Likelihood Surface Explorer — Maximum Likelihood Estimation

Statistical inference means drawing conclusions about an unknown population from a finite sample, and maximum likelihood is the workhorse method for doing it: pick the parameter values that make the observed data most probable. This simulator draws a random sample from a Normal(μ, σ) population and renders its full log-likelihood function as a real 3D landscape over every candidate (μ, σ) pair, colored and height-mapped by log-likelihood. The maximum-likelihood estimate sits exactly at the landscape's peak — the sample mean and the biased sample standard deviation — while a draggable probe slides along the ridge to show how sharply the likelihood falls away from that peak. That fall-off rate is the Fisher information, and its inverse square root is the asymptotic standard error reported alongside almost every fitted statistic in science.