Fastlikelihood fitting and inconsistent Chi square value

[Md-Isha-Ali]

Dear Experts,

Theoretically chi square cannot have negative value . But When I tried to minimize the chi square function defined as -2*log_likelihood_function , I got negative value.
I have used the available code in the website which I am writing below for better understanding . I am confused why chi square is negative ?
------------------------------------------------------------------------code---------------------------------------------------
FL = FastLikelihood(name='My fast likelihood',
observables=['BR(B->Xsgamma)', 'BR(Bs->mumu)', 'BR(B0->mumu)'],
include_measurements=['AS combination Bs->mumu 2021', 'B->Xgamma WA 2017'])

FL.make_measurement(N=1000, threads=8, force=True)

from wilson import Wilson

par = flavio.parameters.default_parameters.get_central_all()

def FLL(x):
Re_C7, Re_C10 = x
w = Wilson({'C10_bsmumu': Re_C10, 'C7_bs': Re_C7},
scale=4.8,
eft='WET', basis='flavio')
return FL.log_likelihood(par, w)

print(FLL([0.0023,0.48]))

from flavio.math.optimize import minimize

def chi2(x):
return -2*FLL(x)

chi2_min = minimize(chi2,[0,0])
chi2_min

Results:
message: Optimization terminated successfully.
success: True
status: 0
fun: -105.37189937874699
x: [ 2.361e-03 4.813e-01]
nit: 7
jac: [-9.537e-07 -2.861e-06]
hess_inv: [[ 1.544e-04 -3.627e-05]
[-3.627e-05 2.791e-02]]
nfev: 33
njev: 11

---

Also likelihood is a multiplication of probability density function where each density function integral value can be maximum 1 . So any likelihood function would have value in range [0,1] and hence log_likelihood have values [-infinity,0] . I have no clue what is happening .
The 'fun' value is chi2_min value and to mention at minimum FLL value is 52 which is inconsistent with my theoretical understanding

Please guide me regarding this .

regards,
Md Ali

[DavidMStraub]

Well,

def chi2(x):
    return -2*FLL(x)

is just wrong.

Try what -2 * log(scipy.stats.norm.pdf(0)) yields – not zero.

Twice the negative log likelihood and the chi-square are only equal up to a constant.