Improve the prior interface for make epi model inference

[SamuelBrand1]

Goals

This PR aims to address modularity problems for priors discussed here #45 . The goal is to have the choice of priors for a sub-process or sub-model "live" with the Turing model definition of the sub-process or sub-model within a struct.

API changes

• The make_epi_inference_model constructor for the overall Turing model now requires positional arguments require args of type LatentProcess for the latent process and ObservationModel for the observation model.
• random_walk and delay_observations are no longer exported by using EpiAware.
• The constructor delay_observations_model creates an ObservationModel with basic delayed observation model here. If priors are not supplied the defaults are used.
• The constructor random_walk_process creates a LatentProcess with basic random walk model here.

Proposed EpiAware model diagram

flowchart LR

    A["Underlying dists.
and specify length of sims
---------------------
EpiData"]

    B["Choice of target
for latent process
---------------------
DirectInfections
    ExpGrowthRate
    Renewal"]

C["Observational Data
---------------------
Obs. cases y_t"]
D["Latent processes
---------------------
random_walk"]
E["Turing model constructor
---------------------
make_epi_inference_model"]
F["Latent Process priors
---------------------
default_rw_priors"]
G[Posterior draws]
H[Posterior checking]
I[Post-processing]
DataW[Data wrangling and QC]
J["Observation models
---------------------
delay_observations"]
K["Observation model priors
---------------------
default_delay_obs_priors"]
ObservationModel["ObservationModel
---------------------
delay_observations_model"]
LatentProcess["LatentProcess
---------------------
random_walk_process"]

A --> EpiModel
B --> EpiModel
EpiModel -->E
C-->E
D-->LatentProcess
F-->LatentProcess
J-->ObservationModel
K-->ObservationModel
LatentProcess-->E
ObservationModel-->E
E-->|sample...NUTS...| G
G-.->H
H-.->I
DataW-.->C

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Closes #45

[seabbs]

This is really nice I think! As discussed f2f we may move away from the NamedTuple to instead use argument splitting. Only outstanding note is that the updated diagram should also go in the README in this PR I think

[seabbs]

As I have caused the pain happy to handle the conflicts when #62 is merged in

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (d672c2c) 100.00% compared to head (792b4bd) 100.00%.

Additional details and impacted files

@@            Coverage Diff            @@
##              main       #61   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            6         6           
  Lines          117       123    +6     
=========================================
+ Hits           117       123    +6     

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[seabbs]

LGTM