Calculating kernel-density estimate in parallel - parallel-processing

Question

I want to perform kernel-density estimate on a grid in parallel. There is some scaling involved and I can't figure out how to obtain the same results when performing the calculation on different threads.
To illustre this, I'm using an simple example from the scipy documentation.
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
def measure(n):
"Measurement model, return two coupled measurements."
m1 = np.random.normal(size=n)
m2 = np.random.normal(scale=0.5, size=n)
return m1+m2, m1-m2
m1, m2 = measure(2000)
xmin = m1.min()
xmax = m1.max()
ymin = m2.min()
ymax = m2.max()
kde_bandwith = 0.5
X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([X.ravel(), Y.ravel()])
values = np.vstack([m1, m2])
kernel = stats.gaussian_kde(values, bw_method=kde_bandwith)
Z = np.reshape(kernel.evaluate(positions).T, X.shape)
I'm performing the last two lines on n_split subsets of the data (in practice this would be performed on different thread but here I kept a simple loop for simplicity):
## split
n_split = 10
values_split = np.array_split(values, n_split, axis=1)
results = []
for v in values_split:
kernel_n = stats.gaussian_kde(v, bw_method=kde_bandwith)
Z_n = np.reshape(kernel_n.evaluate(positions).T, X.shape)
results.append(Z_n)
Z2 = np.sum(results, axis=0)
here I'm simply recombining the results from each subset of data by summing the Z_n of each subset together into Z2.
Finally, a simple code to compare the results: left is the original version, middle is the result obtain from combining the subsets, and right the difference between the two.
fig = plt.figure(figsize=(9,2), dpi=200)
ax1 = fig.add_subplot(1,3,1)
ax2 = fig.add_subplot(1,3,2)
ax3 = fig.add_subplot(1,3,3)
c1 = ax1.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,
extent=[xmin, xmax, ymin, ymax])
#ax1.plot(m1, m2, 'k.', markersize=2)
ax1.set_xlim([xmin, xmax])
ax1.set_ylim([ymin, ymax])
plt.colorbar(c1, shrink=0.6)
c2 = ax2.imshow(np.rot90(Z2), cmap=plt.cm.gist_earth_r,
extent=[xmin, xmax, ymin, ymax])
#ax2.plot(m1, m2, 'k.', markersize=2)
ax2.set_xlim([xmin, xmax])
ax2.set_ylim([ymin, ymax])
plt.colorbar(c2, shrink=0.6)
c3 = ax3.imshow(np.rot90(Z2-Z), cmap=plt.cm.gist_earth_r,
extent=[xmin, xmax, ymin, ymax])
ax3.plot(m1, m2, 'k.', markersize=0.1)
ax3.set_xlim([xmin, xmax])
ax3.set_ylim([ymin, ymax])
plt.colorbar(c3, shrink=0.6)
plt.show()
Notes: It looks like the magnitude of the KDE is n_split larger, but by simply normalizing with 1/n_split or even len(values_split)/len(values) (which in this case is equal), the results are not exactly the same, shown on the next figure as reference.