How do we go about calculating a posterior with a prior given N data points of the form
greater than X or
less than Y, when those data points are noisy (that is,
greater than X can be incorrect)?
We start with the posterior normal distribution of variable X with mean 1 and variance 1. We do series of tests with the following results:
test x=1: less than X test x=2: less than X test x=5: greater than X test x=6: less than X test x=4: greater than X test x=10: greater than X test x=12: greater than X
Given such results, I'd think that that mean of X variable is not
1 - probably something around
5. But how can I derive this mean and variance?