Scientific Plotting with Matplotlib

We require plots, charts and other statistical graphics for the written communication of quantitative ideas.

They allow us to more easily convey relationships and reveal deviations from patterns.

Gelman and Unwin 2011:

A well-designed graph can display more information than a table of the same size, and more information than numbers embedded in text. Graphical displays allow and encourage direct visual comparisons.

Matplotlib is an excellent 2D and 3D graphics library for generating scientific figures in Python. Some of the many advantages of this library includes:

• Easy to get started
• Support for $\LaTeX$ formatted labels and texts
• Great control of every element in a figure, including figure size and DPI.
• High-quality output in many formats, including PNG, PDF, SVG, EPS.
• GUI for interactively exploring figures and support for headless generation of figure files (useful for batch jobs).

One of the of the key features of matplotlib that I would like to emphasize, and that I think makes matplotlib highly suitable for generating figures for scientific publications is that all aspects of the figure can be controlled programmatically. This is important for reproducibility, convenient when one need to regenerate the figure with updated data or changes its appearance.



In [ ]:

%matplotlib inline
import matplotlib.pyplot as plt



MATLAB-like API

As its name suggests, matplotlib is designed to compatible with MATLAB's plotting functions, so it is easy to get started with if you are familiar with MATLAB.

Example

Let's import some data and plot a simple figure with the MATLAB-like plotting API.



In [ ]:

import numpy as np

rain = np.genfromtxt('../data/nashville_precip.txt', delimiter='\t',
names=True, missing_values='NA')




In [ ]:

rain[:3]




In [ ]:

x = rain['Year']
y = rain['Jan']




In [ ]:

plt.figure()
plt.plot(x, y, 'r')
plt.xlabel('Year')
plt.ylabel('Rainfall')
plt.title('January rainfall in Nashville')



It is straightforward to customize plotting symbols and create subplots.



In [ ]:

plt.figure(figsize=(14,6))
plt.subplot(1,2,2)
plt.plot(x, y, 'r--')
plt.subplot(1,2,1)
plt.plot(x, rain['Feb'], 'g*-')



Exercise

Plot the two series on the same axes, and use a legend to label the series. (Hint: you must first give the original plot a label)



In [ ]:



While the MATLAB-like API is easy and convenient, it is worth learning matplotlib's object-oriented plotting API. It is remarkably powerful and for advanced figures, with subplots, insets and other components it is very nice to work with.

Object-oriented API

The main idea with object-oriented programming is to have objects with associated methods and functions that operate on them, and no object or program states should be global.

To use the object-oriented API we start out very much like in the previous example, but instead of creating a new global figure instance we store a reference to the newly created figure instance in the fig variable, and from it we create a new axis instance axes using the add_axes method in the Figure class instance fig.



In [ ]:

fig = plt.figure()

# left, bottom, width, height (range 0 to 1)
# as fractions of figure size
axes = fig.add_axes([0.1, 0.1, 0.8, 0.8])

axes.plot(x, y, 'r', label='rainfall')

axes.set_xlabel('Year')
axes.set_ylabel('Rainfall')



Although a little bit more code is involved, the advantage is that we now have full control of where the plot axes are place, and we can easily add more than one axis to the figure.



In [ ]:

fig = plt.figure()

axes1 = fig.add_axes([0.1, 0.1, 0.9, 0.9]) # main axes
axes2 = fig.add_axes([0.65, 0.65, 0.3, 0.3]) # inset axes

# main figure
axes1.plot(x, y, 'r')
axes1.set_xlabel('Year')
axes1.set_ylabel('Rainfall')
axes1.set_title('January rainfall in Nashville');

# insert
axes2.plot(x, np.log(y), 'g')
axes2.set_title('Log rainfall');



If we don't care to be explicit about where our plot axes are placed in the figure canvas, then we can use one of the many axis layout managers in matplotlib, such as subplots.



In [ ]:

fig, axes = plt.subplots(nrows=4, ncols=1)

months = rain.dtype.names[1:]

for i,ax in enumerate(axes):
ax.plot(x, rain[months[i]], 'r')
ax.set_xlabel('Year')
ax.set_ylabel('Rainfall')
ax.set_title(months[i])



That was easy, but it's not so pretty with overlapping figure axes and labels, right?

