15 D analytical Gaussian

The desired analytical 15 D Gaussian example @matthew-pitkin @gregory.ashton @colm.talbot

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mentioned in issue #387 (closed)

Could you also add an example with the bimodal Gaussian? Like in LALInference you could set them to be 8 sigma apart around a mean of zero. You could just alter the above Likelihood class with the following __init__() and log_likelihood() methods:

def __init__(self, mean, cov):
    super(AnalyticalMultidimensionalCovariantGaussian, self).__init__(parameters=dict())
    self.cov = np.array(cov)
    self.sigma = np.sqrt(np.diag(self.cov))
    self.mean1 = np.array(mean) + 4. * self.sigma
    self.mean2 = np.array(mean) - 4. * self.sigma
    self.pdf1 = multivariate_normal(mean=self.mean1, cov=self.cov)
    self.pdf2 = multivariate_normal(mean=self.mean2, cov=self.cov)

def log_likelihood(self):
    x = np.array([self.parameters["x{0}".format(i)] for i in range(self.dim)])
    return -np.log(2) + self.pdf1.logpdf(x) + self.pdf2.logpdf(x)

@moritz.huebner I've run the script myself now and it all looks good. I get the right evidence and everything!

@matthew-pitkin Nice, I will polish this a bit up then before we merge it in.

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• b0012448 - Some preliminary changes
• 87dffbeb - Added bimodal distribution and cleaned up some stuff

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• 7eec0659 - Reduced prior size

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• dd069b53 - Moved log likelihood calculation into log space

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Hi @moritz.huebner, this all looks good to me, so I'm happy to approve this. I noticed on the review page, that for the bimodal Gaussian one of the modes seems to be slightly more favoured than the other. Could you try re-running with a higher number of live points to see if that evens out the modes a bit more?

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mentioned in commit c3eec19b