Introduction to scientific programming and simulation using R / Owen Jones, Robert Maillardet, and Andrew Robinson.

Format:

Book

Author/Creator:

Jones, Owen (Owen Dafydd)

Contributor:

Maillardet, Robert.

Robinson, Andrew (Andrew P.)

Hazel M. Hussong Fund.

Language:

English

Subjects (All):

Science--Data processing.

Science.

Science--Computer simulation.

Stochastic processes--Mathematical models.

Stochastic processes.

Numerical analysis--Data processing.

Numerical analysis.

Computer programming.

R (Computer program language).

Physical Description:

xix, 453 pages : illustrations ; 24 cm

Other Title:

Scientific programming and simulation using R

Place of Publication:

Boca Raton, FL : Chapman & Hall/CRC, 2009.

Summary:

Known for its versatility, the free programming language R is widely used for statistical computing and graphics, but is also a fully functional programming language well suited to scientific programming.

An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to perform scientific programming while also introducing stochastic modelling. Stochastic modelling in particular, and mathematical modelling in general, are intimately linked to scientific programming because the numerical techniques of scientific programming enable the practical application of mathematical models to real-world problems.

Following a natural progression that assumes no prior knowledge of programming or probability, the book is organised into four main sections:

Programming in R starts with how to obtain and install R (for Windows, MacOS, and Unix platforms), then tackles basic calculations and program flow before progressing to function based programming, data structures, graphics, and object-oriented code

A primer on numerical mathematics introduces concepts of numerical accuracy and program efficiency in the context of root-finding, integration, and optimization

A self-contained introduction to probability theory takes readers as far as the Weak Law of Large Numbers and the Central Limit Theorem, equipping them for point and interval estimation

Simulation teaches how to generate univariate random variables, do Monte-Carlo integration, and variance reduction techniques

In the last section, stochastic modelling is introduced using extensive case studies on epidemics, inventory management, and plant dispersal. A tried and tested pedagogic approach is employed throughout, with numerous examples, exercises, and a suite of practice projects.

Unlike most guides to R, this volume is not about the application of statistical techniques, but rather shows how to turn algorithms into code. It is for those who want to make tools, not just use them.

Contents:

