Introduction to scientific programming and simulation using R

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 Rteaches 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 Rstarts 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 Mathematicsintroduces concepts of numerical accuracy and program efficiency in the context of root-finding, integration, and optimization A Self-contained Introduction to Probability Theorytakes 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.

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This book by Jones, Maillardet, and Robinson (all, mathematics and statistics, Univ. of Melbourne, Australia) is an introduction to programming in R. R is an open source software package that is widely used in statistical analysis. Unlike most other works on R, this book begins by discussing R as a programming language, rather than by using R to perform various kinds of statistical analysis. The second section of the book discusses numerical methods including root finding, integration, and optimization. These first two sections are accessible to lower-level undergraduates with little background in statistics. The volume's third and fourth sections build on the first two sections to introduce the reader to probability, statistics, and Monte Carlo simulation. This work will be of interest to instructors teaching courses in programming to statistics students as well as to users of R who want to learn R programming. Compare this book with P. Dalgaard's Introductory Statistics with R (1st ed., 2002; 2nd ed., 2008), which provides more coverage of the statistical procedures built into R, but does not cover R programming as thoroughly. Summing Up: Recommended. Academic audiences, lower-division undergraduate and above, and professionals/practitioners. B. Borchers New Mexico Institute of Mining and Technology

Preface	p. v
I Programming	p. 1
1 Setting up	p. 3
1.1 Installing R	p. 3
1.2 Starting R	p. 3
1.3 Working directory	p. 4
1.4 Writing scripts	p. 5
1.5 Help	p. 5
1.6 Supporting material	p. 5
2 R as a calculating environment	p. 11
2.1 Arithmetic	p. 11
2.2 Variables	p. 12
2.3 Functions	p. 13
2.4 Vectors	p. 15
2.5 Missing data	p. 18
2.6 Expressions and assignments	p. 19
2.7 Logical expressions	p. 20
2.8 Matrices	p. 23
2.9 The workspace	p. 25
2.10 Exercises	p. 25
3 Basic programming	p. 29
3.1 Introduction	p. 29
3.2 Branching with if	p. 31
3.3 Looping with for	p. 33
3.4 Looping with while	p. 36
3.5 Vector-based programming	p. 38
3.6 Program flow	p. 39
3.7 Basic debugging	p. 41
3.8 Good programming habits	p. 42
3.9 Exercises	p. 43
4 I/O: Input and Output	p. 49
4.1 Text	p. 49
4.2 Input from a file	p. 51
4.3 Input from the keyboard	p. 53
4.4 Output to a file	p. 55
4.5 Plotting	p. 56
4.6 Exercises	p. 58
5 Programming with functions	p. 63
5.1 Functions	p. 63
5.2 Scope and its consequences	p. 68
5.3 Optional arguments and default values	p. 70
5.4 Vector-based programming using functions	p. 70
5.5 Recursive programming	p. 74
5.6 Debugging functions	p. 76
5.7 Exercises	p. 78
6 Sophisticated data structures	p. 85
6.1 Factors	p. 85
6.2 Dataframes	p. 88
6.3 Lists	p. 94
6.4 The apply family	p. 98
6.5 Exercises	p. 105
7 Better graphics	p. 109
7.1 Introduction	p. 109
7.2 Graphics parameters: par	p. 111
7.3 Graphical augmentation	p. 113
7.4 Mathematical typesetting	p. 114
7.5 Permanence	p. 118
7.6 Grouped graphs: lattice	p. 119
7.7 3D-plots	p. 123
7.8 Exercises	p. 124
8 Pointers to further programming techniques	p. 127
8.1 Packages	p. 127
8.2 Frames and environments	p. 132
