6.11 Computer Examples

from sie import *

Beta Distribution Example

3 heads and 9 tails

Plot a beta distribution with 3 heads and 9 tails...

dist=beta(h=1,N=3)
distplot(dist,xlim=[0,1],show_quartiles=False)

Smooth posterior curve for a proportion computed in the sample code: it rises from zero at 0, peaks near 0.33 at a density of about 1.8, and returns to zero at 1.

The median of this distribution...

dist.median()

Show expected output

0.27527583248615201

the 95

credible_interval(dist)

Show expected output

(0.067585986488542985, 0.38572756813238962, 0.80587955031675662)

1 heads and 3 tails

This should be about the same fraction as the previous example, but broader

dist=beta(h=1,N=4)
distplot(dist,xlim=[0,1])

Show expected output

<matplotlib.figure.Figure at 0x108768cd0>

The same posterior curve annotated with dashed percentile lines from the distribution object: 1% at 0.03, 5% at 0.08, 10% at 0.11, 25% at 0.19, 50% at 0.31, 75% at 0.45, 90% at 0.58, 95% at 0.66 and 99% at 0.78.

credible_interval(dist)

Show expected output

(0.052744950526316919, 0.31381017045569742, 0.71641793611808946)

Adapted from Statistical Inference for Everyone, by Brian Blais (Bryant University), licensed under CC BY-SA 4.0 (dual-licensed under the GNU FDL 1.2 or later; this adaptation uses the CC BY-SA grant). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.