I Programming 1

1 Setting up 3

1.1 Installing R 3

1.2 Starting R 3

1.3 Working directory 4

1.4 Writing scripts 5

1.5 Help 5

1.6 Supporting material 5

2 R as a calculating environment 11

2.1 Arithmetic 11

2.2 Variables 12

2.3 Functions 13

2.4 Vectors 15

2.5 Missing data 18

2.6 Expressions and assignments 19

2.7 Logical expressions 20

2.8 Matrices 23

2.9 The workspace 25

2.10 Exercises 25

3 Basic programming 29

3.1 Introduction 29

3.2 Branching with if 31

3.3 Looping with for 33

3.4 Looping with while 36

3.5 Vector-based programming 38

3.6 Program flow 39

3.7 Basic debugging 41

3.8 Good programming habits 42

3.9 Exercises 43

4 I/O: Input and Output 49

4.1 Text 49

4.2 Input from a file 51

4.3 Input from the keyboard 53

4.4 Output to a file 55

4.5 Plotting 56

4.6 Exercises 58

5 Programming with functions 63

5.1 Functions 63

5.2 Scope and its consequences 68

5.3 Optional arguments and default values 70

5.4 Vector-based programming using functions 70

5.5 Recursive programming 74

5.6 Debugging functions 76

5.7 Exercises 78

6 Sophisticated data structures 85

6.1 Factors 85

6.2 Dataframes 88

6.3 Lists 94

6.4 The apply family 98

6.5 Exercises 105

7 Better graphics 109

7.1 Introduction 109

7.2 Graphics parameters: par 111

7.3 Graphical augmentation 113

7.4 Mathematical typesetting 114

7.5 Permanence 118

7.6 Grouped graphs: lattice 119

7.7 3D-plots 123

7.8 Exercises 124

8 Pointers to further programming techniques 127

8.1 Packages 127

8.2 Frames and environments 132

8.3 Debugging again 134

8.4 Object-oriented programming: S3 137

8.5 Object-oriented programming: S4 141

8.6 Compiled code 144

8.7 Further reading 146

8.8 Exercises 146

II Numerical techniques 149

9 Numerical accuracy and program efficiency 151

9.1 Machine representation of numbers 151

9.2 Significant digits 154

9.3 Time 156

9.4 Loops versus vectors 158

9.5 Memory 160

9.6 Caveat 161

9.7 Exercises 162

10 Root-finding 167

10.1 Introduction 167

10.2 Fixed-point iteration 168

10.3 The Newton-Raphson method 173

10.4 The secant method 176

10.5 The bisection method 178

10.6 Exercises 181

11 Numerical integration 187

11.1 Trapezoidal rule 187

11.2 Simpson's rule 189

11.3 Adaptive quadrature 194

11.4 Exercises 198

12 Optimisation 201

12.1 Newton's method for optimisation 202

12.2 The golden-section method 204

12.3 Multivariate optimisation 207

12.4 Steepest ascent 209

12.5 Newton's method in higher dimensions 213

12.6 Optimisation in R and the wider world 218

12.7 A curve fitting example 219

12.8 Exercises 220

III Probability and statistics 225

13 Probability 227

13.1 The probability axioms 227

13.2 Conditional probability 230

13.3 Independence 232

13.4 The Law of Total Probability 233

13.5 Bayes' theorem 234

13.6 Exercises 235

14 Random variables 241

14.1 Definition and distribution function 241

14.2 Discrete and continuous random variables 242

14.3 Empirical cdf's and histograms 245

14.4 Expectation and finite approximations 246

14.5 Transformations 251

14.6 Variance and standard deviation 256

14.7 The Weak Law of Large Numbers 257

14.8 Exercises 261

15 Discrete random variables 267

15.1 Discrete random variables in R 267

15.2 Bernoulli distribution 268

15.3 Binomial distribution 268

15.4 Geometric distribution 270

15.5 Negative binomial distribution 273

15.6 Poisson distribution 274

15.7 Exercises 277

16 Continuous random variables 281

16.1 Continuous random variables in R 281

16.2 Uniform distribution 282

16.3 Lifetime models: exponential and Weibull 282

16.4 The Poisson process and the gamma distribution 287

16.5 Sampling distributions: normal, X2, and t 292

16.6 Exercises 297

17 Parameter Estimation 303

17.1 Point Estimation 303

17.2 The Central Limit Theorem 309

17.3 Confidence intervals 314

17.4 Monte-Carlo confidence intervals 321

17.5 Exercises 322

IV Simulation 329

18 Simulation 331

18.1 Simulating iid uniform samples 331

18.2 Simulating discrete random variables 333

18.3 Inversion method for continuous rv 338

18.4 Rejection method for continuous rv 339

18.5 Simulating normals 345

18.6 Exercises 348

19 Monte-Carlo integration 355

19.1 Hit-and-miss method 355

19.2 (Improved) Monte-Carlo integration 358

19.3 Exercises 360

20 Variance reduction 363

20.1 Antithetic sampling 363

20.2 Importance sampling 367

20.3 Control variates 372

20.4 Exercises 374

21 Case studies 377

21.1 Introduction 377

21.2 Epidemics 378

21.3 Inventory 390

21.4 Seed dispersal 405

22 Student projects 421

22.1 The level of a dam 421

22.2 Roulette 425

22.3 Buffon's needle and cross 428

22.4 Insurance risk 430

22.5 Squash 433

22.6 Stock prices 438.

Notes:

"This volume is not about the application of statistical techniques, but rather shows how to turn algorithms into code"--Back cover.

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

9781420068726

1420068725

OCLC:

156830835

Publisher Number:

99937299820