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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

6.10 Exercises

Posterior density for θ given 10 heads and 20 tails with dashed vertical quartile lines; the curve is narrower than for the 12-flip data and centers near θ=0.33.
Figure 6.10. Posterior probability distribution for the θ values of the bent coin - the probability that the coin will land heads. The distribution is shown for data 10 heads and 20 tails. The various quartiles are shown in the plot, and summarized in the accompanying table.
Beta( heads=10, tails=20)
ValueArea
0.170.01
0.210.05
0.240.10
0.290.25
0.340.50
0.400.75
0.450.90
0.490.95
0.550.99

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.