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📚 Statistical Inference for Everyone
Chapters ▾
1 Introduction to Probability2 Applications of Probability3 Random Sequences and Visualization4 Introduction to Model Comparison5 Applications of Model Comparison6 Introduction to Parameter Estimation7 Priors, Likelihoods, and Posteriors8 Common Statistical Significance Tests9 Applications of Parameter Estimation and Inference10 Multi-parameter Models11 Introduction to MCMC12 Concluding Thoughts13 Appendix A: Computational Analysis14 Appendix B: Notation and Standards15 Appendix C: Common Distributions and Their Properties16 Appendix D: Tables

7.6 Computer Examples

from sie import *

Estimating Lengths

Known deviation, σ

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 σ

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.