improve early calculation

[sbfnk]

Description

This PR closes #902 by

• changing the calculation of prior_infections to be based on the intercept of the linear model instead of mean of first week, if available
• fitting the initial model for seeding_time if greater than 7 (as that is the period for which exponential growth is assumed in the model)
• dividing initial_infections by frac_obs before modelling initial exponential growth
• changing the prior for initial_infections to be approximately Poisson

As a result we've go from

to

in the example mentioned in the Issue - see

EpiNow2/inst/dev/recover-synthetic/rt.R

Line 14 in dbb6536

init <- estimate_infections(example_confirmed[1:100],

More generally the values of initial_growth / initial_infections no longer seem to affect frac_obs, at the expense of (expected) correlation between the initial estimates.

Initial submission checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have tested my changes locally (using devtools::test() and devtools::check()).
• I have added or updated unit tests where necessary.
• I have updated the documentation if required and rebuilt docs if yes (using devtools::document()).
• I have followed the established coding standards (and checked using lintr::lint_package()).
• I have added a news item linked to this PR.

After the initial Pull Request

• I have reviewed Checks for this PR and addressed any issues as far as I am able.

[seabbs]

This looks really great. Not quite understanding the CI fail for as CRAN (requiring future) and haven't checked out the benchmarks. Really good this has solved the correlation we were seeing

noting my preference would be we further explore using the approach from @SamuelBrand1 used in EpiAware where we solve for the implied growth rate based on the generation time and initial Rt estimate. I can knock something up for this (it will look something like this: https://github.com/CDCgov/Rt-without-renewal/blob/0d4095ecf5d67b599b26a8822679adebb40b164a/EpiAware/src/EpiInfModels/utils.jl#L44 but I will probably use the algebraic system solver for simplicity) in a future PR

[seabbs]

Ah touchstone and as CRAN check are just having a fail party everywhere

[sbfnk]

noting my preference would be we further explore using the approach from @SamuelBrand1 used in EpiAware where we solve for the implied growth rate based on the generation time and initial Rt estimate.

Oh yes that would be great!

[SamuelBrand1]

This looks really great. Not quite understanding the CI fail for as CRAN (requiring future) and haven't checked out the benchmarks. Really good this has solved the correlation we were seeing

noting my preference would be we further explore using the approach from @SamuelBrand1 used in EpiAware where we solve for the implied growth rate based on the generation time and initial Rt estimate. I can knock something up for this (it will look something like this: CDCgov/Rt-without-renewal@0d4095e/EpiAware/src/EpiInfModels/utils.jl#L44 but I will probably use the algebraic system solver for simplicity) in a future PR

Yeah, I did it this way because I didn't want to worry about AD through a zero finder so hand rolled a few steps of a Newton solver. Not optimal, I like the look of the algebraic system solver.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 746c3ba is merged into main:

• ✔️default: 20.2s -> 31.2s [-12.76%, +120.57%]
• ✔️no_delays: 25.1s -> 26.8s [-6.46%, +19.85%]
• ❗🐌random_walk: 9.19s -> 12.9s [+33.4%, +47.23%]
• ✔️stationary: 16s -> 18.4s [-49.62%, +78.82%]
• ❗🐌uncertain: 34.1s -> 41.1s [+11.11%, +30.01%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[sbfnk]

Hmm, looks like we get a slowdown and fitting failure(s). This may need more exploration.