Joint Inclusion Probabilities for Maximum Entropy (CPS) Sampling

Computes exact joint inclusion probabilities for Conditional Poisson Sampling (CPS), also known as Maximum Entropy sampling.

up_maxent_jip(pik, eps = 1e-06)

Arguments

pik

numeric vector of first-order inclusion probabilities.

eps

tolerance for boundary detection (default 1e-6).

Value

A symmetric N×N matrix of joint inclusion probabilities.

Details

Uses Aires' formula from Tillé (2006) Expression 5.20: $$\pi_{k\ell} = \frac{r_\ell \pi_k - r_k \pi_\ell}{r_\ell - r_k}$$ where \(r_k = \exp(\lambda_k)\).

References

Aires, N. (1999). Algorithms to find exact inclusion probabilities for conditional Poisson sampling. Methodology and Computing in Applied Probability, 4, 457-469.

Tillé, Y. (2006). Sampling Algorithms. Springer.

Examples

pik <- c(0.2, 0.3, 0.5)
pikl <- up_maxent_jip(pik)