def show_poisson_views():
"""Show different views of a Poisson distribution"""
fig, ax = plt.subplots(3,1)
k = np.arange(25)
pd = stats.poisson(10)
C2_8_mystyle.set(12)
ax[0].plot(k, pd.pmf(k),'x-')
ax[0].set_title('Poisson distribition')
ax[0].set_xticklabels([])
ax[0].set_ylabel('PMF (X)')
ax[1].plot(k, pd.cdf(k))
ax[1].set_xlabel('X')
ax[1].set_ylabel('CDF (X)')
y = np.linspace(0,1,100)
ax[2].plot(y, pd.ppf(y))
ax[2].set_xlabel('X')
ax[2].set_ylabel('PPF (X)')
plt.tight_layout()
plt.show()
def KS_principle(inData):
'''Show the principle of the Kolmogorov-Smirnov test.'''
# CDF of normally distributed data
nd = stats.norm()
nd_x = np.linspace(-4, 4, 101)
nd_y = nd.cdf(nd_x)
# Empirical CDF of the sample data, which range for approximately 0 to 10
numPts = 50
lowerLim = 0
upperLim = 10
ecdf_x = np.linspace(lowerLim, upperLim, numPts)
ecdf_y = stats.cumfreq(data, numPts, (lowerLim, upperLim))[0]/len(inData)
#Add zero-point by hand
ecdf_x = np.hstack((0., ecdf_x))
ecdf_y = np.hstack((0., ecdf_y))
# Plot the data
sns.set_style('ticks')
sns.set_context('poster')
C2_8_mystyle.set(36)
plt.plot(nd_x, nd_y, 'k--')
plt.hold(True)
plt.plot(ecdf_x, ecdf_y, color='k')
plt.xlabel('X')
plt.ylabel('Cumulative Probability')
# For the arrow, find the start
ecdf_startIndex = np.min(np.where(ecdf_x >= 2))
arrowStart = np.array([ecdf_x[ecdf_startIndex], ecdf_y[ecdf_startIndex]])
nd_startIndex = np.min(np.where(nd_x >= 2))
arrowEnd = np.array([nd_x[nd_startIndex], nd_y[nd_startIndex]])
arrowDelta = arrowEnd - arrowStart
plt.arrow(arrowStart[0], arrowStart[1], 0, arrowDelta[1],
width=0.05, length_includes_head=True, head_length=0.02, head_width=0.2, color='k')
plt.arrow(arrowStart[0], arrowStart[1]+arrowDelta[1], 0, -arrowDelta[1],
width=0.05, length_includes_head=True, head_length=0.02, head_width=0.2, color='k')
outFile = 'KS_Example.png'
C2_8_mystyle.printout_plain(outFile)
def generate_probplot():
'''Generate a prob-plot for a chi2-distribution of sample data'''
# Define the skewed distribution
chi2 = stats.chi2(3)
# Generate the data
x = np.linspace(0,10, 100)
y = chi2.pdf(x)
np.random.seed(12345)
numData = 100
data = chi2.rvs(numData)
# Arrange subplots
sns.set_context('paper')
sns.set_style('white')
C2_8_mystyle.set(11)
fig, axs = plt.subplots(1,2)
# Plot distribution
axs[0].plot(x,y)
axs[0].set_xlabel('X')
axs[0].set_ylabel('PDF(X)')
axs[0].set_title('chi2(x), k=3')
sns.set_style('white')
x0, x1 = axs[0].get_xlim()
y0, y1 = axs[0].get_ylim()
axs[0].set_aspect((x1-x0)/(y1-y0))
#sns.despine()
# Plot probplot
plt.axes(axs[1])
stats.probplot(data, plot=plt)
x0, x1 = axs[1].get_xlim()
y0, y1 = axs[1].get_ylim()
axs[1].axhline(0, lw=0.5, ls='--')
axs[1].axvline(0, lw=0.5, ls='--')
axs[1].set_aspect((x1-x0)/(y1-y0))
#sns.despine()
C2_8_mystyle.printout_plain('chi2pp.png')
return(data)
'''
def main():
