# Index

## A

- aes(). assignment / The ggplot2 package
- aesthetic mapping / The ggplot2 package
- agent-based modeling / What is simulation and where is it applied?
- agent-based modeling (ABM) / Choosing the right simulation technique
- agent-based models
- about / Agent-based models

- alias method / The alias method
- arithmetic random number generators / Simulating pseudo random numbers

## B

- Beta distribution / Simulating random numbers from a Beta distribution
- BFGS method / Further general-purpose optimization methods
- bias
- estimating, bootstrap used / Estimating bias with bootstrap

- Bias Corrected alpha (BCa) confidence interval method / Confidence intervals by bootstrap
- Big Boss 2 approach / Why the bootstrap works
- Big Boss approach / Why the bootstrap works
- bootstrap / Why use simulation?
- about / The bootstrap, A closer look at the bootstrap
- motivating example, with odds ratios / A motivating example with odds ratios
- working / Why the bootstrap works
- to estimate standard error / Estimation of standard errors with bootstrapping
- complex estimation, example / An example of a complex estimation using the bootstrap
- bias, estimating / Estimating bias with bootstrap
- confidence intervals / Confidence intervals by bootstrap
- in regression analysis / The bootstrap in regression analysis
- using / Motivation to use the bootstrap
- method / The most popular but often worst method
- by draws from residuals / Bootstrapping by draws from residuals
- in time series / Bootstrapping in time series
- in case of complex sampling designs / Bootstrapping in the case of complex sampling designs

## C

- central limit theorem
- about / The central limit theorem

- CG method / Further general-purpose optimization methods
- classes
- about / Generic functions, methods, and classes

- classical linear regression model / The classical linear regression model
- complex models
- used, for simulating data / Simulating data using complex models

- Comprehensive R Archive Network (CRAN)
- about / The R statistical environment
- reference link / The R statistical environment

- confidence intervals / Confidence intervals
- by bootstrap / Confidence intervals by bootstrap

- congruential generators / Congruential generators
- linear / Linear and multiplicative congruential generators
- multiplicative / Linear and multiplicative congruential generators

- contamination
- adding / Adding contamination

- cross-validation
- about / Cross-validation
- classical linear regression model / The classical linear regression model
- basic concept / The basic concept of cross validation
- classical cross validation / Classical cross validation – 70/30 method
- leave-one-out cross validation / Leave-one-out cross validation
- k-fold cross validation / k-fold cross validation

## D

- data
- simulating, complex methods used / Simulating data using complex models
- model-based simple example / A model-based simple example

- data.table package
- used, for data manipulation / Data manipulation with the data.table package
- variable construction / data.table – variable construction
- indexing / data.table – indexing or subsetting
- subsetting / data.table – indexing or subsetting
- keys / data.table – keys
- fast subsetting / data.table – fast subsetting
- calculations, in groups / data.table – calculations in groups

- data manipulation
- in R / Data manipulation in R
- apply, using / Apply and friends with basic R
- dplyr package, using / Basic data manipulation with the dplyr package
- data.table package, using / Data manipulation with the data.table package

- Data Scientist approach / Why the bootstrap works
- data types, R
- about / Data types
- vectors / Vectors in R
- factors / Factors in R
- list / list
- data.frame / data.frame
- array / array

- design-based simulation
- about / Design-based simulation
- complex survey data, example / An example with complex survey data
- synthetic population, simulation / Simulation of the synthetic population
- interest, estimators / Estimators of interest
- sampling design, defining / Defining the sampling design
- stratified sampling, using / Using stratified sampling
- contamination, adding / Adding contamination
- performing, separately on different domains / Performing simulations separately on different domains

- design-based simulation (DBS) / Choosing the right simulation technique
- design-based simulation studies / Different kinds of simulation and software
- dplyr package
- used, for data manipulation / Basic data manipulation with the dplyr package
- local data frame / dplyr – creating a local data frame
- selection of lines / dplyr – selecting lines
- order / dplyr – order
- selection of columns / dplyr – selecting columns
- uniqueness / dplyr – uniqueness
- variables, creating / dplyr – creating variables
- grouping / dplyr – grouping and aggregates
- aggregates / dplyr – grouping and aggregates
- window functions / dplyr – window functions

- dynamics
- about / Dynamics in love and hate

- dynamic systems
- in ecological modelling / Dynamic systems in ecological modeling

## E

- EM algorithm
- about / The basic EM algorithm
- prerequisites / Some prerequisites
- formal definition / Formal definition of the EM algorithm
- introductory example / Introductory example for the EM algorithm
- explaining, by k-means clustering example / The EM algorithm by example of k-means clustering
- used, for imputation of missing values / The EM algorithm for the imputation of missing values

- estimators
- properties / Properties of estimators, Properties of estimators
- confidence intervals / Confidence intervals
- robust estimators / A note on robust estimators

