An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to perform scientific programming while also introducing stochastic ..
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. Table of Contents Part I: 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 Expressions and assignments Logical expressions Matrices The workspace Basic Programming Introduction Branching with if Looping with for Looping with while Vector-based programming Program flow Basic debugging Good programming habits I/O: Input and Output Text Input from a file Input from the keyboard Output to a file Plotting Programming with Functions Functions Scope and its consequences Optional arguments and default values Vector-based programming using functions Recursive programming Debugging functions Sophisticated Data Structures Factors Dataframes Lists The apply family Better Graphics Introduction Graphics parameters: par Graphical augmentation Mathematical typesetting Permanence Grouped graphs: lattice 3D-plots Pointers to Further Programming Techniques Packages Frames and environments Debugging again Object-oriented programming: S3 Object-oriented programming: S4 Compiled code Further reading Part II: NUMERICAL TECHNIQUES Numerical Accuracy and Program Efficiency Machine representation of numbers Significant digits Time Loops versus vectors Memory Caveat Root-Finding Introduction Fixed-point iteration The Newton-Raphson method The secant method The bisection method Numerical Integration Trapezoidal rule Simpson’s rule Adaptive quadrature 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 Part III: PROBABILITY AND STATISTICS Probability The probability axioms Conditional probability Independence The Law of Total Probability Bayes’ theorem 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 Discrete Random Variables Discrete random variables in R Bernoulli distribution Geometric distribution Negative binomial distribution Poisson distribution Continuous Random Variables Continuous random variables in R Uniform distribution 282 Lifetime models: exponential and Weibull The Poisson process and the gamma distribution Sampling distributions: normal, x2, and t Parameter Estimation Point Estimation The Central Limit Theorem Confidence intervals Monte-Carlo confidence intervals Part IV: SIMULATION Simulation Simulating iid uniform samples Simulating discrete random variables Inversion method for continuous rv Rejection method for continuous rv Simulating normals Monte-Carlo Integration Hit-and-miss method (Improved) Monte-Carlo integration Variance Reduction Antithetic sampling Importance sampling Control variates Case Studies Introduction Epidemics Inventory Seed dispersal Student Projects The level of a dam Roulette Buffon’s needle and cross Insurance risk Squash Stock prices Glossary of R commands Programs and functions developed in the text Index Reviews This book is a good resource for someone who wants to learn R and use R for statistical computing and graphics. It will also serve well as a textbook or a reference book for students in a course related to computational statistics. —Hon Keung Tony Ng, Technometrics, May 2011 … a very coherent and useful account of its chosen subject matter. … The programming section … is more comprehensive than Braun & Murdoch (2007), but more accessible than Venables & Ripley (2000). … The book deserves a place on university library shelves … One very useful feature of the book is that nearly every chapter has a set of exercises. There are also plenty of well-chosen examples throughout the book that are used to explain the material. I also appreciated the clear and attractive programming style of the R code presented in the book. I found very little in the way of typos or solecisms. … I can strongly recommend the book for its intended audience. If I ever again have to teach our stochastic modelling course, I will undoubtedly use some of the exercises and examples from Scientific Programming and Simulation Using R. —David Scott, Australian & New Zealand Journal of Statistics, 2011 It is not often that I think that a statistics text is one that most scientifc statisticians should have in their personal libraries. Introduction to Scientific Programming and Simulation Using R is such a text. … This text provides scientific researchers with a working knowledge of R for both reviewing and for engaging in the statistical evaluation of scientific data. …It is particularly useful for understanding and developing modeling and simulation software. I highly recommend the text, finding it to be one of the most useful books I have read on the subject. —Journal of Statistical Software, September 2010, Volume 36 The authors have written an excellent introduction to scientific programming with R. Their clear prose, logical structure, well-documented code and realistic examples made the book a pleasure to read. One particularly useful feature is the chapter of cases studies at the end, which not only demonstrates complete analyses but also acts as a pedagogical tool to review and integrate material introduced throughout the book. … I would strongly recommend this book for readers interested in using R for simulations, particularly for those new to scientific programming or R. It is also very student-friendly and would be suitable either as a course textbook or for self-study. —Significance, September 2009 I think that the techniques of scientific programming presented will soon enable the novice to apply statistical models to real-world problems. The writing style is easy to read and the book is suitable for private study. If you have never read a book on scientific programming and simulation, then I recommend that you start with this one. —International Statistical Review, 2009
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Mar 11, 2009.. An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to perform scientific programming while also ..