We can deal with that by using the fig.tight_layout method, which automatically adjusts the positions of the axes on the figure canvas so that there is no overlapping content:



In [ ]:

fig, axes = plt.subplots(nrows=4, ncols=1, figsize=(10,10))

months = rain.dtype.names[1:]

for i,ax in enumerate(axes):
ax.plot(rain['Year'], rain[months[i]], 'r')
ax.set_xlabel('Year')
ax.set_ylabel('Rainfall')
ax.set_title(months[i])

fig.tight_layout()



Exercise

Create a 2x2 grid of plots, rather than a single column. Think about how you would iterate over the axes in this case.



In [ ]:



Manipulating figure attributes

Matplotlib allows the aspect ratio, DPI and figure size to be specified when the Figure object is created, using the figsize and dpi keyword arguments. figsize is a tuple with width and height of the figure in inches, and dpi is the dot-per-inch (pixel per inch). To create a figure with size 800 by 400 pixels we can do:



In [ ]:

fig = plt.figure(figsize=(8,4), dpi=100)



The same arguments can also be passed to layout managers, such as the subplots function.



In [ ]:

fig, axes = plt.subplots(figsize=(12,3))

axes.plot(x, y, 'r')
axes.set_xlabel('Year')
axes.set_ylabel('Rainfall')



Saving figures

To save a figure a file we can use the savefig method in the Figure class.



In [ ]:

fig.savefig("jan_rainfall.png", format='jpg')



Notice that the graphic file format is inferred from the extension of the file name (though there is an optional format argument).

Here we can also optionally specify the DPI, and chose between different output formats.



In [ ]:

fig.savefig("jan_rainfall.png", dpi=200)




In [ ]:

fig.savefig("jan_rainfall.svg")



Matplotlib can generate high-quality output in a number formats, including:

• PNG
• JPG
• EPS
• SVG
• PDF

Legends, labels and titles

Now that we covered the basics of how to create a figure canvas and adding axes instances to the canvas, let's look at how decorate a figure with titles, axis labels and legends:

Figure titles

A title can be added to each axis instance in a figure. To set the title use the set_title method in the axes instance:



In [ ]:

ax.set_title("January rainfall")



Axis labels

Similarly, using the methods set_xlabel and set_ylabel we can set the labels of the X and Y axes:



In [ ]:

ax.set_xlabel("Year")
ax.set_ylabel("Rainfall")



Legends

Legends to curves in a figure can be added in two ways. First method is to use the legend method of the axis object and pass a list/tuple of legend texts for the curves that have previously been added:



In [ ]:

ax.legend(["Jan", "Feb"]);



A more robust method for associating labels with plots is to use the label keyword argument when plots a other objects are added to the figure, and then using the legend method without arguments to add the legend.



In [ ]:

ax.plot(x, rain['Jan'], label="Jan")
ax.plot(x, rain['Feb'], label="Feb")
ax.legend()



The advantage with this method is that if curves are added or removed from the figure, the legend is automatically updated accordingly.

The legend function takes and optional keywork argument loc that can be used to specify where in the figure the legend is to be drawn. The allowed values of loc are numerical codes for the various places the legend can be drawn.



In [ ]:

ax.legend(loc=0) # let matplotlib decide the optimal location
ax.legend(loc=1) # upper right corner
ax.legend(loc=2) # upper left corner
ax.legend(loc=3) # lower left corner
ax.legend(loc=4) # lower right corner



The following figure show how to use the figure title, axis labels and legends described above:



In [ ]:

fig, ax = plt.subplots()

ax.plot(x, rain['Jan'], label="Jan")
ax.plot(x, rain['Aug'], label="Aug")
ax.set_xlabel('Year')
ax.set_ylabel('Rainfall')
ax.legend(loc=1); # upper left corner



Text formatting

Matplotlib has great support for $\LaTeX$. All we need to do is to use dollar signs encapsulate $\LaTeX$ in the text, just as with Markdown and MathJax.

In order to properly process $\LaTeX$ commands, which begin with a backslash, we must specify the $\LaTeX$ code as a raw string, by prepending the string with an "r". This is because the backslash is interpreted by Python as the escape code character. For example, rather than "\alpha" we use r"\alpha".



