# Numerical Optimization

Maximum likelihood fixes our observed data and asks: What parameter values most likely generated the data we have? In a likelihood framework, our data is viewed as a joint probability as a function of parameter values for a specified mass or density function. In this case, the joint probability is being maximized with respect to the parameters. A maximum likelihood estimate is one that provides the density or mass function with the highest likelihood of generating the observed data. Numerical optimizers provide the means to estimate our parameters by finding the values that maximize the likelihood of generating our data. This guide helps us understand how optimization algorithms find the best estimates for our coefficients in a step-by-step process.