Some quick example code for parameter estimation with an SIR model, as well as for examining identifiability and uncertainty using the Fisher information matrix and profile likelihoods---see lab assignment pdf for more info (this code is for Part 2). This code was originally developed for an assignment for the 2017 NIMBioS/MBI/CAMBAM Graduate Summer School and for the NIMBioS Uncertainty Quantification Tutorial. Equivalent code is provided in R, Matlab, and python, which goes through the following steps:
- Simulate the model at some starting parameter values
- Estimate the model parameters from (simulated) outbreak data using maximum likelihood (ML) (assuming Poisson with mean given by the model, but can be changed to whatever you prefer, e.g. least squares, etc.)
- Calculate a simplified form of the Fisher information matrix (FIM) and test its rank to evaluate the number of identifiable parameters/combinations
- Generate profile likelihoods for each parameter and determine 95% confidence intervals
Questions? Contact Marisa Eisenberg (marisae@umich.edu). This material is licensed under the MIT License---feel free to use/modify with acknowledgement of the original source (see license text).