如何在matplotlib中可视化95％置信区间？

Question

I have learned how to find the 95% confidence interval with scipy.stats.t like so

In [1]: from scipy.stats import t
In [2]: t.interval(0.95, 10, loc=1, scale=2)  # 95% confidence interval
Out[2]: (-3.4562777039298762, 5.4562777039298762)
In [3]: t.interval(0.99, 10, loc=1, scale=2)  # 99% confidence interval
Out[3]: (-5.338545334351676, 7.338545334351676)

However, visualization is important to me. I am wondering how may I show the confidence interval bar on each node of my curve in matplotlib ?

What I am expecting is something like this

Answer 1

You don't need .interval method, to get the size of confidence interval, you just need the .ppf method.

import numpy as np
import scipy.stats as ss
data_m=np.array([1,2,3,4])   #(Means of your data)
data_df=np.array([5,6,7,8])   #(Degree-of-freedoms of your data)
data_sd=np.array([11,12,12,14])   #(Standard Deviations of your data)
import matplotlib.pyplot as plt
plt.errorbar([0,1,2,3], data_m, yerr=ss.t.ppf(0.95, data_df)*data_sd)
plt.xlim((-1,4))

ss.t.ppf(0.95, data_df)*data_sd is a fully vectorize way to get the (half) size of interval, given the degrees of freedom and standard deviation.

Answer 2

you need to divide by standard deviation, and, second, if your data is two-sided (as plot suggests), you need to allow 2.5% of misses on each side of Gaussian, that is:

ss.t.ppf(0.975, data_df)/np.sqrt(data_df)

Since you miss 2.5% on both sides, you get total 5% miss.