## F

- finite populations
- simulating, with cluster or hierarchical structures / Simulating finite populations with cluster or hierarchical structures

- Fortran** / High performance computing, Profiling to detect computationally slow functions in code

## G

- generators / More generators
- generic functions
- about / Generic functions, methods, and classes, Warm-up example – a high-level plot

- Gibbs sampler
- about / The Gibbs sampler
- two-phase Gibbs sampler / The two-phase Gibbs sampler
- multiphase Gibbs sampler / The multiphase Gibbs sampler
- linear regression, application / Application in linear regression

- gradient ascent/descent method / Gradient ascent/descent
- graphics package
- about / The graphics package
- high-level graphics functions / The graphics package
- low-level graphics functions / The graphics package
- interactive functionsTopicn / The graphics package
- (high-level) plot example / Warm-up example – a high-level plot
- graphics parameters, controlling / Control of graphics parameters

## H

- high-dimensional data
- simulating, example / An example of simulating high-dimensional data

- high-level plot functions / Control of graphics parameters
- high performance computing
- about / High performance computing
- slow functions, detecting with profiling / Profiling to detect computationally slow functions in code
- benchmarking / Further benchmarking
- parallel computing / Parallel computing
- interfaces to C++ / Interfaces to C++

## I

- information visualization
- about / Visualizing information
- graphics system, in R / The graphics system in R
- graphics package / The graphics package
- package ggplot2 / The ggplot2 package

- interactive graphics / Visualizing information
- inversion method / The inversion method

## J

- jackknife
- about / The jackknife
- sample / The jackknife
- disadvantages / Disadvantages of the jackknife
- delete-d jackknife / The delete-d jackknife
- after bootstrap / Jackknife after bootstrap

## K

- k-fold cross validation / k-fold cross validation
- k-means clustering
- used, for EM algorithm demonstration / The EM algorithm by example of k-means clustering

- k-Nearest Neighbor (k-NN) / A model-based simulation study

## L

- L-BFGS-B method / Further general-purpose optimization methods
- leave-one-out cross validation / Leave-one-out cross validation
- lottery
- winning / Winning the lottery

- low-level functions / Control of graphics parameters

## M

- machine numbers
- and rounding, issues / Machine numbers and rounding problems
- 64-bit representation, example / Example – the 64-bit representation of numbers
- convergence / Convergence in the deterministic case
- convergence, example / Example – convergence

- Markov chain Monte Carlo (MCMC) / Choosing the right simulation technique
- Markov chain Monte Carlo (MCMC) methods / What is simulation and where is it applied?
- Marsaglia
- URL / Tests for random numbers

- Mathematician approach / Why the bootstrap works
- method dispatch / Warm-up example – a high-level plot
- methods
- about / Generic functions, methods, and classes

- Metropolis-Hastings
- about / Metropolis-Hastings revisited

- Metropolis Hasting algorithm
- about / Metropolis - Hastings algorithm
- Markov chains / A few words on Markov chains

- Metropolis sampler / The Metropolis sampler
- micro-simulation / What is simulation and where is it applied?
- Minimum Covariance Determinant (MCD) algorithm / An example of a complex estimation using the bootstrap
- missing completely at random (MCAR) / Inserting missing values
- missing not at random (MNAR) / Inserting missing values
- missing values
- imputating, with EM algorithm / The EM algorithm for the imputation of missing values
- inserting / Inserting missing values

- mixtures
- model-based example / A model-based example with mixtures

- model-based approach
- to simulate data / Model-based approach to simulate data

- model-based example
- with mixtures / A model-based example with mixtures

- model-based simple example / A model-based simple example
- model-based simulation (MBS) / Choosing the right simulation technique
- model-based simulation studies
- about / Model-based simulation studies, A model-based simulation study
- latent model example / Latent model example continued
- example / A simple example of model-based simulation

- Modgen
- URL / Agent-based models

- Monte Carlo simulations
- about / What is simulation and where is it applied?
- Bayesian statistics / What is simulation and where is it applied?
- Markov chain Monte Carlo (MCMC) methods / What is simulation and where is it applied?
- statistical uncertainty / What is simulation and where is it applied?
- multi-dimensional integrals / What is simulation and where is it applied?
- numerical optimization / What is simulation and where is it applied?

