Redesign interface

[seabbs]

This is a proposal for a new interface. The basic idea is to build the model up as a series of chunks related to the sub-modules. There are open questions about how much of the data munging process (i.e which formulas use which data) the user should be exposed to.

A possible candidate interface:

epinowcast(
    data, model = enw_model(), reporting = enw_reporting(...), expectation = enw_expectation(...),
    missing = enw_missing(...), observation = enw_obs(...), fit = enw_fit(...)
)

enw_reporting( 
  parametric = ~ 1, | ~ 0 # none
  distribution = "log-normal", # | "none" = no parametric baseline hazard
  non_parametric = ~ 0 # (none) | ~ d (each day i.e discrete) | ~ d + age_group (cox model assuming proportional hazards by age group)
  reporting = ~ rw(week, by = age_group), | ~ 0 (or ~1) #none
  structural = ~ saturdays # (known days reporting cannot happen and hazard to -Inf),
  data = obs
)

enw_expectation(
  ~ rw(date, by = age_group), 
  offset = enw_offset(weights = 1),
  order = 2, #i.e second order = a growth rate model, # third order is difference in growth rate model and so on
  family = "none",  # here could have for example "poisson"
  delay_to_report = 1  # here could have the delay from inf to report as a pmf. Later extend to uncertain dists
  data = obs
)

enw_missing(
   ~ 1, 
   data = obs
)

enw_obs(
  baseline = ~ 1 # we could offfer the ability to model the variance parameter if present by baseline (i.e delay,) report and reference date
  report = ~ 1
  reference = ~ 1
  family = "negbin" #other options could be Poisson etc or even potentially non-count options. 
)

enw_fit(
  init = epinowcast::enw_init,
  fit = epinowcast::enw_sample,
  as_data_list = epinowcast::enw_as_data_list,
  ... # additional parameters passed to fit when called.
)

[seabbs]

Rejigged this a bit to only have parametric and non_parametric.

[seabbs]

Closed by #112