Jones, Owen, Maillardet, Robert, Robinson, Andrew 　著

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目次

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