`scipy.stats._morestats:bayes_mvs`

source: /scipy/stats/_morestats.py :62

Signature

def bayes_mvs ( data , alpha = 0.9 )

Summary

Bayesian confidence intervals for the mean, var, and std.

Parameters

data : array_like: Input data, if multi-dimensional it is flattened to 1-D by bayes_mvs. Requires 2 or more data points.
alpha : float, optional: Probability that the returned confidence interval contains the true parameter.

Returns

mean_cntr, var_cntr, std_cntr : tuple

The three results are for the mean, variance and standard deviation, respectively. Each result is a tuple of the form

(center, (lower, upper))

with center the mean of the conditional pdf of the value given the data, and (lower, upper) a confidence interval, centered on the median, containing the estimate to a probability alpha.

Notes

Each tuple of mean, variance, and standard deviation estimates represent the (center, (lower, upper)) with center the mean of the conditional pdf of the value given the data and (lower, upper) is a confidence interval centered on the median, containing the estimate to a probability alpha.

Converts data to 1-D and assumes all data has the same mean and variance. Uses Jeffrey's prior for variance and std.

Equivalent to tuple((x.mean(), x.interval(alpha)) for x in mvsdist(dat))

Array API Standard Support

bayes_mvs has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

First a basic example to demonstrate the outputs:

from scipy import stats
data = [6, 9, 12, 7, 8, 8, 13]
mean, var, std = stats.bayes_mvs(data)

✓

mean
var
std

✗

Now we generate some normally distributed random data, and get estimates of mean and standard deviation with 95% confidence intervals for those estimates:

n_samples = 100000
data = stats.norm.rvs(size=n_samples)
res_mean, res_var, res_std = stats.bayes_mvs(data, alpha=0.95)

✓

import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)

✓

ax.hist(data, bins=100, density=True, label='Histogram of data')
ax.vlines(res_mean.statistic, 0, 0.5, colors='r', label='Estimated mean')
ax.axvspan(res_mean.minmax[0],res_mean.minmax[1], facecolor='r',
           alpha=0.2, label=r'Estimated mean (95% limits)')
ax.vlines(res_std.statistic, 0, 0.5, colors='g', label='Estimated scale')
ax.axvspan(res_std.minmax[0],res_std.minmax[1], facecolor='g', alpha=0.2,
           label=r'Estimated scale (95% limits)')

✗

ax.legend(fontsize=10)
ax.set_xlim([-4, 4])
ax.set_ylim([0, 0.5])

✗

plt.show()

✓

Aliases

scipy.stats.bayes_mvs