Marginalizing out a branching process model for coronavirus progression

Modeling
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Hi all. See here: https://statmodeling.stat.columbia.edu/2020/03/18/another-bayesian-model-of-coronavirus-progression/
It’s a link to a Bayesian model (not in Stan) with a branching process. Maybe it would be possible to do this in Stan, marginalizing out the branching process. If so, this could be helpful.

If different people working in this area are all writing Stan models, it should be easier for them to communicate with each other and ultimately build better models.

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R code and data

My gut reaction is that marginalizing out a branching process would involve recursive calls to map_rect and even then I am not sure how feasible it is.

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