- Monte Carlo tests
- about / Monte Carlo tests
- motivating example / A motivating example
- permutation test, as special kind of MC test / The permutation test as a special kind of MC test
- for multiple groups / A Monte Carlo test for multiple groups
- Hypothesis testing, bootstrap used / Hypothesis testing using a bootstrap
- multivariate normality, test for / A test for multivariate normality
- test, size / Size of the test
- power comparisons / Power comparisons

## N

- Nelder-Mead method / Further general-purpose optimization methods
- Newton-Raphson method / Newton-Raphson methods
- non-uniform distributed random variables, simulation
- about / Simulation of non-uniform distributed random variables
- inversion method / The inversion method
- alias method / The alias method
- counts in tables, estimation with log-linear models / Estimation of counts in tables with log-linear models
- rejection sampling / Rejection sampling
- values, simulating from normal distribution / Simulating values from a normal distribution
- random numbers, simulating from Beta distribution / Simulating random numbers from a Beta distribution
- truncated distributions / Truncated distributions
- Metropolis Hasting algorithm / Metropolis - Hastings algorithm
- Markov chains / A few words on Markov chains
- Metropolis sampler / The Metropolis sampler
- Gibbs sampler / The Gibbs sampler
- MCMC samples, diagnosis / The diagnosis of MCMC samples

- numerical optimization
- about / Numerical optimization
- gradient ascent/descent method / Gradient ascent/descent
- Newton-Raphson method / Newton-Raphson methods
- general-purpose optimization methods / Further general-purpose optimization methods
- Nelder-Mead method / Further general-purpose optimization methods
- BFGS method / Further general-purpose optimization methods
- CG method / Further general-purpose optimization methods
- L-BFGS-B method / Further general-purpose optimization methods
- SANN method / Further general-purpose optimization methods

## O

- OpenM++
- URL / Agent-based models

- optimization (O) / Choosing the right simulation technique

## P

- parametric bootstrap
- about / The parametric bootstrap

- percentile confidence intervals / Confidence intervals by bootstrap
- plug-in principle
- about / The plug-in principle

- probability distributions
- about / Probability distributions
- discrete probability distributions / Discrete probability distributions
- continuous probability distributions / Continuous probability distributions

- probability theory
- basics / Some basics on probability theory

- problems
- conditions / Condition of problems

- pseudo random number generators
- about / Simulating pseudo random numbers
- arithmetic random number generators / Simulating pseudo random numbers
- recursive arithmetic random number generators / Simulating pseudo random numbers

## R

- R
- statistical environment / The R statistical environment
- about / The R statistical environment
- basics / Basics in R
- overview / Some very basic stuff about R
- installation / Installation and updates
- installation link / Installation and updates
- updates / Installation and updates
- updation link / Installation and updates
- help option / Help
- workspace / The R workspace and the working directory
- working directory / The R workspace and the working directory
- data types / Data types
- missing values / Missing values
- data manipulation / Data manipulation in R

- random
- URL / Real random numbers

- random numbers
- about / Real random numbers
- pseudo random numbers, simulating / Simulating pseudo random numbers
- congruential generators / Congruential generators
- congruential generators, linear / Linear and multiplicative congruential generators
- congruential generators, multiplicative / Linear and multiplicative congruential generators
- lagged Fibonacci generators / Lagged Fibonacci generators
- generators / More generators
- testing / Tests for random numbers
- example / The evaluation of random numbers – an example of a test

- recursive arithmetic random number generators / Simulating pseudo random numbers
- reference links / References, References
- resampling method / Why use simulation?
- robust estimators / A note on robust estimators
- R Project
- reference link / The R statistical environment

- RStudio
- reference link / The R statistical environment

## S

- sampling design
- defining / Defining the sampling design

- SANN method / Further general-purpose optimization methods
- simario
- URL / Agent-based models

- simulation
- about / What is simulation and where is it applied?
- applying, in sampling / What is simulation and where is it applied?
- micro-simulation / What is simulation and where is it applied?
- agent-based modeling / What is simulation and where is it applied?
- Monte Carlo simulations / What is simulation and where is it applied?
- uses / Why use simulation?
- and big data / Simulation and big data
- technique, selecting / Choosing the right simulation technique
- burning fire simulation, URL / Choosing the right simulation technique

- simulations
- types / Different kinds of simulation and software
- performing, separately on different domains / Performing simulations separately on different domains

- statistical simulation
- about / What is simulation and where is it applied?

- stochastic optimization
- about / Dealing with stochastic optimization
- Star Trek / Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)
- Spaceballs / Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)
- Spaceballs princess / Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)
- Metropolis-Hastings / Metropolis-Hastings revisited
- Gradient-based / Gradient-based stochastic optimization

- stratified sampling
- defining / Using stratified sampling

- synthetic population
- simulating / Simulation of the synthetic population

- system dynamics / What is simulation and where is it applied?
- system dynamics (SD) / Choosing the right simulation technique

## V

- variables / The ggplot2 package
- vector selection
- positive way / Vectors in R
- negative way / Vectors in R
- logical way / Vectors in R

## W

- weak law of large numbers
- about / The weak law on large numbers
- Emperor penguins, and boss / Emperor penguins and your boss
- random variables, limits / Limits and convergence of random variables
- random variables, convergence / Limits and convergence of random variables
- sample mean, convergence / Convergence of the sample mean – weak law of large numbers
- displaying, by simulation / Showing the weak law of large numbers by simulation

- window functions
- about / dplyr – window functions
- offsets / dplyr – window functions
- ranking/ordering / dplyr – window functions
- cumulative functions / dplyr – window functions