Multiscale Stochastic Realization
نویسنده
چکیده
We develop a realization theory for a class of Inultiscale stochastic processes having whitenoise driven, scale-recursive dynamics that are indexed by the nodes of a tree. Given the correlation structure of a 1-D or 2-D random process, our methods provide a systematic way to realize the given correlation as the finest scale of a multiscale process. Motivated by Akaike's use of canonical correlation analysis to develop both exact and reduced-order model for time-series, we too harness this tool to develop multiscale models. We apply our realization scheme to build reduced-order multiscale models for two applications, namely linear least-squares estimation and generation of random-field sample paths. For the numerical examples considered, least-squares estimates are obtained having nearly optimal mean-square errors, even with multiscale models of low order. Although both field estimates and field sample paths exhibit a visually distracting blockiness, this blockiness is not an important issue in many applications. For such applications, our approach to multiscale stochastic realization holds promise as a valuable, general tool. *The work of William Irving and Alan Willsky was supported by the Air Force Office of Scientific Research, under grant AFOSR-F496-20-93-1-0604, the Army Research Office, under grant ARO DAAL03-92-G-0015.
منابع مشابه
A canonical correlations approach to multiscale stochastic realization
We develop a realization theory for a class of multiscale stochastic processes having white-noise driven, scale-recursive dynamics that are indexed by the nodes of a tree. Given the correlation structure of a 1-D or 2-D random process, our methods provide a systematic way to realize the given correlation as the finest scale of a multiscale process. Motivated by Akaike’s use of canonical correla...
متن کاملStochastic realization theory for exact and approximate multiscale models
The thesis provides a detailed analysis of the independence structure possessed by multiscale models and demonstrates that such an analysis provides important insight into the multiscale stochastic realization problem. Multiscale models constitute a broad class of probabilistic models which includes the well-known subclass of multiscale autoregressive (MAR) models. MAR models have proven useful...
متن کاملComputationally Ecient Stochastic Realization for Internal Multiscale Autoregressive Models*
In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally ecient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. O...
متن کاملComputationally Eecient Stochastic Realization for Internal Multiscale Autoregressive Models *
In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally eecient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. O...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006