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Introduction to Scientific Programming and Simulation Using R 2nd Edition
출판사 : CRC
저 자 : Jones
ISBN : 9781466569997
발행일 : 2014-6
도서종류 : 외국도서
발행언어 : 영어
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   Introduction to Scientific Programming and Simulation Using R 2nd Edition 목차
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
   도서 상세설명   

Summary

Learn How to Program Stochastic Models

Highly recommended, the best-selling first edition of Introduction to Scientific Programming and Simulation Using R was lauded as an excellent, easy-to-read introduction with extensive examples and exercises. This second edition continues to introduce scientific programming and stochastic modelling in a clear, practical, and thorough way. Readers learn programming by experimenting with the provided R code and data.

The book’s four parts teach:

Core knowledge of R and programming concepts
How to think about mathematics from a numerical point of view, including the application of these concepts to root finding, numerical integration, and optimisation
Essentials of probability, random variables, and expectation required to understand simulation
Stochastic modelling and simulation, including random number generation and Monte Carlo integration
In a new chapter on systems of ordinary differential equations (ODEs), the authors cover the Euler, midpoint, and fourth-order Runge-Kutta (RK4) schemes for solving systems of first-order ODEs. They compare the numerical efficiency of the different schemes experimentally and show how to improve the RK4 scheme by using an adaptive step size.

Another new chapter focuses on both discrete- and continuous-time Markov chains. It describes transition and rate matrices, classification of states, limiting behaviour, Kolmogorov forward and backward equations, finite absorbing chains, and expected hitting times. It also presents methods for simulating discrete- and continuous-time chains as well as techniques for defining the state space, including lumping states and supplementary variables.

Building readers’ statistical intuition, Introduction to Scientific Programming and Simulation Using R, Second Edition shows how to turn algorithms into code. It is designed for those who want to make tools, not just use them. The code and data are available for download from CRAN.

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