Multivariate Normal CDF in Python using scipy

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不思量自难忘° 2020-12-06 01:36

In order to calculate the CDF of a multivariate normal, I followed this example (for the univariate case) but cannot interpret the output produced by scipy:

         


        
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  • 2020-12-06 01:46

    If you don't care about performance (i.e. perform it only occasionally), then you can create the multivariate normal pdf using multivariate_normal, and then calculate the cdf by integrate.nquad

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  • 2020-12-06 02:05

    The scipy multivariate_normal from v1.1.0 has a cdf function built in now:

    from scipy.stats import multivariate_normal as mvn
    import numpy as np
    
    mean = np.array([1,5])
    covariance = np.array([[1, 0.3],[0.3, 1]])
    dist = mvn(mean=mean, cov=covariance)
    print("CDF:", dist.cdf(np.array([2,4])))
    
    CDF: 0.14833820905742245
    

    Documentation for v1.4.1 can be found here.

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  • 2020-12-06 02:07

    After searching a lot, I think this blog entry by Noah H. Silbert describes the only readymade code from a standard library that can be used for computing the cdf for a multivariate normal in Python. Scipy has a way to do it but as mentioned in the blog, it is difficult to find. The approach is based on a paper by Alan Genz’s.

    From the blog, this is how it works.

    from scipy.stats import mvn
    import numpy as np
    low = np.array([-10, -10])
    upp = np.array([.1, -.2])
    mu = np.array([-.3, .17])
    S = np.array([[1.2,.35],[.35,2.1]])
    p,i = mvn.mvnun(low,upp,mu,S)
    print p
    
    0.2881578675080012
    
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