Covid Bayesian Analysis

This project uses Bayesian methods and probabilistic programming to analyze the COVID-19 pandemic. It estimates effective reproduction rate and daily new cases for Hong Kong. The data is obtained from DATA.GOV.HK.

The main idea is based on rtlive and k-sys/covid-19 by Thomas Wiecki and Kevin Systrom. The model is a State Space Model with Gaussian random walk prior, implemented in PyMC.

A few plots are generated to visualize the results. Note that time series plots are mostly in aspect ratio 21:9 for better visualization.^[1][2]

Ideas

• Used state space model and Bayesian model to provide a generalized framework to model the COVID-19 pandemic with building blocks. i.e. The combination allows me to encode any prior knowledge and assumptions into the model iteratively.
• Model infection delay by using generation time distribution
• Model onset to confirmation delay by applying 1d convolution with n days pmf
• Model variance >> mean due to breakouts and settlements in epidemic waves by using negative binomial distribution instead of Poisson to avoid over-dispersion
• Model unpredictable human behavior by using Gaussian random walk prior
• Model excess zeros to avoid downward bias on parameter estimates by using zero-inflated negative binomial distribution

Acknowledgements

Implementations and Tutorials

• rtlive
  • uses State Space Model with Gaussian random walk prior
  • Youtube@The Bayesian Workflow: Building a COVID-19 Model by Thomas Wiecki
  • generative-rtlive.ipynb — Thomas Wiecki
  • rtcovidlive/covid-model/generative.py — Thomas Wiecki
  • rtcovidlive/rtlive-global/Tutorial_model.ipynb — Kevin Systrom
• k-sys/covid-19 — Kevin Systrom, founder of Instagram
  • k-sys/covid-19/Realtime R0.ipynb — Kevin Systrom
    • no probabilistic library, uses max-likelihood estimation
    • uses Gaussian Processes
    • alternatives:
      • farr/covid-19/Stan R0.ipynb — Will M. Farr
        • based on k-sys/covid-19/Realtime R0.ipynb, but using Bayesian posterior
        • similar to k-sys/covid-19/Realtime Rt mcmc.ipynb, but estimating $R_t$ of confirmation instead.
      • discussion on github issue: binomial distribution instead of a Poisson
      • discussion on github issue: smoothing
  • k-sys/covid-19/Realtime Rt mcmc.ipynb — Kevin Systrom
    • Ideas
      • attempt to account for delays between infection, onset, and confirmation
      • Translate Confirmation Dates to Onset Dates
      • Adjust for Right-Censoring
    • Implemented Gaussian random walk prior model and Gaussian process prior model
    • Sample the Posterior with PyMC3
    • inspired by Thomas Vladdeck’s work
    • helped by Thomas Wiecki
• tvladeck/covid-rt — Thomas P. Vladeck
  • uses State Space Model
  • implemented in Stan
  • Blog: Using State Space Models to Estimate Rt — Thomas P. Vladeck
    • background on this is k-sys/covid-19/Realtime R0.ipynb
    • update: Extending the State Space Approach with Mixed Effects
• luisroque/bayesian_time_series | Forecasting new COVID19 cases in Portugal using Gaussian Processes.ipynb
  • uses Gaussian Processes
• Blog: Reflections on two years estimating effective reproduction numbers
• twiecki/covid19 bunch of ipynb — Thomas Wiecki
• Compartmental model
  • dsheldon/covid — Bayesian SEIRD model
  • Youtube@SIR model — Thomas Wiecki
  • Priesemann-Group implementations
    • uses SIR/SEIR models
    • Priesemann-Group/covid19_inference
    • Priesemann-Group/covid19_inference_forecast
    • Research Article published in Science: Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions
    • Talk: Inferring the spread of SARS-CoV-2 --- and measures to mitigate it (Viola Priesemann)
  • Discussion: SIR ODE model with Sunode
• tensorflow/probability/Estimating_COVID_19_in_11_European_countries.ipynb
  • fine tuned bijectors to solve problem of heaviness of tails of lognormal distribution and make inference fast and numerically more stable
• broadinstitute/pyro-cov | Pyro models for SARS-CoV-2 analysis
  • implemented in Pyro
  • Research Article published in Science: Analysis of 6.4 million SARS-CoV-2 genomes identifies mutations associated with fitness
• epidemics/COVIDNPIs
  • Research Article published in Science: Inferring the effectiveness of government interventions against COVID-19
• Causal inference on excess deaths due to COVID-19
  • it is a tutorial on causal inference based on Google’s CausalImpact using PyMC3