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By: Arthur David Snider (Author)
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This book discusses the statistical description of processes, including an extensive review of probability and statistics and the analysis of raw data using spectral methods. Various theoretical models (ARMA, Bernoulli, shot, Markov, and random walks) are explored, as well as techniques that are used for prediction—least mean-squared error, Wiener-Hopf and Kalman filters, etc. Everything in this book is introduced at a nuts and bolts level and fills in the gap between the undergraduate engineering statistics course and the axiomatic approaches venerated by specialists.
This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form.
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