Difference between revisions of "Temporal Concentration"

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A special class of point process that exhibits enhanced clustering is the ''Hawkes process''  (also known as a self-exciting counting process). It is a simple point process but whose conditional intensity depends on the previous even count (hence the occurence of an event may precipitate more events).
 
A special class of point process that exhibits enhanced clustering is the ''Hawkes process''  (also known as a self-exciting counting process). It is a simple point process but whose conditional intensity depends on the previous even count (hence the occurence of an event may precipitate more events).
  
== Measurement ==
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== Measurement using Concentation Indexes ==
* Binning of temporal intervals (e.g. hourly, daily, monthly etc)
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For use cases where an index type measure is appropriate the following steps provide a standard treatment that is used in various domains:
* Aggregation of amounts or counts within interval
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* Binning of the temporal range of observation timestamps into intervals (e.g. hourly, daily, monthly etc)
* Application of standard [[Univariate Concentration Index]]
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* Aggregation of amounts or counts within each interval
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* Application of standard [[:Category:Univariate Concentration Index | Univariate Index]]
  
 
== See Also ==
 
== See Also ==
 
* [[Spatial Concentration]]
 
* [[Spatial Concentration]]
 
* [[Concentration]]
 
* [[Concentration]]
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* [[wikipedia:Scan statistic | Scan statistic]]
  
  
 
[[Category:Concentration Measurement]]
 
[[Category:Concentration Measurement]]

Latest revision as of 23:12, 14 June 2021

Definition

Temporal Concentration (also Temporal Clustering) describes dynamic (time dependent) phenomena where the occurrence (rate, frequency or other measured quantity) of events exhibits non-uniform characteristics

Models

The archetype of a temporal process that does not exhibit concentration or clustering of events is the Poisson process. A variety of other proposed point processes can be used to model temporal concentration.

A special class of point process that exhibits enhanced clustering is the Hawkes process (also known as a self-exciting counting process). It is a simple point process but whose conditional intensity depends on the previous even count (hence the occurence of an event may precipitate more events).

Measurement using Concentation Indexes

For use cases where an index type measure is appropriate the following steps provide a standard treatment that is used in various domains:

  • Binning of the temporal range of observation timestamps into intervals (e.g. hourly, daily, monthly etc)
  • Aggregation of amounts or counts within each interval
  • Application of standard Univariate Index

See Also