hyunjimoon / hyunjimoon/DataInDM

Flow variable as observed data

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Anyone (@jandraor @Dashadower @hazhirr) feel free to comment, please!

@hazhirr mentioned flow variables can be observed data (a.k.a driving data) different from my assumption that only stock can be observed. I wonder whether this can be modeled under the original framework where all `family` distribution is used to penalize the difference between simulated stock variable (`integrated_result`) and observed stock variable.

For instance, assume the model has two of each stock variables (S1,2), flow variables (F1,2), parameters (P1,2). We have three scenarios:
1. Data for S1
2. Data for S1, F1
3. Data for S12, F1

Q1. Based on the insight @jandraor shared that dynamics is the function of only two: exogenous parameters and stocks, may I call each of the three as under-identified, well-identified, over-identified?

Q2. If so, infinite number and no parameter can be expected from the under and over identified case. Would giving prior be the solution to this identification problem?be returned for under-identified problem and would no parameter be returned for 1 and what could we expect from the results of under and over identified?

Q3. For 1, is there any way we can pre-calculate `S2` using `S1, F1` then compare this with the result purely integrated from the start? Integration will happen in `transformed parameter` block whereas comparison will be in `model` block. @Dashadower and I concluded there is no easy way for this but wanted to check with you, @jandraor.

Q4. When we say `state variables` is this equivalent with `stock variable`?

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