Add multiple variants to the inferential model

Data-Science-Brigade / modelo-epidemiologico-sc

Bayesian epidemiological model, with a focus on the state of Santa Catarina and its micro and macroregions. https://arxiv.org/abs/2104.01133

MIT License

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Add multiple variants to the inferential model #58

Open jonjoncardoso opened 3 years ago

jonjoncardoso commented 3 years ago

Add multiple variants to the model

1st step:

[ ] Start from a simple case, without google mobility (Tutorial01)
[ ] Set second variant to start at a certain date
[ ] Use the mock dataset

2nd step:

[ ] Add an integer list variants to the data section
[ ] Break mu distribution into two distributions: for variant in variants: mu[variant] ~ ....
[ ] Rt should be indexed by variants as well. ex: Rt[i, m, v]
[ ] prediction becomes the sum of the products between different Rts and each variant convolution
[ ] How to include a binary variable in the model to "choose" which variant is available and when

Originally posted by @jonjoncardoso in https://github.com/Data-Science-Brigade/modelo-epidemiologico-sc/issues/50#issuecomment-888517434

jonjoncardoso commented 3 years ago

I've just realized that a Bayesian piecewise linear model could help with the final task. Here's a reference where they have implemented just that:

Andras, P. (2012). A Bayesian Interpretation of the Particle Swarm Optimization and Its Kernel Extension. PLoS ONE, 7(11), e48710. https://doi.org/10.1371/journal.pone.0048710

A piecewise linear model is when you separate your X data into disjoint regions, each driven by their own linear equations.

A visual example from _

Cardoso-Silva, J., Papadatos, G., Papageorgiou, L. G., & Tsoka, S. (2018). Optimal Piecewise Linear Regression Algorithm for QSAR Modelling. Molecular Informatics, 0(0). https://doi.org/10.1002/minf.201800028

jonjoncardoso commented 3 years ago

Maybe this is a better/simpler source of a Bayesian piecewise model?

Brilleman, S. L., Howe, L. D., Wolfe, R., & Tilling, K. (2017). Bayesian piecewise linear mixed models with a random change point: An application to BMI rebound in childhood. Epidemiology, 28(6), 827–833. https://doi.org/10.1097/EDE.0000000000000723

jonjoncardoso commented 3 years ago

STAN code for the Brilleman et al paper is here on Github: https://github.com/sambrilleman/2017-Epidemiology/blob/master/stancode_randomchangecorr.stan

jonjoncardoso commented 3 years ago

I've started drafting an R notebook to attempt some progress at this multiwave business using our synthetic data (check this branch) but I believe we will have to revisit the mock data script first before running any STAN model. Our current mock data does not take the infection-to-death temporal delay into consideration.