Modeling Project Two paper outline guide

Project Two involves creating a model of some phenomenon. Unlike Project One, you are not solving an optimization problem. Instead you will investigate how choices you make in creating a model effect the model itself and what the model tells you about the modeled phenomenon.

You are not writing software (though you will most likely need to write code to create your model) or creating a "tool" for solving a class of problems: you will be creating a model to investigate a specific phenomenon or set of phenomena.

To as great an extent as possible, real-world data should be used to formulate your model. If you are not using real-world data, be sure to very carefully explain why you chose not to use real-world data, and your methods for synthesizing data.

• Introduction (5 points)

  Describe what you modeled and what concepts you incorporated in your model (e.g., graphs, markov chains, multidimensional scaling, simulation, queuing theory, etc.) Describe the purpose of the model: what aspects of the phenomenon were you interested in investigating with the model? This section should be written last!

• Background (25 points)

  Describe how your group came up with the idea for your project. What sort of discussions led to this project? Were personal interests of group members an inspiration for this project? (5 points)

  Give the history of similar and related modeling. You should cite at least four past examples of similar modeling efforts.
  Do not describe the history of general methods (e.g., Markov chains, MDS, monte carlo simulation) but instead you should describe the history of applications of your method to phenomena like yours.
  Look for modelings as similar to yours as possible, solved by others (you may need to expand the scope of your search for previous work to include work that, for example, uses a similar technique applied to a not quite identical application).
  Who were some early researchers to mathematically model a phenomenon like yours?
  When did they do their work?
  What mathematical techniques did they use?
  What are some similarities and differences between your work and theirs?
  (20 points)

• The model itself (30 points)

  Thoroughly describe the mathematical model you have developed for your investigation. You should include all data used, or at least a substantial subset of it.

  Be especially careful to describe assumptions you are making in order to create the model, and make it clear where the model differs significantly from the phenomenon being modeled: as far as you are able, discuss what aspects of the phenomenon are represented in your model, and what are left out.

  Present any calculations, describing all methods used, including all code, R commands, etc., to implement the model as a mathematical and/or computational thing.

• Results (20 points)

  What do your model and calculations tell you? How well does it model the phenomenon? How do you know?

• Adjustments and extensions (i.e., working the model) (40 points)

  Modify your model in order to investigate the phenomenon further. In almost all cases, assumptions or choices must have been made to create the model: discuss what happens when you change these assumptions and choices.

• Conclusion (10 points)

  This is not a summary: do not repeat what you did! You should answer the question: what are the major conclusions you can make from your efforts? This may include conclusions about the object of study as well as the methods of attack or any other aspect of your project.

• References (10 points)

  This section should immediately follow your conclusion! That is, it should come before your appendices.

  Cite all sources of quoted material in place. This means that you need to footnote material in your work as you use it. A list of references used should be included at the end of the paper but it is not sufficient.

  Take a look at the Chicago Manual of Style's citation guidelines for ideas of how to format the list of references.

  Note: if you are citing a web source, you must include the URL. If the URL is ridiculously long, feel free to truncate it, but only do so if necessary.

• Appendixes (optional)

  Feel free to put long tables, code, output, etc., in appendices, but be sure to describe and label them well so that one can read them on their own without having to refer back to the rest of the paper.

• Presentation (10 points)

  While not actually part of the paper, it is part of the project. One or more group members should present the highlights of your projects to the class. The presentation should be no more than 10 minutes long: you must select a group member to be responsible for ensuring that the presentation does not go over 10 minutes.

Additional specific comments and requirements of the paper (of varying significance)

• The project paper will be submitted electronically as a pdf. Each group should submit one copy of their paper. Please name your file with the form GroupX-Project2.pdf .
• MDS projects For the purposes of this project, the goal of MDS is to create a useful low-dimensional model of the set of objects you are studying. It is not merely about creating a visualization, or looking at similarities and differences: these things can be achieved without MDS. Be sure to discuss the effect of your choice of distance function on your model. Discuss the choice of dimension (at least one, two and three dimensions should be discussed). Discuss how accurate your model is, using a goodness-of-fit measure (compare this for various choices of distance function and dimension) and by comparing distances in your original set with those in the MDS model. Most importantly, make a strong effort to determine what the dimensions in your model represent; that is, what does your model mean? You must support your claims for these dimensions with plots and/or calculations, not with merely subjective assessment of a few items in your model. For the Adjustments and Extensions section, you should modify your method and/or data set significantly, not merely changing distance functions, model dimensions, or other basic MDS options: these things should be part of the original model, since you need to investigate them to determine the best possible model.
• Simulation Many simulation models have various input parameters, and at least one quantifiable ``output" (e.g., the distribution of the number of items in customers' grocery carts as input, and the average time to checkout as output). Be sure to use your model to study how the input parameters effect the output parameters. Be sure to assess how "convergent" your simulations are: have you run enough/long enough simulations to make the conclusions you would like to make? How do you know?

• Pages should be numbered for easy reference.
• Do not give references to internet files for project material except if it is of excessive size and then only if partial bits are included in the actual paper.
• For bibliography/references/works cited, if you use information from the web, you need to include URLs: the name of the website is not sufficient. If something is printed (e.g., a book), you need to follow usual guidelines for citing works.
• If you copy text from anywhere, you must make it clear that that is what you are doing immediately in your paper. For example, if you want to quote a few lines from Wikipedia, you can do something like this:

  The Wikipedia article on astronomy (en.wikipedia/org/wiki/Astronomy) says

  Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye.

  It is NOT sufficient to simply add the article as a list of references at the end of the paper.
• Images, if copied from elsewhere, need to be sourced *in place*. A common way is with a caption below the figure.
• Be sure to discuss all parameter value choices carefully. For example, if you have a simulation of horses racing on a circular track, you must discuss the choice of the radius of the track and how this choice effects your results.
• Be sure to state what software and version you used, on what machine, for your main calculations. You should also include the approximate time required to perform the calculations.
• Watch out that you don't use acronyms or particularly techical terms without defining them first.
• Subscripts! If you mean x_ij, write that, not xij.
• Never use the pronoun "I" in a group project paper. Either say we, or give the group member's name.
• Be careful about talking about how results are "as expected", or are "intuitive" or "reasonable". Generally, such phrases add nothing, and only force you to explain why they are expected, reasonable, etc. This is generally not necessary. Simply make non-judgemental, clear comparisons with real-world data. Do the results agree with the real-world you are modeling or not? That is what matters.
• Don't be stingy! Once you've done the hard work of making a valid model, make it work for you! Change all the input parameters! Experiment! Figure out what matters and what doesn't, dig deep and compare and discuss!