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Statements

Subject Item
dbr:Norbert_Wiener
dbo:wikiPageWikiLink
dbr:Smoothing_problem_(stochastic_processes)
Subject Item
dbr:Smoothing_(disambiguation)
dbo:wikiPageWikiLink
dbr:Smoothing_problem_(stochastic_processes)
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dbr:Smoothing_problem_(stochastic_processes)
Subject Item
dbr:Smoothing_problem
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dbr:Smoothing_problem_(stochastic_processes)
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dbr:Smoothing_problem_(stochastic_processes)
Subject Item
dbr:Smoothing_problem_(stochastic_processes)
rdfs:label
Smoothing problem (stochastic processes)
rdfs:comment
The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems defined by Norbert Wiener. A smoother is an algorithm that implements a solution to this problem, typically based on recursive Bayesian estimation. The smoothing problem is closely related to the filtering problem, both of which are studied in Bayesian smoothing theory.
dcterms:subject
dbc:Linear_filters dbc:Nonlinear_filters dbc:Signal_estimation dbc:Bayesian_estimation
dbo:wikiPageID
53544517
dbo:wikiPageRevisionID
1117509711
dbo:wikiPageWikiLink
dbr:Norbert_Wiener dbc:Signal_estimation dbr:Filter_design dbr:Recursive_Bayesian_estimation dbr:Density_estimation dbr:Filter_(signal_processing) dbr:Generalized_filtering dbr:Smoothing dbr:Statistics dbr:Wiener_Filter dbc:Bayesian_estimation dbr:Retrodiction dbr:Filtering_problem dbr:Probability_density_function dbr:Image_processing dbr:Kalman_filter dbc:Linear_filters dbc:Nonlinear_filters
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wikidata:Q30601854 yago-res:Smoothing_problem_(stochastic_processes) n14:2qTuW
dbp:wikiPageUsesTemplate
dbt:Reflist dbt:Technical dbt:Cleanup_section
dbp:date
December 2021
dbp:reason
this section needs reorganization and also needs additional citations.
dbo:abstract
The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems defined by Norbert Wiener. A smoother is an algorithm that implements a solution to this problem, typically based on recursive Bayesian estimation. The smoothing problem is closely related to the filtering problem, both of which are studied in Bayesian smoothing theory. A smoother is often a two-pass process, composed of forward and backward passes. Consider doing estimation (prediction/retrodiction) about an ongoing process (e.g. tracking a missile) based on incoming observations. When new observations arrive, estimations about past needs to be updated to have a smoother (more accurate) estimation of the whole estimated path until now (taking into account the newer observations). Without a backward pass (for retrodiction), the sequence of predictions in an online filtering algorithm does not look smooth. In other words, retrospectively, it is as if we are using future observations for improving estimation of a point in past, when those observations about future points become available. Note that time of estimation (which determines which observations are available) can be different to the time of the point that the prediction is about (that is subject to prediction/retrodiction). The observations about later times can be used to update and improved the estimations about earlier times. Doing so leads to smoother-looking estimations (retrodiction) about the whole path.
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6945
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wikipedia-en:Smoothing_problem_(stochastic_processes)
Subject Item
dbr:Switching_Kalman_filter
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dbr:Smoothing_problem_(stochastic_processes)
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wikipedia-en:Smoothing_problem_(stochastic_processes)
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dbr:Smoothing_problem_(stochastic_processes)