msprt

Python mSPRT Package:

This package provides a Python implementation for calculating the Mixture Sequential Probability Ratio Test (mSPRT).

mSPRT is a statistical hypothesis test that can be used to decide if a observed data supports one of two hypotheses, based on a sequence of independent and identically distributed observations.

Main functionalities:

• Calculating mixture variance

$$ \tau^2 = \sigma^2 \frac{\Phi(-b)}{\frac{1}{b}\phi(b)-\Phi(-b)} $$

• Calculating test statistic for normal distribution

$$ \tilde{\Lambda}_n = \sqrt{\frac{2\sigma^2}{V_n + n\tau^2}}\exp\left(\frac{n^2\tau^2(\bar{Y}_n - \bar{X}_n-\theta_0)^2}{4\sigma^2(2\sigma^2+n\tau^2)}\right). $$

• Calculating test statistic for Bernoulli distribution

$$ \tilde{\Lambda}_n = \sqrt{\frac{V_n}{V_n + n\tau^2}}\exp{\left(\frac{n^2\tau^2(\bar{Y}_n - \bar{X}_n-\theta_0)^2}{2V_n(V_n+n\tau^2)}\right)} $$

Installation:

The mSPRT package can be easily installed using pip:

pip install msprt

Pre-requisite

Python >=3.10;<3.13

Dependencies:

The mSPRT package depends on the following Python libraries:

• Numpy
• Scipy
• Matplotlib

These dependencies can also be easily installed using pip:

pip install numpy scipy matplotlib

How to Use:

First, import the mSPRT package:

import numpy as np
from msprt import msprt

Then, prepare the two sample lists that you want to compare.

np.random.seed(42)
n = 500
x = np.random.normal(0, 1, n)
y = np.random.normal(0.2, 1, n)

Next, call the msprt object with observation lists, along with the parameters for the mSPRT test, such as the alpha and the theta values (by default it assumes you are using a normal distribution and alpha is set to 0.05).

result = msprt(x=x, y=y, sigma=1.0)
print(result)

If you want to use a Bernoulli distribution, specify it as such:

result = msprt(x=x, y=y, theta=0.5, distribution='bernoulli')
print(result)

To plot the results, use the plot method:

result.plot()

For detailed information about each parameter, please refer to the comments in the source code.

Contact:

If you find any problems with the implementation, you can leave the ticket on Github.

mSPRT GitHub Page

License:

This project is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation. See the LICENSE file for more information.

References (real heroes)

• Johari, R., Pekelis, L., & Walsh, D. J. (2019). Always Valid Inference: Bringing Sequential Analysis to A/B Testing. arXiv:1512.04922 [math.ST]. Link to the paper
• The R and C++ implementations of the paper are available in the GitHub repository maintained by Erik Stenberg: GitHub Repository.