In [ ]:

import scipy.stats as stats
fig, ax = plt.subplots()

x = np.linspace(-3, 3, 100)
y1 = stats.distributions.norm.pdf(x)
ax.plot(x, y1, label=r"$\sigma=1$")
y2 = stats.distributions.norm.pdf(x, scale=0.5)
ax.plot(x, y2, label=r"$\sigma=0.5$")
ax.set_xlabel('x', fontsize=18)
ax.set_ylabel('f(x)', fontsize=18)
ax.set_title('Normal distributions')
ax.legend(loc=2); # upper left corner



We can also change the global font size and font family, which applies to all text elements in a figure (tick labels, axis labels and titles, legends, etc.):



In [ ]:

import matplotlib as mpl
# Update the matplotlib configuration parameters:
mpl.rcParams.update({'font.size': 18,
'font.family': 'serif'})




In [ ]:

fig, ax = plt.subplots()

x = np.linspace(-3, 3, 100)
y1 = stats.distributions.norm.pdf(x)
ax.plot(x, y1, label=r"$\sigma=1$")
y2 = stats.distributions.norm.pdf(x, scale=0.5)
ax.plot(x, y2, label=r"$\sigma=0.5$")
ax.set_xlabel('x', fontsize=18)
ax.set_ylabel('f(x)', fontsize=18)
ax.set_title('Normal distributions')
ax.legend(loc=2); # upper left corner




In [ ]:

# restore
mpl.rcParams.update({'font.size': 12, 'font.family': 'sans'})



A covenient approach for temporarily changing plotting options is to use a context manager:



In [ ]:

with mpl.rc_context(rc={'font.family': 'serif', 'font.weight': 'bold', 'font.size': 8}):
fig = plt.figure(figsize=(6,3))
ax1.set_xlabel('some random numbers')
ax1.set_ylabel('more random numbers')
ax1.set_title("Random scatterplot")
plt.plot(np.random.normal(size=100), np.random.normal(size=100), 'r.')
plt.hist(np.random.normal(size=100), bins=15)
ax2.set_xlabel('sample')
ax2.set_ylabel('cumulative sum')
ax2.set_title("Normal distrubution")
plt.tight_layout()
plt.savefig("normalvars.png", dpi=150)



Line and marker styles

Colors

matplotlib uses a convenient MATLAB-like shorthand for specifying line and marker attributes for plot. For example, b.- specifies a blue line with dot markers.



In [ ]:

fig, ax = plt.subplots()
ax.plot(x, y1, 'b:') # blue dotted line
ax.plot(x, y2, 'g--') # green dashed line



Exercise

Change the green series above to have a magenta dash-dot line.

If we want a broader range of colors, they can be specified by their name or RGB hex code using the color keyword. An alpha value can also be specified.



In [ ]:

fig, ax = plt.subplots()

ax.plot(x, y1, color="red", alpha=0.1) # faint red
ax.plot(x, y2, color="#15cc55")        # RGB hex code for a greenish color



Line and marker styles

To change the line width we can use the linewidth (or lw) keyword argument, and the line style can be selected using the linestyle (or ls) keyword arguments:



In [ ]:

fig, ax = plt.subplots(figsize=(12,6))

x = np.linspace(0, 10, 10)

ax.plot(x, x+1, color="blue", linewidth=0.25)
ax.plot(x, x+2, color="blue", linewidth=0.50)
ax.plot(x, x+3, color="blue", linewidth=1.00)
ax.plot(x, x+4, color="blue", linewidth=2.00)

# possible linestype options ‘-‘, ‘–’, ‘-.’, ‘:’, ‘steps’
ax.plot(x, x+5, color="red", lw=2, linestyle='-')
ax.plot(x, x+6, color="red", lw=2, ls='-.')
ax.plot(x, x+7, color="red", lw=2, ls=':')

# custom dash
line, = ax.plot(x, x+8, color="black", lw=1.50)
line.set_dashes([5, 10, 15, 10]) # format: line length, space length, ...

# possible marker symbols: marker = '+', 'o', '*', 's', ',', '.', '1', '2', '3', '4', ...
ax.plot(x, x+ 9, color="green", lw=2, ls=':', marker='+')
ax.plot(x, x+10, color="green", lw=2, ls=':', marker='o')
ax.plot(x, x+11, color="green", lw=2, ls=':', marker='s')
ax.plot(x, x+12, color="green", lw=2, ls=':', marker='1')

# marker size and color
ax.plot(x, x+13, color="purple", lw=1, ls='-', marker='o', markersize=2)
ax.plot(x, x+14, color="purple", lw=1, ls='-', marker='o', markersize=4)
ax.plot(x, x+15, color="purple", lw=1, ls='-', marker='o', markersize=8,
markerfacecolor="red")
ax.plot(x, x+16, color="purple", lw=1, ls='-', marker='s', markersize=8,
markerfacecolor="yellow", markeredgewidth=2, markeredgecolor="blue");



Control over axis apperance

The appearance of the axes is an important aspect of a figure that we often need to modify to make a publication quality graphics. We need to be able to control where the ticks and labels are placed, modify the font size and possibly the labels used on the axes.

