Also, σ^2 and c^2 could in principle be found empirically: in this model, the difference of measured weights t days apart is normally distributed with variance (2σ^2 + tc^2). I found a file with a couple years' worth of almost daily weight data of myself from a few years ago and computed the average of (w_n − w_(n − t))^2 for various values of t, and for not-too-large values that's actually approximately linear in t (except it is slightly lower at multiples of 7 days, which I take to be an effect of week cycles -- I tend to eat more on weekends). But the ratio between the c^2 and the σ^2 I found was nowhere near 1/90 -- it was actually about 1/5, which suggests that the Hacker's Diet smoothed average responds to changes in weight much more slowly than it should, even if the weight is reported daily.

(Will anyone bother to find out the formula for the ideal Bayesian estimate of c^2 and σ^2 in this model, assuming uninformative priors?)