A package for simple parameter fitting.
Open Julia REPL in the project directory and run the following commands to instantiate the package environment with all necessary dependencies.
import Pkg
Pkg.activate(".")
Pkg.instantiate()
The installation commands are also included in the installation script.
See the example script that demonstrates fitting of the single-humped function to the data.
The input data are considered to be in the long form as shown in the example data. In this particular example, Month indicates the time vector and rel.eng data vector. The remaining columns are labels describing the individual members of the population. The data can be converted to the wide format by calling load_long_data.
The single-humped function has form
x(t) = 0, if t < τ,
x(t) = R * (t - τ) / (1 + ((t - τ) / θ) ^ n), if t >= τ,
where τ is time delay, R growth rate, θ repression coefficient, and n Hill coefficient. The figure below shows the effects of the individual parameters on the final function.
The following three figures show examples of the fitted single-humped function to various data. The titles of the individual figures indicate the estimated parameters of the single-humped function and additional parameters estimated by the model: area under the curve (AUC), root-mean-square error (RMSE) to quantify the quality of the fit, and the number of available data points (N).
