Calculating Simple and One-Sided DP-UMP Tests

Calculating Simple and One-Sided DP-UMP Tests

umpLeft(theta, size, alpha, epsilon, delta)

umpRight(theta, size, alpha, epsilon, delta)

Arguments

theta	The success probability for each trial (parameter \(\theta\) in Binomial(n, \(\theta\)))
size	The number of trials in Binomial distribution (parameter n in Binomial(n, \(\theta\)))
alpha	Level of the tests
epsilon	Parameter \(\epsilon\) in \((\epsilon, \delta)\)-DP
delta	Parameter \(\delta\) in \((\epsilon, \delta)\)-DP

Value

A vector of one-sided DP-UMP tests

References

Awan, Jordan Alexander, and Aleksandra Slavkovic. 2020. "Differentially Private Inference for Binomial Data". Journal of Privacy and Confidentiality 10 (1). https://doi.org/10.29012/jpc.725.

See also

Calculating unbiased two-sided DP-UMP tests (UMPU) and asymptotically unbiased two-sided DP-UMP tests (umpuApprox)

Examples

#leftUMP
left <- umpLeft(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)

#rightUMP
right <- umpRight(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)

#plot
plot(left, type = "l", main = "One-sided DP UMP",
     xlab = "x", ylab = "Phi (Probability of rejecting the null hypothesis)")
lines(right, lty = 2, col = "blue")
legend("left", legend=c("Left UMP", "Right UMP"), col=c("black", "blue"), lty=1:2, lwd = 1.5)