What this book covers
Chapter 1, Introduction, discusses the general aim of simulation experiments in data science and statistics, why and where simulation is used, and the special case of dealing with big data.
Chapter 2, R and High-Performance Computing, consists of comprehensive text on advanced computing, data manipulation, and visualization with R.
Chapter 3, The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions, reports problems on numerical precision, rounding, and convergence in a deterministic setting.
Chapter 4, Simulation of Random Numbers, starts with the simulation of uniform random numbers and transformation methods to obtain other kinds of distributions. It includes a discussion of various types of Markov chain Monte Carlo (MCMC) methods.
Chapter 5, Monte Carlo Methods for Optimization Problems, introduces deterministic and stochastic optimization methods.
Chapter 6, Probability Theory Shown by Simulation, has a strong focus on basic theorems in statistics; for example, the concept of the weak law of large numbers and the central limit theorem are shown by simulation.
Chapter 7, Resampling Methods, is a comprehensive view on the bootstrap, the jackknife and cross-validation.
Chapter 8, Applications of Resampling Methods and Monte Carlo Tests, shows applications in various fields such as regression, imputation, and time series analysis. In addition, Monte Carlo tests and their variants such as permutation tests and bootstrap tests are presented.
Chapter 9, The EM Algorithm, introduces the expectation maximum method to iteratively obtain an optima. Applications in clustering and imputation of missing values are given.
Chapter 10, Simulation with Complex Data, shows how to simulate synthetic data as well as population data that can be used for the comparison of methods in general or also serve as input for agent-based microsimulation models.
Chapter 11, System Dynamics and Agent-Based Models, discusses agent-based microsimulation models and shows basic models in system dynamics to study complex dynamical systems.
