Introduction to Scientific Programming and Simulation Using R, 2/Ed > 프로그래밍

Table of Contents

Table of Contents

Preface

How to use this book

Programming

Setting up

Installing R

Starting R

Working directory

Writing scripts

Help

Supporting material

R as a calculating environment

Arithmetic

Variables

Functions

Vectors

Missing data: NA

Expressions and assignments

Logical expressions

Matrices

The workspace

Exercises

Basic programming

Introduction

Branching with if

Looping with for

Looping with while

Vector-based programming

Program flow

Basic debugging

Good programming habits

Exercises

Input and output

Text

Input from a file

Input from the keyboard

Output to a file

Plotting

Exercises

Programming with functions

Functions

Arguments

Vector-based programming using functions

Recursive programming

Debugging functions

Exercises

Sophisticated data structures

Factors

Dataframes

Lists

Exercises

Better graphics

Introduction

Graphics parameters: par

Graphical augmentation

Mathematical typesetting

Permanence

Grouped graphs: lattice

Exercises

Pointers to further programming techniques

Packages

Frames and environments

Debugging again

Identifying bottlenecks

Object-oriented programming: S3

Object-oriented programming: S4

Manipulation of data

Compiled code

Further reading

Exercises

Numerical accuracy and program efficiency

Machine representation of numbers

Significant digits

Time

Loops versus vectors

Parallel processing

Memory

Caveat

Exercises

Root-finding

Introduction

Fixed-point iteration

The Newton–Raphson method

The secant method

The bisection method

Exercises

Numerical integration

Trapezoidal rule

Simpson’s rule

Adaptive quadrature 210

11.4 Exercises 214

Optimisation

Newton’s method for optimisation

The golden-section method

Multivariate optimisation

Steepest ascent

Newton’s method in higher dimensions

Optimisation in R and the wider world

A curve-fitting example

Exercises

Systems of ordinary differential equations

Euler’s method

Midpoint method

Fourth-order Runge–Kutta

Efficiency

Adaptive step size

Exercises

Probability

The probability axioms

Conditional probability

Independence

The Law of Total Probability

Bayes’ theorem

Exercises

Random variables

Definition and distribution function

Discrete and continuous random variables

Empirical cdf’s and histograms

Expectation and finite approximations

Transformations

Variance and standard deviation

The Weak Law of Large Numbers

Exercises

Discrete random variables

Discrete random variables in R

Bernoulli distribution

Binomial distribution

Geometric distribution

Negative binomial distribution

Poisson distribution

Exercises

Continuous random variables

Continuous random variables in R

Uniform distribution

Lifetime models: exponential and Weibull

The Poisson process and the gamma distribution

Sampling distributions: normal, χ2, and t

Exercises

Parameter estimation

Point estimation

The Central Limit Theorem

Confidence intervals

Monte Carlo confidence intervals

Exercises

　

　

Markov chains

Introduction to discrete time chains

Basic formulae: discrete time

Classification of states

Limiting behaviour: discrete time

Finite absorbing chains

Introduction to continuous time chains

Rate matrix and associated equations

Limiting behaviour: continuous time

Defining the state space

Simulation

Estimation

Estimating the mean of the limiting distribution

Exercises

Simulation

Simulating iid uniform samples

Simulating discrete random variables

Inversion method for continuous rv

Rejection method for continuous rv

Simulating normals

Exercises

Monte Carlo integration

Hit-and-miss method

(Improved) Monte Carlo integration

Exercises

Variance reduction

Antithetic sampling

Importance sampling

Control variates

Exercises

Case studies

Introduction

Epidemics

Inventory

Seed dispersal

Student projects

The level of a dam

Runoff down a slope

Roulette

Buffon’s needle and cross

The pipe spiders of Brunswick

Insurance risk

Squash

Stock prices

Conserving water

Glossary of R commands

Programs and functions developed in the text

Index