# Bumps 0.7.6 documentation

## bumps.dream.gelman

# Source code for bumps.dream.gelman

    """
    Convergence test statistic from Gelman and Rubin, 1992.
    """

    from __future__ import division

    __all__ = ["gelman"]

    from numpy import var, mean, ones, sqrt

    def gelman(sequences, portion=0.5):
        """
        Calculates the R-statistic convergence diagnostic

        For more information please refer to: Gelman, A. and D.R. Rubin, 1992.
        Inference from Iterative Simulation Using Multiple Sequences,
        Statistical Science, Volume 7, Issue 4, 457-472.
        doi:10.1214/ss/1177011136
        """

        # Find the size of the sample
        chain_len, nchains, nvar = sequences.shape
        #print sequences[:20, 0, 0]

        # Only use the last portion of the sample
        chain_len = int(chain_len*portion)
        sequences = sequences[-chain_len:]

        if chain_len < 2:
            # Set the R-statistic to a large value
            r_stat = -2 * ones(nvar)
        else:
            # Step 1: Determine the sequence means
            mean_seq = mean(sequences, axis=0)

            # Step 1: Determine the variance between the sequence means
            b = chain_len * var(mean_seq, axis=0, ddof=1)

            # Step 2: Compute the variance of the various sequences
            var_seq = var(sequences, axis=0, ddof=1)

            # Step 2: Calculate the average of the within sequence variances
            w = mean(var_seq, axis=0)

            # Step 3: Estimate the target mean
            #mu = mean(mean_seq)

            # Step 4: Estimate the target variance (Eq. 3)
            sigma2 = ((chain_len - 1)/chain_len) * w + (1/chain_len) * b

            # Step 5: Compute the R-statistic
            r_stat = sqrt((nchains + 1)/nchains * sigma2 / w
                          - (chain_len-1)/nchains/chain_len)
            #par=2
            #print chain_len,b[par],var_seq[...,par],w[par],r_stat[par]

        return r_stat

    def test():
        from numpy import reshape, arange, transpose
        from numpy.linalg import norm
        # Targe values computed from octave:
        #    format long
        #    s = reshape([1:15*6*7],[15,6,7]);
        #    r = gelman(s,struct('n',6,'seq',7))
        s = reshape(arange(1.0, 15*6*7+1)**-2, (15, 6, 7), order='F')
        s = transpose(s, [0, 2, 1])
        target = [1.06169861367116, 2.75325774624905, 4.46256647696399,
                  6.12792266170178, 7.74538715553575, 9.31276519155232]
        r = gelman(s, portion=1)
        #print r
        #print "target", array(target), "\nactual", r
        assert norm(r-target) < 1e-14
        r = gelman(s, portion=0.1)
        assert norm(r - [-2, -2, -2, -2, -2, -2]) == 0

    if __name__ == "__main__":
        test()