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18
Prior
pi sample: 5000
6.0
4.0
2.0
0.0
0.1
0.2
0.3
0.4
0.3
0.4
pi sample: 5000
Posterior
6.0
4.0
2.0
0.0
0.1
0.2
Note how the data changes our view of the unemployment rate. For one thing, the data gives
us reason to think that the unemployment rate pi is less than 0.4. There is still plenty
of uncertainty, but it is less than before we took the sample. The standard deviation (sd)
of pi from the prior is 0.072 but is 0.067 from the posterior. The 95% credible interval
shrinks accordingly.
For more practice, and to see the effect of a larger sample on the posterior, rerun the model
with n=140, and r = 40.