#### Overview of this book

Julia, with its dynamic nature and high-performance, provides comparatively minimal time for the development of computational models with easy-to-maintain computational code. This book will be your solution-based guide as it will take you through different programming aspects with Julia. Starting with the new features of Julia 1.0, each recipe addresses a specific problem, providing a solution and explaining how it works. You will work with the powerful Julia tools and data structures along with the most popular Julia packages. You will learn to create vectors, handle variables, and work with functions. You will be introduced to various recipes for numerical computing, distributed computing, and achieving high performance. You will see how to optimize data science programs with parallel computing and memory allocation. We will look into more advanced concepts such as metaprogramming and functional programming. Finally, you will learn how to tackle issues while working with databases and data processing, and will learn about on data science problems, data modeling, data analysis, data manipulation, parallel processing, and cloud computing with Julia. By the end of the book, you will have acquired the skills to work more effectively with your data
Title Page
Dedication
Contributors
Preface
Variables, Types, and Functions
Julia Workflow
Distributed Computing
Other Books You May Enjoy
Index

## Estimation using maximum likelihood

In this recipe, we discuss how you can perform the optimization of a likelihood function using Julia.

Maximum likelihood is one of the basic techniques for the estimation of the parameters of a statistical model; see http://mathworld.wolfram.com/MaximumLikelihood.html or https://en.wikipedia.org/wiki/Maximum_likelihood_estimation for a more detailed discussion. In this recipe, we estimate the mean and standard deviation of a sample coming from a normal distribution. In this case, an analytical solution to this optimization problem is known and the estimate of the mean is the mean of the sample

and the estimate of standard deviation is

, where

is the sample size and

are sample points.

We chose a problem whose analytical solution is known in order to compare whether the results using optimization and exact calculation are similar.

In this recipe, we will use the Optim.jl package. If you do not have it installed, please add it using these commands...