Example: Global Likelihood fitting

In this example, we shall perform likelihood fitting to two data sets at the same time to show how likelihood fitting can be used to fit multiple data sets at the same time.

First we will fit using a different parameter for each data set, and then with the same for both data sets. This shows the ease with which we can experiment with different models.

import numpy as np
from symfit import variables, parameters, Fit, exp, Model
from symfit.core.objectives import LogLikelihood

# Draw samples from a bivariate distribution
np.random.seed(42)
data1 = np.random.exponential(5.5, 1000)
data2 = np.random.exponential(6, 2000)

# Define the model for an exponential distribution (numpy style)
a, b = parameters('a, b')
x1, y1, x2, y2 = variables('x1, y1, x2, y2')
model = Model({
    y1: (1 / a) * exp(-x1 / a),
    y2: (1 / b) * exp(-x2 / b)
})
print(model)

fit = Fit(model, x1=data1, x2=data2, objective=LogLikelihood)
fit_result = fit.execute()
print(fit_result)

# Instead, we could also fit with only one parameter to see which works best
model = Model({
    y1: (1 / a) * exp(-x1 / a),
    y2: (1 / a) * exp(-x2 / a)
})

fit = Fit(model, x1=data1, x2=data2, objective=LogLikelihood)
fit_result = fit.execute()
print(fit_result)