### 23 European Symposium on Computer Aided Process Engineering: Nonlinear process monitoring by integrating manifold learning with **Gaussian** process (Computer Aided Chemical Engineering Book 32)

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In order to monitor nonlinear processes, kernel principal component analysis (KPCA) has become a popular technique. Nevertheless, KPCA suffers from two major disadvantages. First, the underlying manifold structure of data is not considered in process modeling. Second, the selection of kernel function and kernel parameters is always problematic. To avoid such deficiencies, an integrating method of manifolding learning and

**Gaussian**process is proposed in this paper, which extends the utilization of maximum variance unfolding (MVU) to online process monitoring and fault isolation. The proposed method is named as extendable MVU (EMVU), whose effectiveness is verified by the case studies on the benchmark Tennessee Eastman (TE) process.Published by: Elsevier | Publication date: 06/10/2013

Kindle book details: Kindle Edition, 21 pages### Sparse Modeling: Theory, Algorithms, and Applications (Chapman & Hall/Crc Machine Learning & Pattern Recognition)

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Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing.Sparse Modeling: Theory, Algorithms, and Applications provides an introduction t

Published by: CRC Press | Publication date: 12/01/2014

Kindle book details: Kindle Edition, 253 pages### Nonparametric Goodness-of-Fit Testing Under **Gaussian** Models (Lecture Notes in Statistics Book 169)

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This book presents the modern theory of nonparametric goodness-of-fit testing. It fills the gap in modern nonparametric statistical theory by discussing hypothesis testing and addresses mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems relevant in signal detection and transmission and in technical and medical diagnostics among others.

Published by: Springer | Publication date: 10/29/2002

Kindle book details: Kindle Edition, 457 pages### An Introduction to Infinite-Dimensional Analysis (Universitext)

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In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension. Starting from the definition of

**Gaussian**measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.Published by: Springer Berlin Heidelberg | Publication date: 08/25/2006

Kindle book details: Kindle Edition, 208 pages### Detection of Random Signals in Dependent **Gaussian** Noise

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The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with

**Gaussian**noise. To facilitate comprehension the text is divided into three broad areas – reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context.One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis.The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics.Published by: Springer | Publication date: 12/15/2015

Kindle book details: Kindle Edition, 1176 pages### Stochastic Analysis for **Gaussian** Random Processes and Fields: With Applications (Chapman & Hall/CRC Monographs on Statistics & Applied Probability Book 145)

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Stochastic Analysis for

**Gaussian**Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies**Gaussian**random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS before introducing the**Gaussian**process and**Gaussian**random fields. The authors use chaos expansion to define the Skorokhod integral, which generalizes the Itô integral. They show how the Skorokhod integral is a dual operator of Skorokhod differentiation and the divergence operator of Malliavin. The authors also present**Gaussian**processes indexed by real numbers and obtain a Kallianpur–Striebel Bayes' formula for the filtering problem. After discussing the problem of equivalence and singularity of**Gaussian**random fields (including a generalization of the Girsanov theorem), the book concludes with the Markov property of**Gaussian**random fields indexed by measures and generalized**Gaussian**random fields indexed by Schwartz space. The Markov property for generalized random fields is connected to the Markov process generated by a Dirichlet form.Published by: Chapman and Hall/CRC | Publication date: 06/23/2015

Kindle book details: Kindle Edition, 201 pages### The Malliavin Calculus and Related Topics (Probability and Its Applications)

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The Malliavin calculus is an infinite-dimensional differential calculus on a

**Gaussian**space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.Published by: Springer | Publication date: 02/27/2006

Kindle book details: Kindle Edition, 382 pages### Bayesian Networks: With Examples in R (Chapman & Hall/CRC Texts in Statistical Science)

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Understand the Foundations of Bayesian Networks—Core Properties and Definitions Explained Bayesian Networks: With Examples in R introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples in R illustrate each step of the modeling process. The examples start from the simplest notions and gradually increase in complexity. The authors also distinguish the probabilistic models from their estimation with data sets.The first three chapters explain the whole process of Bayesian network modeling, from structure learning to parameter learning to inference. These chapters cover discrete Bayesian,

**Gaussian**Bayesian, and hybrid networks, including arbitrary random variables.The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R and other software packages appropriate for Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein signaling network paper and graphical modeling approaches for predicting the composition of different body parts.Suitable for graduate students and non-statisticians, this text provides an introductory overview of Bayesian networks. It gives readers a clear, practical understanding of the general approach and steps involved.Published by: Chapman and Hall/CRC | Publication date: 06/20/2014

Kindle book details: Kindle Edition, 241 pages### Nonlinear Time Series: Theory, Methods and Applications with R Examples (Chapman & Hall/CRC Texts in Statistical Science)

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Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models—without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes.The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods. The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently. Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.

Published by: Chapman and Hall/CRC | Publication date: 01/06/2014

Kindle book details: Kindle Edition, 551 pages### Optical Fiber Telecommunications VIB: Chapter 4. Optical Satellite Communications (Optics and Photonics)

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Satellite-based communication systems of today are increasingly capacity limited. Based on radio frequency or microwave (generically RF) technologies, current state-of-the-art satellite communications (satcom) are often constrained by hardware and spectrum allocation limitations. Consequently, mobile payload sensors and instruments (on satellite or aircraft) are often implemented with restricted capacity to better match that of the host platform. Such limitations are expected to worsen as future interplanetary, deep-space, and manned missions use more sophisticated data-intensive sensors and as the demand for information—and a bigger return on the space-exploration investment—continues to increase.

Published by: Academic Press | Publication date: 05/11/2013

Kindle book details: Kindle Edition, 76 pages