English: In statistics, maximum likelihood estimation is a technique commonly used to reconstruct unobserved parameters based on observed data. The likelihood of the data is calculated for every possible set of parameters, and an optimization algorithm such as gradient descent is used to find the set of parameters that maximizes that likelihood.

The two axes of the plot represent two coupled parameters. The shading and contours represent the likelihood function, where white is lower and green is higher.

Starting from an arbitrary guess, gradient descent follows the blue path and arrives at the optimal point (the blue triangle), and this set of parameters is accepted as the best answer.

This plot can alternatively be interpreted as maximum a posteriori estimation. The only difference is that the shading and contours then represent the posterior probability distribution of the parameters rather than the likelihood of the data.