>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

>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. The variance of the Gaussian is proportional to a noise-to-signal ratio, so you have to turn it upside-down to get the signal-to-noise we usually work with. But yeah. https://en.wikipedia.org/wiki/Signal-to-noise_ratio https://en.wikipedia.org/wiki/Signal-to-noise_ratio