Projects for Statistics 900

Scope and Expectations

• You should aim for a paper that is "about" 15 pages long.
• If your paper is tightly written and substantially original, then the paper can be shorter.
• If your paper is mostly expository and written in a more expansive style, then the paper should be a bit longer.
• From past experience, I know that many of the papers will be genuinely excellent so don't let yours pale by comparison.

Finding a Topic (or Topics)

• You have massive freedom in your choice of topic. The only requirement is that the paper should live some place in the intersection of probability and optimization. If you go as far as 80% one way or the other, that is still fine, but you should aim to have elements of both optimization and probability theory.
• Discovery of a Topic:
  • If there is something that already has your attention that is a good place to start.
  • Another good place to start is with a paper that you can understand or want to understand.
  • Some examples: Look at the Bandits page, Resource Page, or the short story page. I'll also add a page on "Prophet" inequalities.
  • Google and Google Scholar will serve up many suggestions: Just type something like "optimal stopping" plus something else that may interest you --- say "scrabble" or "Poisson process."
  • You may also want to start with a book chapter.
  • Classic papers are a good place to start. They may be "old" but they are often still the best. You can find these in the bibliography of books, or by chaining back from science citations.
  • If you get stuck, I can make suggestions on the basis of your interests and background.
• You should start searching for a concrete topic right now. Before spring break, you will need to have "settled" on a topic and be prepared to suggested a "tentative outline" for your paper. The outline should be compatible with the advice on this page.
• Naturally, you will modify your plan as you dig more deeply into your work. Still, the more concretely you begin, the more certainly you finish.
• If you do not find a topic that will work for "a whole paper" then you can put together several separate "modules" on different problems. You could do three topics --- or even fifteen. Personally, I have found the modular approach a very productive way to engage research.

How to Start off on the Right Foot

• You should begin with the simplest problem that makes sense in your context.
• It is almost always a good idea to start with an example.
• You can use your example to illustrate any definitions.
• Do not be afraid to be simple!
• Your example should add some intuition and it should motivate the "problem."

How to Stay on the Right Track

• Don't make things any more complicated than they absolutely must be.
• Be committed to being iron-clad clear:
  • Choose notation wisely.
  • When writing inequalities, put the larger quantity on the right unless you have a damn good reason for not doing so.
  • Include pictures. You can draw these by hand and just attach a copy. You don't have to use fancy drawing tools --- but this is a good skill to have.
• Use Sections and Subsections
  • Give the sections and subsections meaningful names
  • Give any important theorems, lemmas, inequalities, conditions, etc. meaningful names.
• Have an abstract: This should state clearly the main achievement of the report.
• Have an introduction but ...
  • NO FLUFF! Do not say something like "networks are of increasing importance" etc. This is just an opinion and, if you think about it, most opinions are just hot air.
  • Say stuff like, "Consider the network in Figure 1. To each red edge attach an independent exponential random variable and to each blue edge ...."
• You should try to coach me (or any reader) toward an honest and interesting level of new understanding. This is not as hard as it sounds if you genuinely make that your objective.
• If you try to sell the "importance" of your problem by citing a lot of papers, you are not speaking to my particular listening. I will judge the interest of the problem by carefully reading actual content of the first few pages. Something that is clear and no harder than it has to be will be interesting. Someting that has "buzz words" will not be interesting.

What Can You Discover?

To honestly understand anything is a wonderful human experience. Oddly enough, to honestly understand something, we often need to explain the thing to someone else. Your report gives you this opportunity.

A project provides you with the chance for discovery --- first of the truth --- and then of the richer truth that you can add.

Being honest is harder than one might think. Most people never even think to try. Honest means: (1) raising every issue --- especially issues like "How did they think of this?" (2) and it means getting answers to those questions

What's the Bottom Line?

• If I learn something from the paper that is a very good thing.
• The "thing" could be an interesting fact (inequality, algorithm, approximation, etc.) but it is better if it is an interesting technique.

What is Bad?

I do want to focus on the positive. This really is the opportunity for a very useful experience. Still, since I have run this kind of experiment before, I suspect it is useful to be very explicit about the ways one can really mess up.

• If I cannot understand the paper that is BAD.
• Failure to give proper credit to any sources used is VERY BAD --- but don't drown me in "begats" --- just cite what you have used.
• If your paper is more complicated than necessary that is BAD.
• If your paper has ambiguities or uncertainties that is BAD.
• If I get even the smallest whiff that you are trying to pull the wool over my eyes that is VERY BAD.
• What would make me the most nuts is for someone to fail to read and to follow the advice that I have put on this page.

More Help?

I am happy to answer any questions that you have about the projects. I can look at your first ideas, sources, plan for development. I can look at preliminary drafts. The goal is to get a good project done and I am willing to do my part to make that happen. Still, it will take a lot of work from you, especially if you have never done anything like this before. I have a few more illustrations and suggestions that you should read.

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