About: Smoothing problem (stochastic processes)

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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.

Attributes	Values
rdfs:label	Smoothing problem (stochastic processes) (en)
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. (en)
dct:subject	Nonlinear filters Signal estimation Linear filters Bayesian estimation
Wikipage page ID	53544517 (xsd:integer)
Wikipage revision ID	1117509711 (xsd:integer)
Link from a Wikipage to another Wikipage	Retrodiction Generalized filtering Statistics Density estimation Nonlinear filters Signal estimation Norbert Wiener Kalman filter Probability density function Linear filters Bayesian estimation Filter (signal processing) Filter design Smoothing Image processing Recursive Bayesian estimation Filtering problem dbr:Wiener_Filter
sameAs	Smoothing problem (stochastic processes) Smoothing problem (stochastic processes) Smoothing problem (stochastic processes)
dbp:wikiPageUsesTemplate	dbt:Cleanup_section dbt:Reflist dbt:Technical
date	December 2021 (en)
reason	this section needs reorganization and also needs additional citations. (en)
has 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. (en)
prov:wasDerivedFrom	wikipedia-en:Smoothing_problem_(stochastic_processes)?oldid=1117509711&ns=0
page length (characters) of wiki page	6945 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Smoothing_problem_(stochastic_processes)
is Link from a Wikipage to another Wikipage of	Norbert Wiener Smoothing (disambiguation) Smoothing problem Switching Kalman filter
is Wikipage redirect of	Smoothing problem
is Wikipage disambiguates of	Smoothing (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Smoothing_problem_(stochastic_processes)

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