'''Demonstrate the generation of different statistical standard plots'''
# Univariate data -------------------------
# Generate data that are normally distributed
x = np.random.randn(500)
# Set the fonts the way I like them
sns.set_context('poster')
sns.set_style('ticks')
C2_8_mystyle.set(fs=32)
# Scatter plot
plt.scatter(np.arange(len(x)), x)
plt.xlim([0, len(x)])
# Save and show the data, in a systematic format
C2_8_mystyle.printout('scatterPlot.png', xlabel='x', ylabel='y', title='Scatter')
# Histogram
plt.hist(x)
C2_8_mystyle.printout('histogram_plain.png', xlabel='Data Values', ylabel='Frequency', title='Histogram, default settings')
plt.hist(x,25)
C2_8_mystyle.printout('histogram.png', xlabel='Data Values', ylabel='Frequency', title='Histogram, 25 bins')
# Cumulative probability density
numbins = 20
plt.plot(stats.cumfreq(x,numbins)[0])
C2_8_mystyle.printout('CumulativeFrequencyFunction.png', xlabel='Data Values', ylabel='CumFreq', title='Cumulative Frequncy')
# KDE-plot
sns.kdeplot(x)
C2_8_mystyle.printout('kde.png', xlabel='Data Values', ylabel='Density',
title='KDE_plot')
# Boxplot
# The ox consists of the first, second (middle) and third quartile
plt.boxplot(x, sym='*')
C2_8_mystyle.printout('boxplot.png', xlabel='Values', title='Boxplot')
plt.boxplot(x, sym='*', vert=False)
plt.title('Boxplot, horizontal')
plt.xlabel('Values')
plt.show()
# Errorbars
x = np.arange(5)
y = x**2
errorBar = x/2
plt.errorbar(x,y, yerr=errorBar, fmt='o', capsize=5, capthick=3)
plt.xlim([-0.2, 4.2])
plt.ylim([-0.2, 19])
C2_8_mystyle.printout('Errorbars.png', xlabel='Data Values', ylabel='Measurements', title='Errorbars')
# Violinplot
nd = stats.norm
data = nd.rvs(size=(100))
nd2 = stats.norm(loc = 3, scale = 1.5)
data2 = nd2.rvs(size=(100))
# Use pandas and the seaborn package for the violin plot
df = pd.DataFrame({'Girls':data, 'Boys':data2})
sns.violinplot(df)
C2_8_mystyle.printout('violinplot.png', title='Violinplot')
# Barplot
df = pd.DataFrame(np.random.rand(10, 4), columns=['a', 'b', 'c', 'd'])
df.plot(kind='bar', grid=False)
C2_8_mystyle.printout('barplot.png', title='Barplot')
# Grouped Boxplot
sns.set_style('whitegrid')
sns.boxplot(df)
C2_8_mystyle.set(fs=28)
C2_8_mystyle.printout('groupedBoxplot.png', title='sns.boxplot')
# Bivariate Plots
df2 = pd.DataFrame(np.random.rand(50, 4), columns=['a', 'b', 'c', 'd'])
df2.plot(kind='scatter', x='a', y='b', s=df['c']*300);
C2_8_mystyle.printout('bivariate.png')
# Pieplot
series = pd.Series(3 * np.random.rand(4), index=['a', 'b', 'c', 'd'], name='series')
oldPalette = sns.color_palette()
sns.set_palette("husl")
series.plot(kind='pie', figsize=(6, 6))
C2_8_mystyle.printout('piePlot.png', title='pie-plot')
sns.set_palette(oldPalette)
"miR-137" is a short non-coding RNA molecule that functions to regulate
the expression levels of other genes.
