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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

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.