Poissonsäie

Poissonsäie is a term used in probability theory and applied statistics to describe a sieve-like thinning of a Poisson process. In its simplest form, events from a homogeneous Poisson process with rate λ are examined sequentially, and each event is kept or discarded according to a predefined rule. The resulting set of retained events is referred to as the thinned process.

Formally, if each event is kept independently with probability p (which may be constant or a function of time), the retained events constitute a Poisson process with rate λ' = λ·p when p is constant, or a time-varying rate λ'(t) = λ·p(t) when p depends on time. This thinning property is a standard result in Poisson process theory and is widely used in simulations and modeling to represent selective sampling or sensor reliability.

Variants of Poissonsäie include independent thinning, where retention decisions are independent across events, and dependent thinning, where the decision to retain an event may depend on previous events or marks associated with events. Dependent thinning can produce processes that are no longer Poisson, requiring more complex analysis.

Applications of the concept span queuing theory, telecommunications, reliability engineering, ecological sampling, and Monte Carlo simulations. It provides a mathematically tractable way to model interventions, sensor limitations, or selective observation within a Poisson framework.

Etymology and usage: the name combines the Poisson lineage (in reference to Poisson processes) with a sieve-like metaphor. The term is not universally standardized in English-language texts and appears mainly in German-language discussions and some informal expositions. See also Poisson process, thinning of Poisson processes, and Poisson point processes.