Parameter fitting

Computational parameter fitting repeatedly evaluates a model while searching for parameter values that optimise a statistical objective.

Least-squares example

from scipy.optimize import least_squares

def residuals(theta):
    prediction = simulate(theta, t_data)
    return y_data - prediction

fit = least_squares(residuals, x0=[0.2, 0.1])

Constraints and transformations

Biological parameters such as rates may need to remain non-negative. Bounds or suitable parameter transformations can enforce meaningful ranges.

Checking the result

Optimisation success does not guarantee identifiability or a unique optimum. Residuals, alternative starting values and uncertainty should also be examined.