7.6 Computer Examples

from sie import *

Estimating Lengths

Known deviation, $\sigma$

x=[5.1, 4.9, 4.7, 4.9, 5.0]
sigma=0.5

mu=sample_mean(x)
N=len(x)

dist=normal(mu,sigma/sqrt(N))
distplot(dist)

Show expected output

<matplotlib.figure.Figure at 0x10713c710>

Posterior curve for the true length computed by the sample code, with dashed percentile lines: 1% at 4.40, 5% at 4.55, 25% at 4.77, 50% at 4.92, 75% at 5.07, 95% at 5.29 and 99% at 5.44.

credible_interval(dist)

Show expected output

(4.4817387297117088, 4.9199999999999999, 5.358261270288291)

Unknown $\sigma$

mu=sample_mean(x)
s=sample_deviation(x)
print mu,s

Show expected output

4.92 0.148323969742

dist=tdist(N-1,mu,s/sqrt(N))

distplot(dist,xlim=[4.6,5.4])

Show expected output

<matplotlib.figure.Figure at 0x1085b5c50>

A narrower posterior curve for the true length from the Student-t form, with dashed percentile lines: 1% at 4.67, 5% at 4.78, 25% at 4.87, 50% at 4.92, 75% at 4.97, 95% at 5.06 and 99% at 5.17.

credible_interval(dist)

Show expected output

(4.7358314667008017, 4.9199999999999999, 5.1041685332991982)

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.

7.6 Computer Examples

Estimating Lengths

Known deviation, σ\sigma

Unknown σ\sigma

Known deviation, $\sigma$

Unknown $\sigma$