63 lines
2.2 KiB
Python
63 lines
2.2 KiB
Python
import numpy as np
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import scipy.stats as st
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import matplotlib.pyplot as plt
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from plotstyle import *
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rng = np.random.RandomState(637281)
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# generate correlated data:
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n = 200
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a = 0.2
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x = rng.randn(n);
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y = rng.randn(n) + a*x;
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#x = rng.exponential(1.0, n);
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#y = rng.exponential(2.0, n) + a*x;
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rd = np.corrcoef(x, y)[0, 1]
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# permutation:
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nperm = 1000
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rs = []
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for i in range(nperm) :
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xr=rng.permutation(x)
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yr=rng.permutation(y)
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rs.append( np.corrcoef(xr, yr)[0, 1] )
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# pdf of the correlation coefficients:
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h, b = np.histogram(rs, 20, density=True)
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# significance:
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rq = np.percentile(rs, 95.0)
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print('Measured correlation coefficient = %.2f, correlation coefficient at 95%% percentile of bootstrap = %.2f' % (rd, rq))
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ra = 1.0-0.01*st.percentileofscore(rs, rd)
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print('Measured correlation coefficient %.2f is at %.4f percentile of bootstrap' % (rd, ra))
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rp, ra = st.pearsonr(x, y)
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print('Measured correlation coefficient %.2f is at %.4f percentile of test' % (rp, ra))
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fig, ax = plt.subplots(figsize=cm_size(figure_width, 1.2*figure_height))
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fig.subplots_adjust(**adjust_fs(left=4.0, bottom=2.7, right=0.5, top=1.0))
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ax.annotate('Measured\ncorrelation\nis significant!',
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xy=(rd, 1.1), xycoords='data',
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xytext=(rd, 2.2), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0),
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connectionstyle="angle3,angleA=10,angleB=80") )
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ax.annotate('95% percentile',
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xy=(0.14, 0.9), xycoords='data',
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xytext=(0.2, 4.0), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.1,0.0),
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connectionstyle="angle3,angleA=30,angleB=70") )
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ax.annotate('Distribution of\nuncorrelated\nsamples',
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xy=(-0.08, 3.6), xycoords='data',
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xytext=(-0.22, 5.0), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.0),
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connectionstyle="angle3,angleA=150,angleB=100") )
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ax.bar(b[:-1], h, width=b[1]-b[0], **fsC)
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ax.bar(b[:-1][b[:-1]>=rq], h[b[:-1]>=rq], width=b[1]-b[0], **fsB)
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ax.plot( [rd, rd], [0, 1], **lsA)
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ax.set_xlim(-0.25, 0.35)
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ax.set_xlabel('Correlation coefficient')
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ax.set_ylabel('Probability density of H0')
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plt.savefig('permutecorrelation.pdf')
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