'''
# author: Thomas Haslwanter, date: Jun-2015
# Import standard packages
import matplotlib.pyplot as plt
import C2_8_mystyle as mystyle
# additional packages
from lifelines.datasets import load_waltons
from lifelines import KaplanMeierFitter
from lifelines.statistics import logrank_test
# Set my favorite font
mystyle.set()
# Load and show the data
df = load_waltons() # returns a Pandas DataFrame
print(df.head())
'''
T E group
0 6 1 miR-137
1 13 1 miR-137
2 13 1 miR-137
3 13 1 miR-137
4 19 1 miR-137
'''
T = df['T']
# author: Thomas Haslwanter, date: July-2015
# Import standard packages
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
import seaborn as sns
import C2_8_mystyle
x = np.logspace(-9,1,1001)+1e-9
lnd = stats.lognorm(2)
y = lnd.pdf(x)
sns.set_style('ticks')
C2_8_mystyle.set(18)
fig, axs = plt.subplots(1,2, sharey=True)
sns.set_context('poster')
axs[0].plot(x,y)
axs[0].set_xlim(-0.1,8)
axs[0].set_xlabel('x')
axs[0].set_ylabel('pdf(x)')
axs[1].plot(np.log(x), y)
axs[1].set_xlim(-12,5)
axs[1].set_xlabel('log(x)')
outFile = 'logNormal.png'
C2_8_mystyle.printout_plain(outFile)
# additional packages
import C2_8_mystyle
# Calculate the values
nd = stats.norm()
x = np.linspace(-3,3,100)
yp = nd.pdf(x)
y = nd.cdf(x)
x1 = np.linspace(-3, 1)
y1 = nd.pdf(x1)
# Make the plot
sns.set_context('paper')
sns.set_style('white')
C2_8_mystyle.set(12)
figs, axs = plt.subplots(1,2)
axs[0].plot(x,yp, 'k')
axs[0].fill_between(x1, y1, facecolor='#CCCCCC')
axs[0].text(0, 0.1, 'CDF(x)', family='cursive', fontsize=14, horizontalalignment='center', style='italic')
axs[0].set_xlabel('x')
axs[0].set_ylabel('PDF(x)')
sns.despine()
axs[1].plot(x, y, '#999999', lw=3)
axs[1].set_xlabel('x')
axs[1].set_ylabel('CDF(x)')
plt.vlines(0, 0, 1, linestyles='--')
sns.despine()
ax.xaxis.set_ticks([50,150,250])
ax.set_xticklabels(['Group1', 'Group2', 'Group3'])
ax.yaxis.set_ticks([])
ax.set_title(title)
grandMean = np.mean(groupMean)
ax.axhline(grandMean, color='#999999')
ax.plot([80, 220], [groupMean[1], groupMean[1]], '#999999')
ax.plot([80, 120], [groupMean[1]+0.2, groupMean[1]+0.2], '#999999')
ax.annotate('', xy=(210, grandMean), xytext=(210,groupMean[1]),
arrowprops=dict(arrowstyle='<->, head_width=0.1', facecolor='black'))
ax.annotate('', xy=(90, groupMean[1]), xytext=(90,groupMean[1]+0.2),
arrowprops=dict(arrowstyle='<->, head_width=0.1', facecolor='black'))
ax.text(210, (grandMean + groupMean[1])/2., '$SS_{Treatment}$', fontsize=36)
ax.text(90, groupMean[1]+0.1, '$SS_{Error}$', ha='right', fontsize=36)
if __name__ == '__main__':
centers = [5, 5.3, 4.7]
np.random.seed(123)
C2_8_mystyle.set(30)
fig = plt.figure()
ax = fig.add_subplot(111)
std = 0.1
numData = 100
show_fig(0.1, ax, 'Sum-Squares')
# Save and show
C2_8_mystyle.printout_plain('anova_annotated.png')
def simplePlots():
'''Demonstrate the generation of different statistical standard plots'''
# Univariate data -------------------------
# Make sure that always the same random numbers are generated
np.random.seed(1234)
# Generate data that are normally distributed
x = np.random.randn(500)
# Other graphics settings
sns.set(context='poster', style='ticks', palette=sns.color_palette('muted'))
# Set the fonts the way I like them
C2_8_mystyle.set(fs=32)
# Scatter plot
plt.scatter(np.arange(len(x)), x)
plt.xlim([0, len(x)])
