# Fits with shared parameters¶

We demonstrate how to simultaneously fit two datasets with different models that shares a common parameter.

[1]:

from iminuit import Minuit
from iminuit.cost import UnbinnedNLL
from iminuit.util import describe
from matplotlib import pyplot as plt
import numpy as np
from numba_stats import norm

[2]:

# generate two data sets which are fitted simultaneously
rng = np.random.default_rng(1)

width = 2.0
data1 = rng.normal(0, width, size=1000)
data2 = rng.normal(5, width, size=1000)

[3]:

# use two pdfs with different names for non-shared parameters,
# so that they are fitted independently

def pdf1(x, μ_1, σ):
return norm.pdf(x, μ_1, σ)

def pdf2(x, μ_2, σ):
return norm.pdf(x, μ_2, σ)

# combine two log-likelihood functions by adding them
lh = UnbinnedNLL(data1, pdf1) + UnbinnedNLL(data2, pdf2)

print(f"{describe(lh)=}")

describe(lh)=['μ_1', 'σ', 'μ_2']


The σ parameter is shared between the data sets, while the means of the two normal distributions are independently fitted.

[4]:

def plot(cost, xe, minuit, ax, **style):
signature = describe(cost)
data = cost.data

values = minuit.values[signature]
errors = minuit.errors[signature]

cx = (xe[1:] + xe[:-1]) / 2

ym = np.diff(norm.cdf(xe, *values)) * np.sum(w)
t = []
for n, v, e in zip(signature, values, errors):
t.append(f"${n} = {v:.3f} ± {e:.3f}$")
ax.plot(cx, ym, label="\n".join(t), **style)

[5]:

m = Minuit(lh, μ_1=1, μ_2=2, σ=1)

fig, ax = plt.subplots(1, 2, figsize=(14, 5))

hists = [np.histogram(lhi.data, bins=50) for lhi in lh]

# draw data and model with initial parameters
for lhi, (w, xe), axi in zip(lh, hists, ax):
cx = (xe[1:] + xe[:-1]) / 2
axi.errorbar(cx, w, np.sqrt(w), fmt="ok", capsize=0, zorder=0)
plot(lhi, xe, m, axi, ls="--")