Notes on value of information runs with uniform noise

  • Debug Sethi with large uniform noise: needed to avoid havest > stock in definition of f.

I ran the value of information calculations using the Sethi settings of a logistic map and uniform noise, which does indeed replicate their results, where the measurement error escapement is lower than the “all low noise” (“deterministic”) escapement until stock get above carrying capacity.  results

Kinda of interesting that this patterns isn’t robust to the noise distribution; I still find the lognormal noise pattern a bit more intuitive. Also rather interesting that nothing shows up when restricted to 10% noise range

There’s also the updated value of information table in the results. As Mike predicted, with this symmetric noise distribution, the presence of growth noise no longer increases the value. Perhaps the only surprise is that adding extra forms of stochasticity that aren’t present has little impact on the value, presumably from the linearity? Some sample differences:

  • cost of reckless (det - all real noise): 668 - 414 = 254
  • cost of caution (det - all imagined noise): 668 - 672 = -4
  • cost of stochasticity (det - all): 668 - 450 = 218
  • assuming measurement uncertainty when absent ([g,g] - [g, g+m]): 678-663 = 15
  • ignoring when present ([g+m, g+m] - [g+m, g]): 568-550 = 18

However, the asymmetric comparison is much more dramatic when implementation uncertainty is also present:

  • Assuming measurement uncertainty when absent: ([gi, gi] - [gi, gmi]) = 626-629
  • Ignoring when present: ([gmi, gmi] - [gmi, gi]) = 449 - 374

  • Running with more replicates to tighten the monte carlo integration. (nice 19 on 0)
  • Running with the wide uniform noise on an allee model with nontrivial alternative stable states