89 lines
3.0 KiB
Python
89 lines
3.0 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.gridspec as gridspec
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from plotstyle import *
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fig = plt.figure(figsize=cm_size(figure_width, 1.8*figure_height))
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spec = gridspec.GridSpec(nrows=2, ncols=2, hspace=0.6,
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**adjust_fs(fig, left=5.5))
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# the data:
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n = 40
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rng = np.random.RandomState(54637281)
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sigma = 0.5
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rmu = 2.0
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xd = rng.randn(n)*sigma+rmu
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# and possible pdfs:
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x = np.arange(0.0, 4.0, 0.01)
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mus = [1.5, 2.0, 2.5]
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g=np.zeros((len(x), len(mus)))
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for k, mu in enumerate(mus) :
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g[:,k] = np.exp(-0.5*((x-mu)/sigma)**2.0)/np.sqrt(2.0*np.pi)/sigma
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# plot it:
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ax = fig.add_subplot(spec[0, :])
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ax.set_xlim(0.5, 3.5)
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ax.set_ylim(-0.02, 0.85)
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ax.set_xticks(np.arange(0, 5))
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ax.set_yticks(np.arange(0, 0.9, 0.2))
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ax.set_xlabel('x')
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ax.set_ylabel('Prob. density')
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s = 1
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for mu in mus :
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r = 5.0*rng.rand()+2.0
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cs = 'angle3,angleA={:.0f},angleB={:.0f}'.format(90+s*r, 90-s*r)
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s *= -1
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ax.annotate('', xy=(mu, 0.02), xycoords='data',
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xytext=(mu, 0.75), textcoords='data',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5),
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connectionstyle=cs), zorder=10)
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if mu > rmu :
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ax.text(mu-0.1, 0.04, '?', zorder=10, ha='right')
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else :
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ax.text(mu+0.1, 0.04, '?', zorder=10)
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for k, ls in enumerate([lsCm, lsBm, lsDm]) :
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ax.plot(x, g[:,k], zorder=5, **ls)
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ax.plot(xd, 0.05*rng.rand(len(xd))+0.2, zorder=10, **psAm)
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# likelihood:
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thetas=np.arange(1.5, 2.6, 0.01)
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ps=np.zeros((len(xd),len(thetas)));
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for i, theta in enumerate(thetas) :
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ps[:,i]=np.exp(-0.5*((xd-theta)/sigma)**2.0)/np.sqrt(2.0*np.pi)/sigma
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p=np.prod(ps,axis=0)
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# plot it:
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ax = fig.add_subplot(spec[1, 0])
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ax.set_xlabel(r'Parameter $\mu$')
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ax.set_ylabel('Likelihood')
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ax.set_xticks(np.arange(1.6, 2.5, 0.4))
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ax.annotate('Maximum',
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xy=(2.0, 5.5e-11), xycoords='data',
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xytext=(1.0, 1.1), textcoords='axes fraction', ha='right',
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arrowprops=dict(arrowstyle="->", relpos=(0.0,0.5),
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connectionstyle="angle3,angleA=10,angleB=70"))
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ax.annotate('',
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xy=(2.0, 0), xycoords='data',
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xytext=(2.0, 5e-11), textcoords='data',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5),
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connectionstyle="angle3,angleA=90,angleB=80"))
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ax.plot(thetas, p, **lsAm)
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ax = fig.add_subplot(spec[1, 1])
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ax.set_xlabel(r'Parameter $\mu$')
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ax.set_ylabel('Log-Likelihood')
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ax.set_ylim(-50,-20)
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ax.set_xticks(np.arange(1.6, 2.5, 0.4))
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ax.set_yticks(np.arange(-50, -19, 10.0))
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ax.annotate('Maximum',
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xy=(2.0, -23), xycoords='data',
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xytext=(1.0, 1.1), textcoords='axes fraction', ha='right',
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arrowprops=dict(arrowstyle="->", relpos=(0.0,0.5),
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connectionstyle="angle3,angleA=10,angleB=70"))
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ax.annotate('',
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xy=(2.0, -50), xycoords='data',
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xytext=(2.0, -26), textcoords='data',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5),
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connectionstyle="angle3,angleA=80,angleB=100"))
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ax.plot(thetas,np.log(p), **lsAm)
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plt.savefig('mlemean.pdf')
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