Plot range

We can specify the axis range using the set_ylim and set_xlim methods of the axis object, or axis('tight') for automatrically setting axes ranges.

Exercise

In the figure below, give the second set of axes a tight axis range, and constrain the x- and y-ranges of the third subplot to a subset of their respective ranges:



In [ ]:

fig, axes = plt.subplots(3, 1, figsize=(8, 12))

axes[0].plot(rain['Year'], rain['Jan'], rain['Year'], rain['Feb'])
axes[0].set_title("default axis ranges")

axes[1].plot(rain['Year'], rain['Jan'], rain['Year'], rain['Feb'])
axes[1].set_title("tight axes")

axes[2].plot(rain['Year'], rain['Jan'], rain['Year'], rain['Feb'])
axes[2].set_title("custom axis ranges");



Ticks and tick labels

We can customize the placement of axis ticks using the set_xticks and set_yticks methods, which take a list of values for the tick locations. Similarly, we can use the methods set_xticklabels and set_yticklabels to provide a list of custom text labels for each tick.



In [ ]:

fig, ax = plt.subplots(figsize=(10, 4))

ax.plot(rain['Year'], rain['Jan'], rain['Year'], rain['Feb'])
ax.set_xlim(1880, 1970)

ax.set_xticks([1900, 1920, 1940, 1960])
ax.set_xticklabels(['Turn of\ncentury', 'Twenties', 'Forties', 'Sixties'],
fontsize=12)

yticks = [2, 6, 10, 14]
ax.set_yticks(yticks)
ax.set_yticklabels(['dry', 'moist', 'wet', 'soggy'], fontsize=18)



Axis grid

The axis method grid toggles grid lines in the plotting canvas. We can customize the appearence of the gridlines, using the same keywork arguments as with plot.



In [ ]:

fig, axes = plt.subplots(1, 2, figsize=(10,3))

# default grid appearance
axes[0].plot(rain['Year'], rain['Jan'], linewidth=2)
axes[0].grid(True)

# custom grid appearance
axes[1].plot(rain['Year'], rain['Jan'], linewidth=2)
axes[1].grid(True)



Exercise

Give the second set of axes above a grid with a dashed line with a line width of 0.5.

Axis spines

There are several methods for customizing the axis itself.



In [ ]:

fig, ax = plt.subplots(figsize=(6,2))

ax.plot(rain['Year'], rain['Jan'])
ax.spines['top'].set_color('none')

ax.spines['left'].set_color('none')
ax.spines['left'].set_linewidth(2)

ax.spines['right'].set_color("none")
ax.xaxis.tick_top()



Exercise

Change the color of the X-axis above from black to red.

Secondary axes

Sometimes it is useful to have dual x or y axes in a figure, for example when plotting curves with differnt units together. Matplotlib supports this with the twinx and twiny functions:



In [ ]:

fig, ax1 = plt.subplots()

ax1.plot(rain['Year'], rain['Jan'], color='blue')
ax1.set_ylabel("rain (mm)", fontsize=18, color="blue")
for label in ax1.get_yticklabels():
label.set_color("blue")

ax2 = ax1.twinx()
ax2.plot(rain['Year'], np.log(rain['Jan']), color='red')
ax2.set_ylabel("rain (log mm)", fontsize=18, color="red")
for label in ax2.get_yticklabels():
label.set_color("red")



Axes can be placed at arbitrary locations, with the commonest choice being $x=0$ and $y=0$.



In [ ]:

fig, ax = plt.subplots()

ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')

# Set location of x-axis
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))

# Set location of y-axis
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))

x = np.linspace(-1, 1., 100)
ax.plot(x, x**3);



Plot Types

There are a variety of plotting functions for generating common types of plots.



In [ ]:

fig, axes = plt.subplots(2, 2, figsize=(12,6))

axes[0,0].scatter(rain['Jan'], rain['Jul'])

axes[0,1].step(rain['Year'][:10], np.cumsum(rain['Jan'][:10]), lw=2)

axes[1,0].bar(rain['Year'][:10], rain['Apr'][:10], align="center", width=0.5, alpha=0.5)

minrain = [np.nanmin(rain[m]) for m in months]
maxrain = [np.nanmax(rain[m]) for m in months]
axes[1,1].fill_between(range(12), minrain, maxrain, color="green", alpha=0.2)
_ = axes[1,1].set_xticklabels(months[::2])



Exercise: Histograms

Create a histogram of the 1000 normal random variates below, with 50 bins.



