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E-217-PROG-2010-1: Simulation 1 Thorisson Lecture Notes


Simulation A model of a process that can transform an initial state to a future state. S → S'
Scientific Method In Western science, the usage of a set of principles that facilitate the production of reliable knowledge
Theory (isl. kenning) Explain the connections between things in the world.
“A set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena.” REF
A theory is a relatively big explanation, covering several phenomena, often through a single principle, or a set of simple principles.
Hypothesis (isl. tilgáta) Is a prediction about the relationship between a limited set of phenomena, as explained by a particular theory
Experimental design “A planned interference in the natural order of events”
Dependent variable(s) These are “the things we want to measure”, e.g. the speedup seen with the new word processor.
Values are measured during and/or after the experiment.
Independent variables These are factors that need to be controlled for the results to be more intelligible. Example: If we want to study the efficiency speedup seen by a new multi-cultural word processor we would want to have all or some of the cultures represented when we do the study.
We select their values - the values are known when we start an experiment.
Any independent variable must have at least 2 levels (values), so its effect can be evaluated.
Sample: Subject selection from a “population” A representative subset, drawn from a population, of the phenomenon we are studying. Typically you can't study all the individuals of a particular subject pool, so in your experiment you use a sample and hope that the results generalize to the rest of the subjects.
a. Siggi, Maggi and Biggi representing human males.
b. 10 lakes representing all freshwater on the Earth's surface.
c. rust on bottom of doors representing the overall state of an automobile.
A sample should be randomly chosen to (1) minimize spurious correlations and thus (2) maximize the generalizability of the results of measuring only a small subset of the phenomenon.
Randomness It is hypothesized in quantum physics that the universe may possibly be built on a truly random foundation, which means that some things are by their very nature unpredictable. Randomness in the aggregate, however, does seem to follow some predictable laws (c.f. the concept of “laws of probability”).
Sample Distribution If you sample data many times it may not always give the same result.
Example: If you measure the temperature repeatedly over a full day, the values you get will not be identical, they will be distributed.
Normal distribution The Bell Curve. Also called Gaussian Distribution.
Bell Curve
See picture
Data Typically “raw numbers” – only contain low-level semantics
Information Processed and prepared data
Statistics Mathematical methods for dealing with uncertainty

The Scientific Method: Classical Description

Identification, description and formalization of phenomenon 1. Observation and description of a phenomenon or group of phenomena.
Hypothesis, null-hypothesis 2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.
Creation of experimental setup to test hypothesis 3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.
Performance of experiment, collection and analysis of results 4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments. Basic assumption: Repeatability — Can be repeated by anyone anywhere
Repeatability requires formal framework Detailed description, clear goals, clear (limited) scope, hence the formalities in their execution
Key idea: Comparsion Baseline collected in same experimental setup without any other intervention by experimenter

Where Simulation Fits In Science

“Connecting Glue” a. Bridges between real-world experimentation, theory and hypotheses
b. Can be considered part of the Comparative Experiment paradigm
More flexible than real-world experiments: Easy to pose WHAT-IF questions
Example: CCP runs a virtual world with its own economy; they can run “mixed-world” experiments that benefit from the flexibility of software
Less reliable than real-world experiments
Foundation Computer science + biology AND psychology AND economics AND geology AND meteorology AND …
Challenges a. Grounding Simulations
b. Detail
c. Abstraction
Grounding The connection between a simulation (model) and reality
Complexity How complex should we make a model/simulation? More complexity ≠ more explanatory power
Abstraction How abstract can we make things?
What is the difference between simulating market behavior by modeling every individual consumer, versus modeling the market behavior grossly as “percent of those who buy”?

Simulation Concepts

Variable A value that can vary. Typically a simulation will have many dependent variables that change their values as a function of the simulation running.
Types of variables Endogeneous and Exogeneous
Endogeneous variables Dependent variable generated within a model and, therefore, a variable whose value is changed (determined) by one of the functional relationships in that model. For example, consumption expenditure and income is considered endogenous to a model of income determination. REF
Exogeneous variables Independent variable that affects a model without being affected by it, and whose qualitative characteristics and method of generation are not specified by the model builder. An exogenous variable is used for setting arbitrary external conditions, and not in achieving a more realistic model behavior. For example, the level of government expenditure is exogenous to the theory of income determination. REF

When to Use Simulation

Simulation Simulations are the newest methodology that science offers in our study of the (natural) world.
Relation between theories and simulations Before a model can be built and a simulation can be done we need a theory that tells us how things relate to each other.
For visualizing mathematical models When mathematical models are too complex to calculate in other ways.
When dealing with complex causal relationships When the complexity of that which is to be modeled/understood becomes so great that mathematical models are intractable and hypothesis falsification would take decades, centuries or millenia.
In systems such as societies, ecosystems, minds, a complex relationship exists, sometimes at many levels of detail, between phenomena.
When developing theories Simulations help in formulating hypotheses about causal relationships, and thus helps scientists create theories.
When tying together many disconnected theories Simulation can help tie disconnected theories together, even from different scientific fields (theory generalization).
As a tool for thinking about phenomena When studying complex systems it is often difficult to know where to start. Simulation and modeling can help in advancing in a principled way.
When real-world experiments are not possible In scientific fields such as psychology and astrophysics, many types of experiments are not possible.
As augmentation to real-world experiments It is not only when experiments are not possible that simulations can be a powerful aid.

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