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Abstract: A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. These models are interesting because they can be used to represent a broad class of physical phenomena and because they lead to efficient algorithms for estimation and likelihood calculation. In this paper, we provide a complete statistical characterization of the error associated with smoothed estimates of the multiscale stochastic processes described by these models. In particular, ... (Update)
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...error variances) is easy. 3 Multiscale Modeling The multiscale models of interest in this paper and originally introduced in [4, 23, 24] are scale recursive models defined on index sets that are organized as multilevel trees. A simple example of such a tree (a...
...aggregate measurement obtained by taking a weighted average of the data. 6 Other elements of P may be computed using the results of [16]. 11 of Figure 3 requires a lifting operator G y for the measurements: y l = G y y (12) and a lifted measurement model y l = C l x l v l...
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BibTeX entry: (Update)
M. Luettgen and A. Willsky. "Multiscale smoothing error models". Technical Report LIDS-P2234, Massachusetts Institute of Technology, Laboratory for Information and Decision Systems, 1994. To appear in IEEE Transactions on Automatic Control. http://citeseer.ist.psu.edu/luettgen94multiscale.html More
@misc{ luettgen94multiscale,
author = "M. Luettgen and A. Willsky",
title = "Multiscale smoothing error models",
text = "M. Luettgen and A. Willsky. Multiscale smoothing error models. Technical
Report LIDS-P2234, Massachusetts Institute of Technology, Laboratory for
Information and Decision Systems, 1994. To appear in IEEE Transactions on
Automatic Control.",
year = "1994",
url = "citeseer.ist.psu.edu/luettgen94multiscale.html" }
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50 Multiscale representations of Markov random fields - Luettgen, Karl et al. - 1993
42 Likelihood calculation for a class of multiscale stochastic .. - Luettgen, Willsky - 1993
42 Likelihood calculation for a class of multiscale stochastic .. - Luettgen, Willsky - 1993
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9 Modeling and estimation of discrete time Gaussian reciprocal.. (context) - Levy, Frezza et al. - 1990
5 A stochastic realization approach to the smoothing problem (context) - Badawi, Lindquist et al. - 1979
4 Non-causal estimation for Markov random fields (context) - Levy - 1990
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2 Smoothing error dynamics and their use in the solution of sm.. (context) - Bello, Willsky et al. - 1986
2 Discrete-time complementary models and smoothing (context) - Ackner, Kailath - 1989
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