Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
He was born in rural Missouri, and it was immediately clear that he was different from the rest. He caught his first criminal when he was just two years old. By his sixth birthday, he had located burglars, missing children, drug dealers, rapists, and murderers—including Utah’s most wanted criminal. Known to friends as JJ, to law enforcement as Michael Serio’s partner, and to captured criminals as “that damned dog,” Jessie Jr., an exceptionally talented bloodhound, bayed like a sea lion that had swallowed a fog horn. Before JJ, few police departments in the West used bloodhounds, and none in Utah. But just when JJ was finally convincing naysayers, he and Officer Serio ran into something worse than resistance: the despair of failure amid high hope. JJ had been tracking Brian David Mitchell, the man who abducted Elizabeth Smart, when he was pulled off the track. Elizabeth later told investigators that on the day she was kidnapped she heard a dog baying in the woods behind her. In almost nine years of service, JJ helped apprehend nearly 300 criminal suspects in the Salt Lake City area. Here is his remarkable story, fleas and all. Click here to view the trailer for Bloodhound in Blue.
Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi?cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950’s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today’s computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di?culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions.
This book introduces readers to Web content credibility evaluation and evaluation support. It highlights empirical research and establishes a solid foundation for future research by presenting methods of supporting credibility evaluation of online content, together with publicly available datasets for reproducible experimentation, such as the Web Content Credibility Corpus. The book is divided into six chapters. After a general introduction in Chapter 1, including a brief survey of credibility evaluation in the social sciences, Chapter 2 presents definitions of credibility and related concepts of truth and trust. Next, Chapter 3 details methods, algorithms and user interfaces for systems supporting Web content credibility evaluation. In turn, Chapter 4 takes a closer look at the credibility of social media, exemplified in sections on Twitter, Q&A systems, and Wikipedia, as well as fake news detection. In closing, Chapter 5 presents mathematical and simulation models of credibility evaluation, before a final round-up of the book is provided in Chapter 6. Overall, the book reviews and synthesizes the current state of the art in Web content credibility evaluation support and fake news detection. It provides researchers in academia and industry with both an incentive and a basis for future research and development of Web content credibility evaluation support services.
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