I'm playing around with a Metropolis-Hastings MCMC algorithm as described in this post.
I made an example data set with points taken from two lines shown below.
Both lines have a y-intercept of 0 and the normally distributed noise has standard deviation of 0.1 for both. One line has a slope of 1 and one line has a slope of 10.
I tried computing the posterior distribution for all three parameters; slope, intercept, and standard deviation of noise. I wanted to see that the slope parameter posterior had a bi-modal distribution, with one mode at 1 and the other at 10. However, it just looked like a normal distribution with a mean around 5.
What is going on? I expected the Bayesian analysis to show that there were two values for the slope that are equally likely. I don't really see how it is more useful than least squares regression otherwise.