By James V. Candy
New Bayesian process is helping you remedy difficult difficulties in sign processing very easily. sign processing is predicated in this primary conceptthe extraction of serious info from noisy, doubtful information. so much suggestions depend upon underlying Gaussian assumptions for an answer, yet what occurs while those assumptions are inaccurate? Bayesian suggestions stay clear of this problem by means of supplying a totally different strategy which can simply comprise non-Gaussian and nonlinear methods in addition to all the ordinary tools presently to be had. this article allows readers to totally take advantage of the various a. Read more...
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Extra info for Bayesian signal processing: classical, modern, and particle filtering methods
ML estimates are consistent. 2. ML estimates are asymptotically efficient with RX|X = −1 . 3 BATCH MAXIMUM LIKELIHOOD ESTIMATION 25 3. ML estimates are asymptotically Gaussian with (X, RX̃ X̃ ). 4. ML estimates are invariant, that is, if X̂ ML , then any function of the ML estimate is the ML estimate of the function, f̂ML = f (X̂ ML ). 5. ML estimates of the sufficient statistic are equivalent to the ML estimates over the original data. These properties are asymptotic and therefore imply that a large amount of data must be available for processing.
To be more precise, we mathematically formulate the general “missing data” problem by first defining the unknown parameters or variables to be estimated as ???? ∈ N???? ×1 with ???? ∈ Θ, the parameter space. We further define three distinct spaces for our problem: (1) the complete data space, ; (2) the incomplete data space, ; and (3) the missing data space, , where the complete space is the union: = (, ). Analogously, we define the corresponding complete, incomplete, and missing/hidden vectors as: z ∈ Nz ×1 , y ∈ Ny ×1 , and x ∈ Nx ×1 , respectively.
Casella, Monte Carlo Statistical Methods (New York: Springer, 1999). 16 INTRODUCTION 13. M. Tanner, Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 2nd Ed. (New York: Springer-Verlag, 1993). 14. J. Ruanaidh and W. Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing (New York: Springer-Verlag, 1996). 15. W. Gilks, S. Richardson, and D. Spiegelhalter, Markov Chain Monte Carlo in Practice (New York: Chapman & Hall/CRC Press, 1996).
Bayesian signal processing: classical, modern, and particle filtering methods by James V. Candy