Thank you, that's a very clever explaination. Even though I can't grok the mathematics off the top of my head (I would have to look up the conjugate gaussian-gaussian formula and work this out) I think converting this to a posterior probability calculation is much more intuitive, then the article's explaination.

So, my crude understanding is that therefore the signal and noise is the mean and variance of the Gaussian, respectively. The posterior uncertainty in this is case is thus a function of a weighted average of the sample data, weighted by the priors, normalized by the data, which results in a higher signal-to-noise ratio, or lower uncertainty.