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Lectures on Probability and Second Order Random Fields

Lectures on Probability and Second Order Random Fields
Author: Diego Bricio Hern ndez
Publisher: World Scientific
Total Pages: 172
Release: 1995
Genre: Mathematics
ISBN: 9789810219086

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This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered.The book is a valuable guide for higher level engineering students.


Random Fields: Analysis And Synthesis (Revised And Expanded New Edition)

Random Fields: Analysis And Synthesis (Revised And Expanded New Edition)
Author: Erik Vanmarcke
Publisher: World Scientific Publishing Company
Total Pages: 363
Release: 2010-07-21
Genre: Mathematics
ISBN: 9813101997

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Random variation is a fact of life that provides substance to a wide range of problems in the sciences, engineering, and economics. There is a growing need in diverse disciplines to model complex patterns of variation and interdependence using random fields, as both deterministic treatment and conventional statistics are often insufficient. An ideal random field model will capture key features of complex random phenomena in terms of a minimum number of physically meaningful and experimentally accessible parameters. This volume, a revised and expanded edition of an acclaimed book first published by the M I T Press, offers a synthesis of methods to describe and analyze and, where appropriate, predict and control random fields. There is much new material, covering both theory and applications, notably on a class of probability distributions derived from quantum mechanics, relevant to stochastic modeling in fields such as cosmology, biology and system reliability, and on discrete-unit or agent-based random processes.Random Fields is self-contained and unified in presentation. The first edition was found, in a review in EOS (American Geophysical Union) to be “both technically interesting and a pleasure to read … the presentation is clear and the book should be useful to almost anyone who uses random processes to solve problems in engineering or science … and (there is) continued emphasis on describing the mathematics in physical terms.”


The Geometry of Random Fields

The Geometry of Random Fields
Author: Robert J. Adler
Publisher: SIAM
Total Pages: 296
Release: 1981-01-01
Genre: Mathematics
ISBN: 0898718988

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Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields; closed form expressions for the various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles; descriptions of the local behavior of random fields in the neighborhoods of high maxima; and a treatment of the Markov property for Gaussian fields. Audience: researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students.


Some Observations on Measurable Properties of Random Processes and Fields. i

Some Observations on Measurable Properties of Random Processes and Fields. i
Author: David Middleton
Publisher:
Total Pages: 54
Release: 1964
Genre:
ISBN:

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A number of useful, measurable properties of random processes and random fields are de, ined and discussed, and it is shown how these results may be applied to observations necessarily finite in time and in space. Time and space stationarity and ergodicity are considered, as are the definition and construction of hierarchies of probability distribution (densities) defining these stochastic processes and fields. The notion of the intensity spectrum in one or more dimensions is introduced, along with extended versions of the Wiener-Khintchine theorem relating the spectrum to the covariance functions. Cross- and auto-spectral densities are also briefly treated. Some tests of practical stationarity and homogeneity are suggested for finite data sets and single representations, from which approximately statistical (or regular) properties of the ensemble as a whole may be deduced. (Author).


Conditional Random Fields for Activity Recognition

Conditional Random Fields for Activity Recognition
Author:
Publisher:
Total Pages: 205
Release: 2008
Genre:
ISBN:

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To act intelligently in presence of others, robots must use information from their sensors to recognize behaviors and activities of other agents in their environment. We explore how to bridge the gap from noisy, continuous observations about the world to high-level, discrete activity labels. We contribute the use of conditional random fields (CRFs) for activity recognition in multirobot domains. We explore appropriateness of CRFs with an empirical comparison to hidden Markov models. We elucidate the properties of CRFs that make them well suited to the activity recognition, namely discriminative training, the ability to robustly incorporate rich features of observations, and their nature as conditional models, with a variety of synthetic and real robot data. Accurate activity recognition requires complex and rich features of the observations. We choose the most informative features from a large set of candidates using feature selection. We adapt two feature selection algorithms, grafting and '1 regularization, to conditional random fields. We also investigate a third feature selection algorithm, which was originally proposed for CRFs in a natural language processing domain, in an activity recognition context. In particular, we focus on scaling feature selection to very large sets of candidate features that we define succinctly using a rich relational feature specification language. The reduced feature sets that we discover via feature selection enable efficient, real-time inference. However, feature selection and training for conditional random fields is computationally expensive. We adapt an M-estimator, introduced by Jeon and Lin for log-density estimation in ANOVA models, for fast, approximate parameter estimation in CRFs. We provided an in depth, empirical evaluation of the properties of the M-estimator and then we introduce a new, efficient feature selection algorithm for CRFs based around M-estimation to identify the most important features.