Registry
Module Specifications
Archived Version 2022 - 2023
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Description The purpose of this course is to demonstrate how to build models for simulations of complex systems and provide the underlying mathematical foundation necessary for constructions of such models. The course will teach students basic topics such as Time Series Analysis as well as more complex ones such as how to translate social or physical behaviour (from micro to macro environments) to computational prediction models and how to deduce unknown model parameters from noisy/incomplete data sets. Key topics will include Monde Carlo methods, Markov models, Cellular Automata and Agent Based Modelling. | |||||||||||||||||||||||||||||||||||||
Learning Outcomes 1. Understand the different types of Time Series Models and decompose a such a series into parts such as Trend, Seasonality and Residual Components 2. Examine ARMA/ ARIMA models to study suitable choice of coefficients and build ARMA/ ARIMA models for given datasets 3. Perform basic forecasting using time series models, recognising the limits of these forecasts 4. Understand what constitutes a complex system and differentiate between bottom-up and top-down approach to modelling. 5. Build probabilistic, predictive models using techniques such as Monte Carlo, Markov Chain MC, Hidden Markov models and Bayesian networks. 6. Construct spatial models using Cellular Automata and Agent Based techniques. Translate complex system of choice into a CA/ABM model. 7. Explore different languages and frameworks that can be used to implement models of complex systems (e.g. Flame, NetLogo etc.). | |||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities Fundamentals of Time Series AnalysisWhat is a time series? Some common examples of Time Series? Decomposing a time series into Trend, Seasonal and Residual Components. Building an ARMA, ARIMA and SARIMA model. Introduction to ForecastingFundamentals of complexity and probabilityWhat is a complex system? Botom-up vs. top-down approach. Explaining the need for modelling. Discussing emergent systems. Reviewing probability distributions sampling, power-law, eigenvalues and eigenvectors, uncertainty and confidence intervals.Random number generationPseudo-random numbers and random variables, Linear congruential generator, Mersenne Twister, generation of random distribution data (inverse transformation and acceptance-rejection method).Probabilistic Modelling MethodsDirect Monte Carlo, Markov Chain MC, Hidden Markov models, Bayesian networks, basics of Genetic Algorithms.Spatial ModelsTranslating physical systems into Cellular Automata/Agent Based Models with emphasis on properties, behaviour and granularity. Reference CA/ABM models for various applications.Inverse ModelsExtracting unknown model parameters from complex data sets by using a set of techniques such as Inverse Monte Carlo, Gibbs Sampling, Simulated Annealing. | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources 43726, Website, Rob Hyndman, 0, Forecasting: Principles & Practice, https://otexts.com/fpp2/, | |||||||||||||||||||||||||||||||||||||
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