Statistical Computing 1

Tidyverse The Tidyverse is a set of inter-compatible packages that are used throughout data science. The Tidyverse provides powerful tools that allow us to quickly `tidy’ data into data frames, transform the data, and then visualize it. This will then allow us to produce models. Throughout this report we will explore a real dataset found on Kaggle. Pipes The pipe operator %>% is provided by the magrittr R package. Pipes are a powerful tool that allow us to clearly express a sequence of operations....

Debugging When writing code it is common to encounter problems which you do not expect. Functions for complex statistical tasks often do not return the output you want — in some cases it is obvious, but not always. It’s important to have a strong understanding of the debugging options offered by R and particular IDEs such as RStudio. Knowledge of these tools can make debugging much more efficient. When debugging code we should:...

Matrices In this report we will look at how R treats matrices. We will explore the Matrix package, which extends the basic R functionality for matrices. For example, it seems odd that base R does not have a method of determining the rank of a matrix up to a certain tolerance — the Matrix package adds this functionality. Dense matrices A matrix is a two dimensional data structure in R....

Numerical Optimization An optimization problem is the problem of finding the best solution within a set of feasible solutions. There are many characteristics of optimization problems that define them and determine the methods needed to solve them. For example, we may have continuous or discrete problems; convex or non-convex problems; linear or non-linear problems. In this document we will consider continuous problems, and make no explicit assumptions on the convexity or the linearity of the problem....

Numerical Integration Quadrature “Quadrature rules” are integral approximations which use a finite number of evaluations of the function. All of the quadrature rules below approximate a function using interpolating polynomials. We will first look at some key ideas in numerical integration by approximating definite integrals over a finite interval. We will then extend these ideas to semi-infinite and infinite intervals. We will also consider multiple integrals. In practice we can use Rs integrate function for one-dimensional integrals, and the cubature package for multiple integrals....