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damonbayer / semi_parametric_COVID_19_OC_model

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Prior distribution for constant alpha #4

Open fkrauer opened 8 months ago

fkrauer commented 8 months ago

Hi Damon,

I just came across your model, and I am thinking of implementing the same beta-binomial LL to incorporate Testing behaviour in my model. However, I am stuck in your code at this line: https://github.com/damonbayer/semi_parametric_COVID_19_OC_model/blob/70528d9c8cf0a883d1e9e279c86add24a2236b66/src/bayes_seird.jl#L24

Where does the I come from, i.e. what is it? And from where is the Zeros() function? If I want to use a constant α, what does the prior distribution have to look like? Thanks a lot for your help.

Also, why is it a Multivariate-Normal, instead of a Normal?

Bw, Fabienne

damonbayer commented 8 months ago

Hi @fkrauer,

Thanks for checking out my work!

I is an identity matrix. It comes from LinearAlgebra.jl: https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.I

Zeros comes from FillArrays.jl: https://juliaarrays.github.io/FillArrays.jl/stable/#FillArrays.Zeros

The prior on α can technically be an unbounded distribution on the real numbers, but to make practical sense it should be strictly positive, since α = 0 corresponds to randomly sampling tests from the population and α > 0 corresponds to oversampling people who have the disease (e.g. people who have symptoms).

Here is a figure from an older version of our paper that may give you some intuition: latent_incidence_test_pos_plot.pdf

fkrauer commented 8 months ago

That's very helpful, thanks so much. I had a quick look at the supplement (table 1,1), and I am fitting it now with your LogNormal prior now (for both α and phi_C). Fingers crossed!