8.3 Debugging again	p. 134
8.4 Object-oriented programming: S3	p. 137
8.5 Object-oriented programming: S4	p. 141
8.6 Compiled code	p. 144
8.7 Further reading	p. 146
8.8 Exercises	p. 146
II Numerical techniques	p. 149
9 Numerical accuracy and program efficiency	p. 151
9.1 Machine representation of numbers	p. 151
9.2 Significant digits	p. 154
9.3 Time	p. 156
9.4 Loops versus vectors	p. 158
9.5 Memory	p. 160
9.6 Caveat	p. 161
9.7 Exercises	p. 162
10 Root-finding	p. 167
10.1 Introduction	p. 167
10.2 Fixed-point iteration	p. 168
10.3 The Newton-Raphson method	p. 173
10.4 The secant method	p. 176
10.5 The bisection method	p. 178
10.6 Exercises	p. 181
11 Numerical integration	p. 187
11.1 Trapezoidal rule	p. 187
11.2 Simpson's rule	p. 189
11.3 Adaptive quadrature	p. 194
11.4 Exercises	p. 198
12 Optimisation	p. 201
12.1 Newton's method for optimisation	p. 202
12.2 The golden-section method	p. 204
12.3 Multivariate optimisation	p. 207
12.4 Steepest ascent	p. 209
12.5 Newton's method in higher dimensions	p. 213
12.6 Optimisation in R and the wider world	p. 218
12.7 A curve fitting example	p. 219
12.8 Exercises	p. 220
III Probability and statistics	p. 225
13 Probability	p. 227
13.1 The probability axioms	p. 227
13.2 Conditional probability	p. 230
13.3 Independence	p. 232
13.4 The Law of Total Probability	p. 233
13.5 Bayes' theorem	p. 234
13.6 Exercises	p. 235
14 Random variables	p. 241
14.1 Definition and distribution function	p. 241
14.2 Discrete and continuous random variables	p. 242
14.3 Empirical cdf's and histograms	p. 245
14.4 Expectation and finite approximations	p. 246
14.5 Transformations	p. 251
14.6 Variance and standard deviation	p. 256
14.7 The Weak Law of Large Numbers	p. 257
14.8 Exercises	p. 261
15 Discrete random variables	p. 267
15.1 Discrete random variables in R	p. 267
15.2 Bernoulli distribution	p. 268
15.3 Binomial distribution	p. 268
15.4 Geometric distribution	p. 270
15.5 Negative binomial distribution	p. 273
15.6 Poisson distribution	p. 274
15.7 Exercises	p. 277
16 Continuous random variables	p. 281
16.1 Continuous random variables in R	p. 281
16.2 Uniform distribution	p. 282
16.3 Lifetime models: exponential and Weibull	p. 282
16.4 The Poisson process and the gamma distribution	p. 287
16.5 Sampling distributions: normal, X2, and t	p. 292
16.6 Exercises	p. 297
17 Parameter Estimation	p. 303
17.1 Point Estimation	p. 303
17.2 The Central Limit Theorem	p. 309
17.3 Confidence intervals	p. 314
17.4 Monte-Carlo confidence intervals	p. 321
17.5 Exercises	p. 322
IV Simulation	p. 329
18 Simulation	p. 331
18.1 Simulating iid uniform samples	p. 331
18.2 Simulating discrete random variables	p. 333
18.3 Inversion method for continuous rv	p. 338
18.4 Rejection method for continuous rv	p. 339
18.5 Simulating normals	p. 345
18.6 Exercises	p. 348
19 Monte-Carlo integration	p. 355
19.1 Hit-and-miss method	p. 355
19.2 (Improved) Monte-Carlo integration	p. 358
19.3 Exercises	p. 360
20 Variance reduction	p. 363
20.1 Antithetic sampling	p. 363
20.2 Importance sampling	p. 367
20.3 Control variates	p. 372
20.4 Exercises	p. 374
21 Case studies	p. 377
21.1 Introduction	p. 377
21.2 Epidemics	p. 378
21.3 Inventory	p. 390
21.4 Seed dispersal	p. 405
22 Student projects	p. 421
22.1 The level of a dam	p. 421
22.2 Roulette	p. 425
22.3 Buffon's needle and cross	p. 428
22.4 Insurance risk	p. 430
22.5 Squash	p. 433
22.6 Stock prices	p. 438
Glossary of R commands	p. 441
Programs and functions developed in the text	p. 447
Index	p. 449

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