Sending a value assuming a mixture of two
equal Gaussians
The blue curve is the
normalized sum of the
two Gaussians.
The point halfway between the two Gaussians should
cost –log(p(x)) bits where p(x) is its density under one of
the Gaussians.
But in the MDL story the cost should be –log(p(x))
plus one bit to say which Gaussian we are using.
How can we make the MDL story give the right