Table of Contents
E-217-PROG-2010-1: Simulation 1 Thorisson Lecture Notes
Concepts
| 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. Examples: 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.  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. |