# Save and show the data, in a systematic format
C2_8_mystyle.printout('scatterPlot.png', xlabel='Datapoints', ylabel='Values', title='Scatter')
# Histogram
plt.hist(x)
C2_8_mystyle.printout('histogram_plain.png', xlabel='Data Values',
ylabel='Frequency', title='Histogram, default settings')
plt.hist(x,25)
C2_8_mystyle.printout('histogram.png', xlabel='Data Values', ylabel='Frequency',
title='Histogram, 25 bins')
# Cumulative probability density
numbins = 20
plt.plot(stats.cumfreq(x,numbins)[0])
C2_8_mystyle.printout('CumulativeFrequencyFunction.png', xlabel='Data Values',
ylabel='CumFreq', title='Cumulative Frequency')
# KDE-plot
sns.kdeplot(x)
C2_8_mystyle.printout('kde.png', xlabel='Data Values', ylabel='Density',
title='KDE_plot')
# Boxplot
# The ox consists of the first, second (middle) and third quartile
plt.boxplot(x, sym='*')
C2_8_mystyle.printout('boxplot.png', xlabel='Values', title='Boxplot')
plt.boxplot(x, sym='*', vert=False)
plt.title('Boxplot, horizontal')
plt.xlabel('Values')
plt.show()
# Errorbars
x = np.arange(5)
y = x**2
errorBar = x/2
plt.errorbar(x,y, yerr=errorBar, fmt='o', capsize=5, capthick=3)
plt.xlim([-0.2, 4.2])
plt.ylim([-0.2, 19])
C2_8_mystyle.printout('Errorbars.png', xlabel='Data Values', ylabel='Measurements', title='Errorbars')
# Violinplot
nd = stats.norm
data = nd.rvs(size=(100))
nd2 = stats.norm(loc = 3, scale = 1.5)
data2 = nd2.rvs(size=(100))
# Use pandas and the seaborn package for the violin plot
df = pd.DataFrame({'Girls':data, 'Boys':data2})
sns.violinplot(df)
C2_8_mystyle.printout('violinplot.png', title='Violinplot')
# Barplot
# The font-size is set such that the legend does not overlap with the data
np.random.seed(1234)
C2_8_mystyle.set(20)
df = pd.DataFrame(np.random.rand(10, 4), columns=['a', 'b', 'c', 'd'])
df.plot(kind='bar', grid=False, color=sns.color_palette('muted'))
C2_8_mystyle.printout_plain('barplot.png')
C2_8_mystyle.set(28)
# Bivariate Plots
df2 = pd.DataFrame(np.random.rand(50, 3), columns=['a', 'b', 'c'])
df2.plot(kind='scatter', x='a', y='b', s=df2['c']*500);
plt.axhline(0, ls='--', color='#999999')
plt.axvline(0, ls='--', color='#999999')
C2_8_mystyle.printout('bivariate.png')
# Grouped Boxplot
sns.set_style('whitegrid')
sns.boxplot(df)
C2_8_mystyle.set(fs=28)
C2_8_mystyle.printout('groupedBoxplot.png', title='sns.boxplot')
sns.set_style('ticks')
# Pieplot
txtLabels = 'Cats', 'Dogs', 'Frogs', 'Others'
fractions = [45, 30, 15, 10]
offsets =(0, 0.05, 0, 0)
plt.pie(fractions, explode=offsets, labels=txtLabels,
autopct='%1.1f%%', shadow=True, startangle=90,
colors=sns.color_palette('muted') )
plt.axis('equal')
C2_8_mystyle.printout('piePlot.png', title=' ')
import C2_8_mystyle
def show_fig(std, ax, title):
'''Create a plot of normally distributed data in a given axis'''
for ii in range(3):
data = stats.norm(centers[ii], std).rvs(numData)
offset = ii*numData
ax.plot( offset+np.arange(numData), data, '.', ms=10)
ax.xaxis.set_ticks([50,150,250])
ax.set_xticklabels(['Group1', 'Group2', 'Group3'])
ax.set_title(title)
sns.despine()
if __name__ == '__main__':
# Set up the figure
sns.set_context('paper')
sns.set_style('whitegrid')
C2_8_mystyle.set(14)
# Create 2 plots of 3 different, normally distributed data groups, with different SDs
fig, axs = plt.subplots(1, 2)
centers = [5, 5.3, 4.7]
stds = [0.1, 2]
numData = 100
show_fig(0.1, axs[0], 'SD=0.1')
show_fig(2, axs[1], 'SD=2.0')
C2_8_mystyle.printout_plain('anova_oneway.png')
