Lexical scoping is a useful concept in optimization because it allows you to abstract away much of the complexity involved in creating and using objective functions. For example, the `make.NegLogLik()` function in the previous section takes a dataset and a vector of fixed parameters as input, and returns a function that can be minimized to find maximum likelihood estimates in a statistical model. The function is able to do this because it uses lexical scoping to access the data and fixed parameters from the environment in which it was defined.
This makes it possible to write very concise and easy-to-understand code for optimization problems. For example, the following code shows how to use the `make.NegLogLik()` function to estimate the parameters of a normal distribution:
set.seed(1)
normals <- rnorm(100, 1, 2)
nLL <- make.NegLogLik(normals)
optim(c(mu = 0, sigma = 1), nLL)$par
This code first generates some data from a normal distribution, and then uses the `make.NegLogLik()` function to create a function that can be minimized to find the maximum likelihood estimates of the mean and standard deviation of the distribution. The `optim()` function then minimizes the function and returns the estimates.
