Answer Session 1 Para 4

Here are results for 5000 iterations with non informative B(1,1) priors for pi and pi2

Node statistics

node mean sd MC error 2.5% median 97.5% start sample

diff 0.1852 0.1697 0.002972 -0.1475 0.1903 0.5185 1001 5000

 

 

node mean sd MC error 2.5% median 97.5% start sample

ratio 1.881 1.082 0.01731 0.6733 1.622 4.617 1001 5000

 

FOR diff

WHAT IS YOUR posterior MEAN?___0.1852_______

MEDIAN?____0.1903______

95% credible interval?______-0.1475 to 0.5185__________________

Campare these with the sample value of r2/N2 - r/N = 0.50 - 0.28 = 0.22

 

FOR ratio

WHAT IS YOUR posterior MEAN?_____1.881_____

MEDIAN?____1.622_____

95% credible interval?_______0.6733 to 4.617_________________

Is there evidence that these two proportions are different?___no, because the 95% credible interval for the difference includes 0_

And the 95% credible interval for the ratio includes 1

 

Make a sketch of the posterior density for the difference

With only 5000 samples this is a bit noisy. Since we used flat priors for the proportions the mode here should be the MLE which will be 0.22.

And for the ratio

Now much more skewed, with the right tail corresponding to very small values of pi.