Poisson sampling

{{Short description|Survey methodology process}}

{{distinguish|Poisson disk sampling}}

In survey methodology, Poisson sampling (sometimes denoted as PO sampling{{rp|61}}) is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample.{{cite book

|title = Model Assisted Survey Sampling

|author=Carl-Erik Sarndal |author2=Bengt Swensson |author3=Jan Wretman

|isbn= 978-0-387-97528-3

|year = 1992

}}{{rp|85}}Ghosh, Dhiren, and Andrew Vogt. "Sampling methods related to Bernoulli and Poisson Sampling." Proceedings of the Joint Statistical Meetings. American Statistical Association Alexandria, VA, 2002. [http://www.asasrms.org/Proceedings/y2002/Files/JSM2002-001080.pdf (pdf)]

Each element of the population may have a different probability of being included in the sample ($\backslash pi\_i$). The probability of being included in a sample during the drawing of a single sample is denoted as the first-order inclusion probability of that element ($p\_i$). If all first-order inclusion probabilities are equal, Poisson sampling becomes equivalent to Bernoulli sampling, which can therefore be considered to be a special case of Poisson sampling.