PoissonBinomial: Specify a model based on a Poisson-binomial mixture.

In StatisticsNZ/demest: Bayesian Demographic Estimation and Forecasting

Specify a model based on a Poisson-binomial mixture.

Description

Specify a model of the form

y_i = U_i + V_i

U_i \sim Poisson((1-p) n_i)

V_i \sim binomial(n_i, p)

.

Usage

PoissonBinomial(prob)

Arguments

prob	The probability that a person or event is correctly enumerated. A number between 0 and 1, and typically close to 1.

Details

The model is useful mainly as a way of representing the relationship between a true set of counts (the n_i) and measurements of those counts (the y_i.) For instance, n_i could be true counts of births, and y_i could be births recorded in an accurate births registration system.

Subscript i denotes a cell within a classification defined by variables such as age, sex, and time. For instance cell i might be 30-34 year old females in 2020.

Higher values of p imply greater accuracy; p can be interpreted as the probability that a person or event is enumerated in the correct cell i.

One limitation of the model is that it does not allow for the possibility that y_i > 0 when n_i = 0. In other words, it does not allow for the possibility that a person or event is erroneously enumerated in a cell that has no people or events.

Value

An object of class SpecLikelihood.

See Also

PoissonBinomial is typically used as part of a call to function Model.

Examples

PoissonBinomial(prob = 0.98)

StatisticsNZ/demest documentation built on Nov. 2, 2023, 7:56 p.m.