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Some ideas for improving the documentation

1. This sounds good. Please let us know what specifically you want help with.
2. Include installation instructions in the beginning of the documentation either in a separate section or within the getting started section.
3. I am not entirely sure what is the difference between the HospitalAdmissionsModel in Pyrenew demo and the one in Fitting a Hospital Admissions-only model. Perhaps clarify what the two tutorials are trying to convey.
4. If I understand correctly there are two different model implementation - Hospital Admissions and Reproduction Number Renewal Infections. But it isn't clear from the tutorial, suggesting reorganizing the tutorials to make these two model instances examples clear.
5. Change the order of tutorial and reference in the documentation

I can make most of these changes (might need some help on 1) if we think these would be useful.

1. This will be covered (at least partially) by Adding Repository Structure And Resources Sections To The README #197
2. I think installation instructions can go in both the main website page and the getting started tutorial. Note that installation instructions are also here, which is not on the website: https://github.com/CDCgov/multisignal-epi-inference/tree/main/model#readme. This may need to be updated.
3. Agreed that these are confusing/redundant. I would lean toward merging the PyRenew Demo and Fitting a Hospital Admissions-only Model tutorials. Probably by keeping Fitting a Hospital Admissions-only Model mostly as is, but bringing over anything useful from PyRenew Demo that it is missing.
4. That's correct. I agree making this more obvious would be useful. We provide two pre-built models: RtInfectionsRenewalModel and HospitalAdmissionsModel. HospitalAdmissionsModel uses RtInfectionsRenewalModel and builds upon it.
5. Sounds good.

4. That's correct. I agree making this more obvious would be useful. We provide two pre-built models: RtInfectionsRenewalModel and HospitalAdmissionsModel. HospitalAdmissionsModel uses RtInfectionsRenewalModel and builds upon it.

I liked the diagram here: https://github.com/CDCgov/multisignal-epi-inference/tree/main/model#readme and can be effective visualization to show HospitalAdmissionsModel uses RtInfectionsRenewalModel and builds upon it.

@sbidari Would it be appropriate to also address these comments from @cherz4 in this PR? If not, please create additional issues related to the points discussed on Teams.

Yes, will include more instructions for poetry installation.

Re: 2 - I think this would be a good place to add some installation instructions:

Specifically, I'd suggest a Prerequisites section before The fundamentals that reads something like this:

Prerequisites

This tutorial assumes some pre-existing knowledge of infectious disease dynamics and Python programming. Before you dive in, we recommend:

• Installing Python3
• Familiarity with installing and loading modules in python, and with virtual environment management (we recommend poetry)
• Familiarity with the concept of a class and metaclass in python
• Familiarity with Bayesian inference, and a working understanding of MCMC methods used to fit Bayesian models to data (link to resources like statistical rethinking?)

Minor: I think this phrasing makes it sound like we're taking the ratio $\frac{I_t}{I_{t-s}}$, rather than considering all previous timesteps in the denominator.

The pyrenew package models the real-time reproductive number $R_t$, the ratio of new infections at 
time $t$ to previous infections at some time $t-s$, as a renewal process model

https://github.com/CDCgov/multisignal-epi-inference/blob/da3fae6a73e5b16e83cfaf986860d33fa39730ac/model/docs/getting_started.qmd#L65C1-L65C236

Changes to the tutorial/documentation in this PR:

• added a page with Prerequisite and installation information
• merge/remove pyrenew demo
• rename 'example_with_dataset' to 'hospital_admissions_model'
• demonstrate extraction of samples from the fitted model