By James V. Candy
New Bayesian method is helping you resolve tricky difficulties in sign processing conveniently. sign processing relies in this basic conceptthe extraction of serious info from noisy, doubtful info. so much suggestions depend on underlying Gaussian assumptions for an answer, yet what occurs while those assumptions are misguided? Bayesian concepts avoid this dilemma via providing a totally different method which may simply comprise non-Gaussian and nonlinear techniques besides all the ordinary equipment at the moment to be had. this article allows readers to completely make the most the various a. Read more...
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This revised version is an unabridged and corrected republication of thesecond variation of this booklet released by way of McGraw-Hill Publishing Company,New York, long island, in 1988 (ISBN 0-07-047794-9), and in addition released earlierby Macmillan, Inc. , big apple, manhattan, 1988 (ISBN 0-02-389380-X). Allcopyrights to this paintings reverted to Sophocles J.
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Additional info for Bayesian signal processing: classical, modern, and particle filtering methods
5 Think of measuring the temperature of a liquid in a beaker heated by a burner. Suppose we use a thermometer immersed in the liquid and periodically observe the temperature and record it. (a) Construct a measurement model assuming that the thermometer is linearly related to the temperature, that is, y(t) = k △T(t). Also model the uncertainty of the visual measurement as a random sequence ????(t) with variance R???????? . (b) Suppose we model the heat transferred to the liquid from the burner as Q(t) = CA △T(t) where C is the coefficient of thermal conductivity, A is the cross-sectional area, and △T(t) is the temperature gradient with assumed random uncertainty ????(t) and variance R???????? .
It evolved further from such areas as computational physics, biology, chemistry, mathematics, engineering, materials and finance to name a few. Monte Carlo methods offer an alternative approach to solving classical numerical integration and optimization problems. Inherently, as the dimensionality of the problem increases, classical methods are prone to failure while MC methods tend to increase their efficiency by reducing the error—an extremely attractive property. For example, in the case of classical grid-based numerical integration or optimization problems, as the number of grid points increase along with the number of problem-defining vector components, there is an accompanying exponential increase in computational time [10–15].
Maximum likelihood produces the “best” estimate as the value which maximizes the probability of the measurements given that the parameter value is “most likely” true. In the estimation problem, the measurement data are given along with the underlying structure of the probability density function (as in the Bayesian case), but the parameters of the density are unknown and must be determined from the measurements; therefore, the maximum likelihood estimate can be considered heuristically as that value of the parameter that best “explains” the measured data giving the most likely estimation.