Population Distribution
![](http://lh3.google.com/stender/Rx2zQVNEhPI/AAAAAAAAAaA/VlQfChCeFNw/s400/pophist.jpg)
Sample n = 225
![](http://lh3.google.com/stender/Rx20fVNEhQI/AAAAAAAAAaM/eT-eYpLfPD8/s400/hist.jpg)
Prior and Posterior for mu
I assume data is generated from a normal distribution and additionally assume a normal prior for mu. Set mu_prior = 3.166 and sd_prior = 2.85, the approximate true mean and standard deviation for the population.
Back out the Bayesian test probability as 1 - pr(mu_1 < mu_2) from numerical integration.
![](http://lh6.google.com/stender/Rx2zQFNEhOI/AAAAAAAAAZ4/bGdqMFItN14/s400/prior_posterior.jpg)
MC Study: KS-test p-value vs. Bayesian Probability
Repeat the experiment n=100 times.
![](http://lh6.google.com/stender/Rx2zQFNEhNI/AAAAAAAAAZw/ZXvHYFIeODI/s400/mc_test.jpg)