0

・7 min read

For any scientific measurement, accurate accounting for errors is nearly as important, if not more important, than accurate reporting of the number itself. For example, imagine that I am using some astrophysical observations to estimate the Hubble Constant, the local measurement of the expansion rate of the Universe. I know that the current literature suggests a value of around 71 (km/s)/Mpc, and I measure a value of 74 (km/s)/Mpc with my method. Are the values consistent? The only correct answer, given this information, is this: there is no way to know.

Suppose I augment this information with reported uncertainties: the current literature suggests a value of around 71 $\pm$ 2.5 (km/s)/Mpc, and my method has measured a value of 74 $\pm$ 5 (km/s)/Mpc. Now are the values consistent? That is a question that can be quantitatively answered.

In visualization of data and results, showing these errors effectively can make a plot convey much more complete information.

A basic errorbar can be created with a single Matplotlib function call:

Here the `fmt`

is a format code controlling the appearance of lines and points, and has the same syntax as the shorthand used in `plt.plot`

, outlined in Simple Line Plots and Simple Scatter Plots.

In addition to these basic options, the `errorbar`

function has many options to fine-tune the outputs.
Using these additional options you can easily customize the aesthetics of your errorbar plot.
I often find it helpful, especially in crowded plots, to make the errorbars lighter than the points themselves:

In addition to these options, you can also specify horizontal errorbars (`xerr`

), one-sided errorbars, and many other variants.
For more information on the options available, refer to the docstring of `plt.errorbar`

.

In some situations it is desirable to show errorbars on continuous quantities.
Though Matplotlib does not have a built-in convenience routine for this type of application, it's relatively easy to combine primitives like `plt.plot`

and `plt.fill_between`

for a useful result.

Here we'll perform a simple *Gaussian process regression*, using the Scikit-Learn API (see Introducing Scikit-Learn for details).
This is a method of fitting a very flexible non-parametric function to data with a continuous measure of the uncertainty.
We won't delve into the details of Gaussian process regression at this point, but will focus instead on how you might visualize such a continuous error measurement:

We now have `xfit`

, `yfit`

, and `dyfit`

, which sample the continuous fit to our data.
We could pass these to the `plt.errorbar`

function as above, but we don't really want to plot 1,000 points with 1,000 errorbars.
Instead, we can use the `plt.fill_between`

function with a light color to visualize this continuous error: