mSPRT: Calculate mixture Sequential Probability Ratio Test

In shitoushan/mixtureSPRT: Mixture Sequential Probability Ratio Test

Description

Calculate mixture Sequential Probability Ratio Test

Usage

mSPRT(x, y, xpre = NULL, ypre = NULL, sigma, tau, theta = 0,
  distribution = "normal", alpha = 0.05, useCpp = F)

Arguments

x, y	Numeric vectors
xpre, ypre	Numeric vectors of pre-experiment data
sigma	Population standard deviation
tau	Mixture variance
theta	Hypothesised difference between x and y
distribution	The desired distribution.
alpha	Significance level
useCpp	Boolean. Use C++ for calculations? Useful for running many tests as it reduces runtime substantially

Value

The likelihood ratio

Details

With normal data and normal prior, the closed form solution of the probability ratio after n observations have been collected is:

\tilde{Λ}_n = √{\frac{2σ^2}{V_n + nτ^2}}\exp{≤ft(\frac{n^2τ^2(\bar{Y}_n - \bar{X}_n-θ_0)^2}{4σ2(2σ^2+nτ^2)}\right)}.

With Bernoulli data, the closed form solution is:

\tilde{Λ}_n = √{\frac{V_n}{V_n + nτ^2}}\exp{≤ft(\frac{n^2τ^2(\bar{Y}_n - \bar{X}_n-θ_0)^2}{2V_n(V_n+nτ^2)}\right)}.

References

Johari, R., Koomen, P., Pekelis, L. & Walsh, D. 2017, 'Peeking at A/B Tests: Why it matters, and what to do about it', ACM, , pp. 1517

shitoushan/mixtureSPRT documentation built on Sept. 29, 2021, 7:46 a.m.