GLMM : draw graphs of mixture distributions.

01_preparation.py

%matplotlib inline 
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as st
from matplotlib import animation as ani
plt.style.use('ggplot')
plt.rc('text', usetex=True)

02_draw_graphs.py

n = 10000
s = 3

if s != 0:
    r = rd.normal(0, s, size=n)
else:
    r = np.zeros(n)
    
    
def logis(x):
    return 1./(1+np.exp(-x))
q = logis(r)
fig = plt.figure(figsize=(9,18))


plt.subplot(311)
xx = np.linspace(-10,10,500)
ytop = 3000
plt.ylim(0,ytop)
plt.xlim(-10,10)
plt.plot(xx, logis(xx)*ytop)
plt.title("Histgram of r. s={0:.3f}".format(s))
plt.hist(r,range=(-10,10), bins=31, color="lightblue")

plt.subplot(312)
plt.xlim(0, 1)
plt.ylim(0, 1700) 
plt.xticks(np.linspace(0,1,11))
plt.title("Histgram of q. s={0:.3f}".format(s))
plt.hist(q, color="lightgreen", bins=20)

plt.subplot(313)
res = np.zeros(9)
for f in q:
    res += np.array([st.binom.pmf(i, n=9, p=f) for i in range(9)])

plt.title("Sum of binomial histgram with various q. s={0:.3f}".format(s))
plt.bar(range(9), res, width=1, color="blue", alpha=0.5)

plt.show()

03_draw_animation.py

# Please see the following page for generating animation graph with Python
# http://qiita.com/kenmatsu4/items/573ca0733b192d919d0e

num_frame = 31
n = 10000
ss = np.array(range(num_frame))/30. * 3

def animate(nframe):
    global num_frame
    plt.clf()
    sys.stdout.write("{}, ".format(nframe))
    
    s = ss[nframe]
    
    if s != 0:
        r = rd.normal(0, s, size=n)
    else:
        r = np.zeros(n)

    def logis(x):
        return 1./(1+np.exp(-x))
    q = logis(r)
    
    plt.subplot(312)
    plt.xlim(0, 1)
    plt.ylim(0, 1700) 
    plt.xticks(np.linspace(0,1,11))
    plt.title("Histgram of q. s={0:.3f}".format(s))
    plt.hist(q, color="lightgreen", bins=20)
    
    plt.subplot(311)
    
    xx = np.linspace(-10,10,500)
    ytop = 3000
    plt.ylim(0,ytop)
    plt.xlim(-10,10)
    plt.plot(xx, logis(xx)*ytop)
    plt.title("Histgram of r. s={0:.3f}".format(s))
    plt.hist(r,range=(-10,10), bins=31, color="lightblue")
    
    plt.subplot(313)
    res = np.zeros(9)
    for f in q:
        res += np.array([st.binom.pmf(i, n=8, p=f) for i in range(9)])
    plt.title("Sum of binomial histgram with various q. s={0:.3f}".format(s))
    plt.bar(range(9), res, width=1, color="blue", alpha=0.5)
    plt.ylim(0,3000)


fig = plt.figure(figsize=(9,18))
anim = ani.FuncAnimation(fig, animate, frames=num_frame, blit=True)
anim.save('mix_poisson_norm.gif', writer='imagemagick', fps=3, dpi=64)