In [ ]:



Error bars



In [ ]:

x = np.linspace(1, 10, 30)
y = [np.random.normal(0, xi, 20) for xi in x]

fig, ax = plt.subplots()
plt.errorbar(x, np.mean(y, 1), np.std(y, 1), fmt='.k')



Polar plot



In [ ]:

# polar plot using add_axes and polar projection
fig = plt.figure()
ax = fig.add_axes([0.0, 0.0, .6, .6], polar=True)
t = np.linspace(0, 2 * np.pi, 12)
ax.plot(t, list(rain[1])[1:], color='blue', lw=3)
_ = ax.set_xticklabels(months)



Text annotation

Annotating text in matplotlib figures can be done using the text function. It supports LaTeX formatting just like axis label texts and titles:



In [ ]:

fig, ax = plt.subplots()

xx = np.linspace(-0.75, 1., 100)
ax.plot(xx, xx**2)
ax.plot(xx, xx**3)

ax.text(0.15, 0.2, r"$y=x^2$", fontsize=20, color="blue")
ax.text(0.65, 0.1, r"$y=x^3$", fontsize=20, color="green");



Figures with multiple subplots and insets

Axes can be added to a matplotlib Figure canvas manually using make_axes or using sub-figure layout manager such as subplots or subplot2grid or gridspec:

subplots



In [ ]:

fig, ax = plt.subplots(2, 3)
for i,m in enumerate(months[:6]):
(ax.ravel()[i]).plot(rain['Year'], rain[m])
(ax.ravel()[i]).set_title(m)
fig.tight_layout()



subplot2grid

subplot2grid is a helper function that is similar to pyplot.subplot but uses 0-based indexing and let subplot to occupy multiple cells.

To use subplot2grid, you provide geometry of the grid and the location of the subplot in the grid. For a simple single-cell subplot:



In [ ]:

ax = plt.subplot2grid((2,2),(0, 0))



Here, the grid is specified by shape=(2,2), at location of loc=(0,0).

This is identical to:



In [ ]:

ax = plt.subplot(2,2,1)



It is handy when we are assembling a figure composed of heterogeneously-sized subplots.



In [ ]:

fig = plt.figure()
ax1 = plt.subplot2grid((3,3), (0,0), colspan=3)
ax2 = plt.subplot2grid((3,3), (1,0), colspan=2)
ax3 = plt.subplot2grid((3,3), (1,2), rowspan=2)
ax4 = plt.subplot2grid((3,3), (2,0))
ax5 = plt.subplot2grid((3,3), (2,1))
fig.tight_layout()



gridspec

gridspec is a module which specifies the location of the subplot in the figure.

• GridSpec specifies the geometry of the grid that a subplot will be placed. The number of rows and number of columns of the grid need to be set. Optionally, the subplot layout parameters (e.g., left, right, etc.) can be tuned.
• SubplotSpec specifies the location of the subplot in the given GridSpec.

A gridspec.GridSpec instance provides array-like (2d or 1d) indexing that returns a SubplotSpec instance. For, SubplotSpec that spans multiple cells, use slice.



In [ ]:

import matplotlib.gridspec as gridspec




In [ ]:

fig = plt.figure()

gs = gridspec.GridSpec(3, 3)
# identical to ax1 = plt.subplot(gs.new_subplotspec((0,0), colspan=3))
ax1 = plt.subplot(gs[0, :], axisbg='red')

ax2 = plt.subplot(gs[1,:-1], axisbg='blue')
ax3 = plt.subplot(gs[1:,-1], axisbg='magenta')
ax4 = plt.subplot(gs[-1,0], axisbg='yellow')
ax5 = plt.subplot(gs[-1,-2], axisbg='cyan')

plt.tight_layout()



As we previewed above, adding axes with add_axes is useful for adding insets to figures:



In [ ]:

fig, ax = plt.subplots()

ax.plot(rain['Year'], rain['Jan'])

# inset
inset_ax = fig.add_axes([0.6, 0.6, 0.35, 0.3], axisbg='white') # X, Y, width, height

inset_ax.plot(rain['Year'], rain['Jan'])
inset_ax.set_title('zoom to 1950\'s')

# set inset axis range
inset_ax.set_xlim(1949, 1961)



Colormap and contour

Colormaps and contour figures are useful for plotting functions of two variables, where we use a colormap to encode the third dimension.

