R and Python for Computer Simulation
Preface
This book introduces computer simulation as a core methodological tool in modern statistics for analysing complex systems and modelling uncertainty when analytical solutions are unavailable or impractical. Students will develop an understanding of the capabilities and limitations of simulation, and how simulation complements theoretical and data-driven statistical approaches.
The book adopts a computational and algorithmic approach to simulation. Students will learn to design, implement, and verify simulation procedures in an appropriate computing environment, with emphasis on Monte Carlo methods, simulation of univariate and multivariate random variables, dependence structures, and simulation-based statistical inference. Simulation is treated as a structured experimental process, from problem formulation and model design to implementation and evaluation.
Students will develop skills in the analysis, visualisation, and interpretation of simulation output, including assessing variability, uncertainty, and convergence.
The book is hands-on, with computational activities using R and/or Python. Students will complete a substantial project in which they apply simulation techniques to a discipline-specific problem, demonstrating the ability to develop, analyse, and report a simulation study in a clear, rigorous, and professional manner.
Unit Materials
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| # | Lecture | Slide | CN | WS | WS Solutions |
|---|---|---|---|---|---|
| 1 | Introduction to Computer Simulation | π₯οΈ | π | π§π»βπ» | |
| 2 | Statistical Distribution | π₯οΈ | π | π§π»βπ» | |
| 3 | Joint Distributions and Statistical Inference | π₯οΈ | π | π§π»βπ» | |
| 4 | Simulation of Discrete Random Variables | π₯οΈ | π | π§π»βπ» | |
| 5 | Simulation of Continuous Random Variables | π₯οΈ | π | π§π»βπ» | |
| 6 | Multivariate Simulation | π₯οΈ | π | π§π»βπ» | |
| 7 | Stochastic Modelling | π₯οΈ | π | π§π»βπ» | |
| 8 | Time Series Modelling | π₯οΈ | π | π§π»βπ» | |
| 9 | Monte Carlo Integration and MCMC | π₯οΈ | π | π§π»βπ» | |
| 10 | Simulation in Practice | π₯οΈ | π | N/A | N/A |
Program Calendar
| Week | Lecture Content | Workshop |
|---|---|---|
| 1 | Introduction to Simulation β’ Monte Carlo history & motivation β’ Simulation workflow β’ Simulation vs analytical solutions β’ PRNGs (LCG, Mersenne Twister) β’ Probability revision & LLN intuition |
Implement LCG; compare with built-in RNG; empirical LLN |
| 2 | Statistical Distributions (Univariate & Joint) β’ Univariate distributions β’ Conditional probabilities β’ Bayesian inference (Intro) |
Univariate distributions simulation and visualisations |
| 3 | Statistical Inference (Frequentist & Bayesian) β’ Joint distributions & dependence β’ Frequentist inference β’ Bayesian inference |
Joint distributions simulation; Frequentist inference; MLE; |
| 4 | Simulation of Discrete RVs β’ Discrete inverse CDF method β’ The precision method β’ Case study: Epidemic SIR Modelling |
Bayesian inference; simulation using precision method |
| 5 | Test 1 | Test 1 |
| 6 | Simulation of Continuous RVs β’ Inverse Transform Sampling β’ Acceptanceβrejection β’ Precision of Simulation Results |
Project Clinic 1 Implement inverse transform sampling and AβR sampling |
| 7 | Multivariate Simulation β’ Transformation of multiple rvs β’ Linear transformations β’ Multivariate Normal β’ Cholesky decomposition β’ Copulas β’ Simulation dependent variable |
β’ Simulate correlated rvs using linear transformations β’ Multivariate normal samples β’ Cholesky decomposition β’ Copula-based simulation β’ Case study: Air Pollution Monitoring β’ Case study: Portfolio Risk Simulation |
| 8-9 | Tuition Free Week | |
| 10 | Stochastic Modelling β’ Stochastic process β’ Poisson process β’ Thinning algorithm β’ Markov process β’ Queueing theory |
β’ Simulate HPP and NHPP β’ M/M/\(c\) queues β’ Case study: EV Charging Bays Simulation |
| 11 | Time Series β’ White noise β’ Autoregressive (AR) models β’ Behaviour via \(\phi\) β’ Mean Reversion β’ Autocorrelation Function (ACF) β’ Shock propagation |
β’ Simulate AR models β’ Shock propagation analysis β’ Case Study: Traffic Flow Simulation |
| 12 | Test 2 | Test 2 |
| 13 | Monte Carlo Integration & MCMC β’ Monte Carlo integration & CLT β’ Gibbs sampling & intuition β’ Case Study: Estimating Household Energy Savings |
Guest Lecture β’ Monte Carlo integration |
| 14 | Simulation in Practice β’ Metropolis-Hastings algorithm β’ Variance reduction methods (importance sampling, stratified, Latin Hypercube Sampling) β’ Simulation optimisation (Intuitive Overview) |
Revision Project Clinic 2 |
| 15 | Study Week | |
| 16-17 | Centrally Scheduled Examination |