Data-fitting project
This project connects observed biological data to a mechanistic model. Suppose observations \(y_i\) are recorded at times \(t_i\), and the model prediction is \(m(t_i;\theta)\).
Least squares
Estimate parameters by minimising
\[S(\theta)=\sum_{i=1}^{n}[y_i-m(t_i;\theta)]^2.\]Workflow
Inspect and document the data, choose a model and observation quantity, specify parameters to estimate, solve the model for each trial parameter set, optimise the objective and compare fitted predictions with observations.
After fitting
Inspect residuals and parameter sensitivity, assess uncertainty and test whether different parameter combinations produce nearly indistinguishable fits. Where possible, evaluate predictive performance on data not used for fitting.
Project outcome. Treat parameter fitting as a complete modelling workflow rather than simply obtaining the optimiser's best parameter values.