointly model variation across multiple sample groups and data modalities.
Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern ...invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, from a key seventeenth-century precursor--England's plague-driven initiative to register vital statistics--right up to the latest advances. In a highly readable, richly illustrated story of invention and inventor that mixes science and politics, intrigue and scandal, revolution and shopping, Howard Wainer validates Thoreau's observation that circumstantial evidence can be quite convincing, as when you find a trout in the milk.
The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures.
Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world.
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