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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def gelman_rubin(self, chain=None, threshold=0.05):
 r""" Runs the Gelman Rubin diagnostic on the supplied chains. Parameters chain : int|str, optional Which chain to run the diagnostic on. By default, this is `None`, which will run the diagnostic on all chains. You can also supply and integer (the chain index) or a string, for the chain name (if you set one). threshold : float, optional The maximum deviation permitted from 1 for the final value :math:`\hat{R}` Returns ------- float whether or not the chains pass the test Notes ----- I follow PyMC in calculating the Gelman-Rubin statistic, where, having :math:`m` chains of length :math:`n`, we compute .. math:: B = \frac{n}{m-1} \sum_{j=1}^{m} \left(\bar{\theta}_{.j} - \bar{\theta}_{..}\right)^2 W = \frac{1}{m} \sum_{j=1}^{m} \left[ \frac{1}{n-1} \sum_{i=1}^{n} \left( \theta_{ij} - \bar{\theta_{.j}}\right)^2 \right] where :math:`\theta` represents each model parameter. We then compute :math:`\hat{V} = \frac{n_1}{n}W + \frac{1}{n}B`, and have our convergence ratio :math:`\hat{R} = \sqrt{\frac{\hat{V}}{W}}`. We check that for all parameters, this ratio deviates from unity by less than the supplied threshold. """

        if chain is None:
            return np.all([self.gelman_rubin(k, threshold=threshold) for k in range(len(self.parent.chains))])

        index = self.parent._get_chain(chain)
        assert len(index) == 1, "Please specify only one chain, have %d chains" % len(index)
        chain = self.parent.chains[index[0]]

        num_walkers = chain.walkers
        parameters = chain.parameters
        name = chain.name
        data = chain.chain
        chains = np.split(data, num_walkers)
        assert num_walkers > 1, "Cannot run Gelman-Rubin statistic with only one walker"
        m = 1.0 * len(chains)
        n = 1.0 * chains[0].shape[0]
        all_mean = np.mean(data, axis=0)
        chain_means = np.array([np.mean(c, axis=0) for c in chains])
        chain_var = np.array([np.var(c, axis=0, ddof=1) for c in chains])
        b = n / (m - 1) * ((chain_means - all_mean)**2).sum(axis=0)
        w = (1 / m) * chain_var.sum(axis=0)
        var = (n - 1) * w / n + b / n
        v = var + b / (n * m)
        R = np.sqrt(v / w)

        passed = np.abs(R - 1) < threshold
        print("Gelman-Rubin Statistic values for chain %s" % name)
        for p, v, pas in zip(parameters, R, passed):
            param = "Param %d" % p if isinstance(p, int) else p
            print("%s: %7.5f (%s)" % (param, v, "Passed" if pas else "Failed"))
        return np.all(passed)