standard deviation and errors bars in seaborn tsplot function in Python [duplicate]

Question

How does Seaborn compute its error bars? example:

import numpy as np; np.random.seed(22)
import seaborn as sns; sns.set(color_codes=True)
x = np.linspace(0, 15, 31)
data = np.sin(x) + np.random.rand(10, 31) + np.random.randn(10, 1)
ax = sns.tsplot(data=data, err_style="ci_bars")
plt.show()

how are the ci_bars (or ci_bands) calculated?

also, is it possible to make tsplot plot in ci_bars style where the error bars or bands correspond to the standard deviation of the values at each time point? (and not standard error of mean, or bootstraps)

Answer 1

In Seaborn v0.8.0 (July 2017) was added the ability to use error bars to show standard deviations rather than bootstrap confidence intervals in most statistical functions by putting ci="sd". So this now works

sns.tsplot(data=data, ci="sd") 

For previous Seaborn versions a workaround for plotting standard deviation could be to use matplotlib errorbar on top of seaborn tsplot:

import numpy as np;
import seaborn as sns;
import pandas as pd
import matplotlib.pyplot as plt

# create a group of time series
num_samples = 90
group_size = 10
x = np.linspace(0, 10, num_samples)
group = np.sin(x) + np.linspace(0, 2, num_samples) + np.random.rand(group_size, num_samples) + np.random.randn(group_size, 1)
df = pd.DataFrame(group.T, index=range(0,num_samples))

# plot time series with seaborn
ax = sns.tsplot(data=df.T.values) #, err_style="unit_traces")

# Add std deviation bars to the previous plot
mean = df.mean(axis=1)
std  = df.std(axis=1)
ax.errorbar(df.index, mean, yerr=std, fmt='-o') #fmt=None to plot bars only

plt.show()

Answer 2

Since the tsplot function does not provide a way to set the error bar values directly or to change the method used to calculate them, the only solution I found was to monkey patch the timeseries module:

import seaborn.timeseries

def _plot_std_bars(*args, central_data=None, ci=None, data=None, **kwargs):
    std = data.std(axis=0)
    ci = np.asarray((central_data - std, central_data + std))
    kwargs.update({"central_data": central_data, "ci": ci, "data": data})
    seaborn.timeseries._plot_ci_bars(*args, **kwargs)

def _plot_std_band(*args, central_data=None, ci=None, data=None, **kwargs):
    std = data.std(axis=0)
    ci = np.asarray((central_data - std, central_data + std))
    kwargs.update({"central_data": central_data, "ci": ci, "data": data})
    seaborn.timeseries._plot_ci_band(*args, **kwargs)

seaborn.timeseries._plot_std_bars = _plot_std_bars
seaborn.timeseries._plot_std_band = _plot_std_band

Then, to plot with the standard deviation error bars use

ax = sns.tsplot(data, err_style="std_bars", n_boot=0)

or

ax = sns.tsplot(data, err_style="std_band", n_boot=0)

to plot with a standard deviation band.

Edit: Inspired by this answer on SO, another (probably more sensible) approach would be to use the following instead of tsplot:

import pandas as pd
import seaborn as sns

df = pd.DataFrame.from_dict({
    "mean": data.mean(axis=0),
    "std": data.std(axis=0)
}).reset_index()

g = sns.FacetGrid(df, size=6)
ax = g.map(plt.errorbar, "index", "mean", "std")
ax.set(xlabel="", ylabel="")

Edit2: Since you asked about how tsplot calculates its confidence intervals: it uses bootstrapping to estimate the distribution of the mean value at each time point and then finds the low and high percentile values (that correspond to the confidence interval being used) from these distributions. The default confidence interval is 68% – equivalent to ± one standard deviation of the mean, assuming normal distribution. The respective low and high percentiles are 16% and 84%. You can change the confidence interval via the ci keyword argument.