All simulators
Log-Likelihood Explorer
Move the parameter along a Bernoulli log-likelihood; see the peak, its curvature and the LR test.
Day 11: Maximum Likelihood Estimationℓ(p)quadratic approximationcandidate p and its slope (score)95% LR interval
MLE p̂ = S/N
0.600
SE = 1/√(Fisher info)
0.0894
Score at candidate
25.00
uphill → move right
LR test of p = 0.5
1.21
do not reject (≤ 3.84)
The log-likelihood peaks at p̂ = S/N. The dashed parabola is the quadratic approximation whose curvature (Fisher information) gives the SE. The green band is the 95% likelihood-ratio interval: all p within 1.92 log-points of the peak.