notes/calibration.md

In bbolker/McMasterPandemic: Pandemic Model

An attempt to get some words down to describe the current state of the calibration procedure.

22 April 2020

• We have abandoned the "intercept & slope" method we were using earlier (i.e. compute intercept and slope from a NB fit to exponential-phase time series, calibrate parameters to desired $r$ (= slope) and $x(0)$ by projecting backward and using the dominant eigenvector to guess relative magnitudes). Two reasons: (1) this only works simply if we're still in exponential phase, otherwise we go back down the rabbit hole of guessing what time period to use in the statistical model; (2) there are various issues (numerical instability, rounding, etc.) in the back-projection (i.e. numerical instability can throw the initial phase off from the expected exponential growth). We could find ways to deal with these problems, but decided to move on.
• Pure-MLE approach; calibrate mean generation interval, then pick a set of parameters (including beta0 and E0), starting time, which observables to use, etc.
  • in simplest sim examples (run_caltest_nobreak) no breakpoint, fit to reports only) we get bias for (at least) three reasons.
    • observation noise is in the wrong place in the model (should occur after convolutions, not before)
    • calibration sims start (currently) 15 days before observed time series
    • rounding
  • these should be the only differences between the initial sim and the calibration sims
  • if we want to fix/minimize these differences:
    • fix obs noise model
    • try fitting to hospitalization or some other response that doesn't have the convolution
    • cut the calibration data to a subset (not starting as far back)
    • use a smaller time offset (change in make_state() to use dominant eigenvector by default should help with this)
  • next-most-complicated sim examples (run_caltest)
• fits to
  • many choices: which time series? hosp, ICU, reports, deaths?
  • which breakpoints?
  • which auxiliary params to try to calibrate?
  • should we try to stabilize?
• known problems with calibration
  • H mismatch in model (H in model=acute care only, should include ICU as well)
  • no I -> death flow (yet)
  • nbdisp not allowed to vary across series (might need to allow Poisson?)

bbolker/McMasterPandemic documentation built on Aug. 25, 2024, 6:35 p.m.