Provides functionality for performing multinomial tests using monte carlo simulation
This library contain python code that can be used to test whether a given set of observations are likely to be drawn from a multinomial distribution with a given set of parameters (probabilities for each case). The test is done using Monte Carlo methods. A bunch of random samples from the hypothesised distribution is drawn and the probability of each sample is calculated. These are all compared to the probability of the sample under test. The p-value of the null-hypothesis (that the sample comes from the distribution) is simply the fraction of random samples with probability smaller than the sample under test.
The library is inspired by met, which achieve the same objective as mmct, but does so by painstakingly enumerating every possible case for the given multinomial distribution and calculating the p-value exactly. While this is certainly preferable, it becomes very slow very quickly, so for performing many tests or tests with a large parameter space, a monte carlo approximation may be good enough. mmct has also drawn inspiration from the XNomial package, which performs an identical task in the R programming language.
The package is most easlily installed via pip:
pip install mmct
The source code is also available on GitHub and is free for use and modification: mmct on GitHub
When the package has been installed, a test can be performed following the example below, in which we test whether a set of dice rolls could have been generated from rolling two fair dice 20 times and adding the eyes:
import mmct
import numpy as np
# Eyes 2 3 4 5 6 7 8 9 10 11 12
x = np.array([0, 0, 2, 4, 5, 2, 3, 1, 0, 1, 2])
# Hypothsised probabilities:
p = np.array([1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36])
# Initialise tester:
t = mmct.mt_tester() # Use the multithreaded tester class
# Set number of Monte Carlo samples to generate
t.n_samples = 100000
pval = t.do_test(x,p)
The result of the test will of course vary (unless the random simulator is seeded), but should in general result in a p-value around 0.34, i.e. we cannot reject the hypothesis that the numbers above are taken from a fair dice rolling (which they actually are).