For example, let's generate probabilities corresponding to a bivariate normal distribution across a grid in both dimensions:



In [ ]:

#from pymc.distributions import mv_normal_cov_like as mvnorm
from scipy.stats import multivariate_normal as mvnorm

x1 = x2 = np.linspace(-4, 4, 100)
mu = np.array([0,0])
Sigma = [[1, 0.5],[0.5, 1]]
z = np.array([[mvnorm(mu, Sigma).pdf([xi,yi]) for xi in x1] for yi in x2])



pcolor



In [ ]:

fig, ax = plt.subplots()

x, y = np.meshgrid(x1, x2)
p = ax.pcolor(x, y, z, cmap=mpl.cm.Reds)
cb = fig.colorbar(p)



imshow



In [ ]:

fig, ax = plt.subplots()

im = plt.imshow(z, cmap=mpl.cm.RdBu)
im.set_interpolation('bilinear')

cb = fig.colorbar(im)



contour



In [ ]:

fig, ax = plt.subplots()

cnt = plt.contour(z, cmap=mpl.cm.Blues, vmin=abs(z).min(), vmax=abs(z).max(), extent=[0, 1, 0, 1])



Backends

Matplotlib has a number of "backends", which are responsible for rendering graphs. The different backends are able to generate graphics with different formats or using different display technologies. There is a distinction between noninteractive backends (such as 'agg', 'svg', 'pdf', etc.) that are only used to generate images files (with for example the savefig function), and interactive backends (such as Qt4Agg, GTK, MaxOSX) that can display a GUI window for interactively exploring figures.

A list of available backends are:



In [ ]:

mpl.rcsetup.all_backends



The standard backend is called agg, and is based on a library for raster graphics and is great for generating raster formats such as PNG.

Normally we don't need to bother with changing the default backend, but sometimes it can be useful to switch to for example the PDF or GTKCairo (if you are using Linux) to produce high-quality vector graphics instead of raster based graphics.

xkcd plots



In [ ]:

import matplotlib.pyplot as plt
import numpy as np

with plt.xkcd():
# Based on "Stove Ownership" from XKCD by Randall Monroe
# http://xkcd.com/418/

fig = plt.figure()
ax = fig.add_axes((0.1, 0.2, 0.8, 0.7))
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
plt.xticks([])
plt.yticks([])
ax.set_ylim([-30, 10])

data = np.ones(100)
data[70:] -= np.arange(30)

plt.annotate(
'THE DAY I REALIZED\nI COULD COOK BACON\nWHENEVER I WANTED',
xy=(70, 1), arrowprops=dict(arrowstyle='->'), xytext=(15, -10))

plt.plot(data)

plt.xlabel('time')
plt.ylabel('my overall health')
fig.text(
0.5, 0.05,
'"Stove Ownership" from xkcd by Randall Monroe',
ha='center')

# Based on "The Data So Far" from XKCD by Randall Monroe
# http://xkcd.com/373/

fig = plt.figure()
ax = fig.add_axes((0.1, 0.2, 0.8, 0.7))
ax.bar([-0.125, 1.0 - 0.125], [0, 100], 0.25)
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks([0, 1])
ax.set_xlim([-0.5, 1.5])
ax.set_ylim([0, 110])
ax.set_xticklabels(['CONFIRMED BY\nEXPERIMENT', 'REFUTED BY\nEXPERIMENT'])
plt.yticks([])

plt.title("CLAIMS OF SUPERNATURAL POWERS")

fig.text(
0.5, 0.05,
'"The Data So Far" from xkcd by Randall Monroe',
ha='center')



Exercise: Bootstrap resampling

To get some practice using Matplotlib, we will generate some data from various distributions and resample it, to visualize how bootstrapping preserves the properties of the original samples.



In [ ]:

random_dists = ['Normal(1,1)',' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
'Triangular(2,9,11)']
num_dists = len(random_dists)

N = 500
norm = np.random.normal(1,1, N)
logn = np.random.lognormal(1,1, N)
expon = np.random.exponential(1, N)
gumb = np.random.gumbel(6, 4, N)
tri = np.random.triangular(2, 9, 11, N)



Resampling is easy: we can simply generate random integers (with replacement) and use them to index the values of the original sample.



In [ ]:

resample_indices = np.random.randint(0, N-1, N)
norm_resample = norm[resample_indices]
expon_resample = expon[resample_indices]
gumb_resample = gumb[resample_indices]
logn_resample = logn[resample_indices]
tri_resample = tri[resample_indices]



As closely as possible, try to replicate this plot:



In [ ]: