Undergraduate Research Projects

These are undergraduate in the sense of not requiring research-level mathematical probability knowledge (see Open Problems for ones which do). On the other hand they are intended to be serious in that successful results will often become a small part of some future published scholarly paper. For further suggestions from my undergraduate course click here.

During the semesters there is a weekly meeting in which everyone says what they have done in the last week.

Current students (Spring 2013)

The weekly meeting is Friday, 9.45 - 10.30am, room 443 Evans.

Students Project Description

Weijian (James) Han [work-study]

Wen Liang [senior thesis] Life Expectancy Index model and Risk Management Understanding what J.P.Morgan's LifeMetrics does.

Bonghyun Kim [Independent study] Event Dispersal Simulation Simulating the dispersal of Facebook Events.

Misha Jhaveri [Independent study] Investigating the game of Hangman Progress report

MoonSoo Choi [Independent study] Statistical Analysis of Nuel Tournaments. These are N-person duels. Here is the Cal Day poster.

Seungjun Lee and Mingu Jo [Independent study] Simulation of Interactions on Campus Data and modeling of the chance of meeting different students while walking on campus. Note a nice example of a poster for Cal Day.

Wenyu Zhang [Independent study] Trends in Iphone 5 Sales on Ebay Collection and analysis of data.

Yu Haihan (Mark) [Independent study] Expanding Civilizations and the Fermi Paradox Simulation of a model.

Students	Project	Description
Weijian (James) Han [work-study]
Wen Liang [senior thesis]	Life Expectancy Index model and Risk Management	Understanding what J.P.Morgan's LifeMetrics does.
Bonghyun Kim [Independent study]	Event Dispersal Simulation	Simulating the dispersal of Facebook Events.
Misha Jhaveri [Independent study]	Investigating the game of Hangman	Progress report
MoonSoo Choi [Independent study]	Statistical Analysis of Nuel Tournaments.	These are N-person duels. Here is the Cal Day poster.
Seungjun Lee and Mingu Jo [Independent study]	Simulation of Interactions on Campus	Data and modeling of the chance of meeting different students while walking on campus. Note a nice example of a poster for Cal Day.
Wenyu Zhang [Independent study]	Trends in Iphone 5 Sales on Ebay	Collection and analysis of data.
Yu Haihan (Mark) [Independent study]	Expanding Civilizations and the Fermi Paradox	Simulation of a model.

General styles of possible future projects

Data collection

How can one obtain data concerning the contexts where "ordinary people" think about chance? I have analyzed 3 types of data from blogs, from twitter and from Bing queries. Can you think of any other source of data that you could actually acquire?
Ropeik, in How Risky is it Really?, lists 13 psychological factors which can make a risk seem more threatening or less threatening than it really is. These are copied in section 5.2 of my lectures. (In each case the direction of the effect is intuitively clear). Take some risks that are currently in the news, and see how well they fit these psychological factors.
I have a short list of textbook predictions that one can verify on new data. Can you think of other such predictions?
Look at written descriptions of football games where the point spread was near zero. To what extent do the descriptions of the game refer to skill or to luck? This is an empirical aspect of the Narrative Fallacy.
Professional ice hockey players who grew up in Canada are said to have substantial non-uniformity of birthdays. A 1985 paper Birthdate and success in minor hockey by Roger Barnsley and A. H. Thompson, and subsequent work, popularized in Gladwell's Outliers, attributes this to the annual age cutoff for starting minor hockey. Is this still true, and does the "birthday problem" prediction for coincidence hold for this non-uniform distribution?
Average class size at a college is different from the instructor's viewpoint than from the students' viewpoint. I suspect that when colleges advertize "small class size" and quote an average, they quote the former average rather than the more relevant (and larger) latter average. Can you get data?
I often say "the most common iconic visual image for randomness is a die". Is this correct, and what are the second, third ...... most common? One could start by looking on amazon.com at covers of books dealing with randomness, as done on this page.
There are a lot of tasks related to my Annotated list of contexts where we perceive chance . One is to find some (non-obvious) graphic for each context. At some time in tbe future I will create a talk on this topic, and I would like someone to experiment with Prezi as a way of combining a list with a dynamic presentation.
Observing real queues for the Waves in long lines model below (near bottom of table).
Here are some comments on probability-related topics which appear in popular science style books rather than textbooks, and which of these have Wikipedia entries. It would be useful (to me) for someone to do a more thorough analysis -- how much space is devoted to each topic in books/Wikipedia -- and perhaps combine this with using the Google Ngram viewer to see frequency of different phrases in books (as a function of year published).

Simulation - drawing static pictures

For this Lake Wobegon process.

In fact all of these would be even nicer as moving pictures, below.

Simulation - drawing moving pictures

The processes below are very easy to simulate, but I want "moving pictures", in Java or whatever, to illustrate their dynamics.

Another one bites the dust. This birth-and-assassination process would look good accompanied by the Queen song.

Inventing good heuristic algorithms and writing code

Optimal spatial networks. Given positions of n cities, we want to connect them with a road network which is optimal according to certain criteria. Finding the optimal network is not easy --see section 1.2 of this paper for details on the project.

Physical experiments

Real shuffles. There's some elegant math theory about "random riffle shuffles", e.g. that it takes about 7 shuffles to make a card deck random (see Bayer-Diaconis or the more elementary Aldous-Diaconis paper. The theory assumes a kind of idealized shuffle which isn't quite what the average person really does. So there are interesting possible experiments where you compare shuffling 2 times, or 3 times, or 4 times, and then gather statistics (e.g. shape of bridge hands) from the resulting deals. See the recent paper Assaf et al for related theory.
To physically mix a large number of objects is much harder than you think. Here's a project. Imagine you want to run a lottery with say 100 names, and you do this by writing names on pieces of paper (e.g. stiff paper like business cards), putting them in some container (e.g. a cardboard box) and then just shaking, turning over, etc the box for 5 minutes. Then reach in and draw out tickets. My prediction is that this does a bad job of mixing -- one can do statistical tests on the results that show the order of the 100 draws are non random. It would be interesting to do enough experiments to estimate how the number of shakes needed to mix grows with the number of tickets.

Statistical analysis

Math theory

I don't encourage undergrads to attempt to do new math research. But a good project is

Writing a Wikipedia article

on some topic you have learned from a course or a textbook.

Previous projects and students

A link under ``project" indicates a write-up of specifically the student's work. Where the work features as part of a broader write-up, the link is under ``discussion". Some projects were under the URAP and VIGRE programs. Projects directly relevant to the "Probability in the Real World" project are marked (RW).

Students Project Description

Fayd Shelley (Summer 2006); Sunny Zhao (Fall 2008) Coincidences in Wikipedia (RW) Data appears in this unfinished draft paper.

Dennis Moy (Fall 2006) A regression model using common baseball statistics to project offensive and defensive efficiency. Undergraduate honors thesis.

Yanjiao Cheng, Jesse Friedman, Yu-Jay Huoh, Wayne Lee, Harrison Liu (Spring 2007) Statistics of road networks Data collection for Figure 1 of this paper. URAP and VIGRE.

Tamar Lando (Spring 2008) Efficient Networks and Enumerations on Forests Masters thesis. Part will appear as section xxx of xxx.

Julian Shun (Spring 2008) Optimal spatial networks Simulations, forming a substantial part of our joint paper.

Robert Huang (Spring 2008) Exploratory data analysis of amazon.com book review data. VIGRE.

Eric Chao and Regina Wu (Spring 2009) This and the next are continuations of the same project. URAP.

Timothy Wong (Spring 2009) Exploratory Data Analysis of Amazon.com Book Reviews Undergraduate honors thesis.

Amy Huang and Irvin Liu (Spring 2009) References to chance in blogs (RW) What type of things do "ordinary people" attribute to chance? One way to study this is to search through blogs. URAP.

Amy Huang and Irvin Liu (Spring 2009) The 1.4 trillion dollar project (RW). A Google search on "1.4 trillion dollars" gets a surprisingly large number of hits, which can be traced back to some smaller number of different appearances of "1.4 trillion dollars" in some authoritative data. The project was to count this "number of different appearances" for a variety of dollar amounts (2.8 trillion; 1.8 billion, etc) to see whether they follow a particular "informationless" distribution. URAP.

Tung Phan (Spring 2009) Benford's law. (RW) Data collection, forming a substantial part of our short joint paper When Can One Test an Explanation? Compare and Contrast Benford's Law and the Fuzzy CLT exhibiting a typical undergrad project.

Priscilla Ku and Janet Larwood (Spring 2009) 40,000 coin tosses yield ambiguous evidence for dynamical bias (RW) Testing a prediction of Persi Diaconis et al that in coin-tossing there is a small bias -- maybe 1/100 - towards the coin landing the same way as it started. URAP.

Alan Choi (Spring 2009) Statistics of road networks Data collection, forming a substantial part of our short joint paper A Route-Length Efficiency Statistic for Road Networks .

Wei Zhou and Jonathan Ong (Spring 2009) Empires and percolation . Simulations and pictures, used to complement theory in our joint paper Empires and percolation: stochastic merging of adjacent regions.

Bowei Zheng (2008-2009) Java simulations for a "parking process" The process was studied analytically in this old paper.

Tung Phan (Fall 2009) What can you predict about a team's performance next season? (RW) Quantifies the regression effect for sports teams.

Karthik Ganesan [VIGRE] (Spring 2012) Empirical Study on Route-Length Efficiency of Road Networks Data collection for route-length efficiency of road networks. Graphics used in this talk

Hyerim Hong [Independent study] (Spring 2012) Perception on role of chance in different aspects of life Via a survey

Bowen Huang [VIGRE] (Spring 2012) City Growth Model Simulation Here is a slightly complicated model for city growth in which cities have positions, populations and spheres of influence. It's not hard to simulate the process, but I want some pretty pictures of the spheres of influence.

Willy Lai [VIGRE] (Spring 2012) Fitting power-law distributions to data Testing data for fit to power-law distributions. e.g. this data on family names.

Russell Mays [volunteer] (Spring 2012) Road route networks linking 4 addresses Take 4 street addresses, whose positions form roughly a square, of side length roughly 5 miles or 50 miles or 500 miles. Use e.g. Google maps to find the routes between each of the 6 pairs of addresses, and draw a map showing these 6 routes together. Mathematically there are about 45 topologically different possibilities for the map; presumably some come up often and others rarely, but which? And does it vary with distance (side-length of square)?

Max Moacanin [volunteer] (Spring 2012) Lucky vs Unlucky teams Assuming gambling odds give true probabilities, one can classify a team as having been lucky or unlucky so far. Do results of matches between lucky and unlucky teams fit the gambling odds?

Selene Xu [Independent study] (Spring 2012) Study of Auction Theory in eBay Data Collecting and studying data about auction prices.

Amy Zhang [honors thesis] (Spring 2012) Pairs trading A simulation study to explore possible relationship and connection between profit and different variables associated with stock selections in pairs trading.

Yiming Zhou [Independent study] (Spring 2012) Spatial Poisson processes Draft of possible Wikipedia article

Xiaoyu (Lily) Wang [Volunteer] (Summer 2012) Design of simulation of efficient road networks Continuing the theme of heuristic algorithms in this paper to study models with junctions.

Jian Li [Volunteer] (Summer 2012) Dynamic random Gabriel networks Computer simulations and graphics.

Morgan Thompson [graduate volunteer] (Fall 2011 - Summer 2012) Data on dust-to-dust models Producing data used in Chapter 11 of Draft write-up of 13 lectures.

Karthik Ganesan [Independent study] (Summer-Fall 2012) math models of road networks Graphics and simulation data for the "binary hierarchy" model; to be included in next version of this paper

Bowen Huang [Volunteer] (Summer-Fall 2012) Simulations of a model for city growth Graphics and simulation data appear in this paper.

Xiaoyu (Lily) Wang [Independent study] (Fall 2012) Dynamic Gabriel graphs The file of dynamic simulations of a network model is too large to show, but here is a static snapshot.

Weijian (James) Han [work-study] (Fall 2012) References to chance in micro-blogs Examples/analysis posted here.

Weijian (James) Han [work-study] (Fall 2012) Simulations of the Waves in long lines model Brief write-up of model description, simulation results and math conjectures.

Weijian (James) Han [work-study] (Fall 2012) Distribution of Losses Due to Structural Fires Analysis of data from Berkeley CA.

Weijian (James) Han [work-study] (Spring 2013) Simulation of a model of Random Particle Motion related to this model. Description on this page (applet doesn't work on Macs).

Max Moacanin [volunteer] (Spring 2013) Simulation data from the iPod process where favorites are played.

Students	Project	Description
Fayd Shelley (Summer 2006); Sunny Zhao (Fall 2008)	Coincidences in Wikipedia (RW)	Data appears in this unfinished draft paper.
Dennis Moy (Fall 2006)	A regression model using common baseball statistics to project offensive and defensive efficiency.	Undergraduate honors thesis.
Yanjiao Cheng, Jesse Friedman, Yu-Jay Huoh, Wayne Lee, Harrison Liu (Spring 2007)	Statistics of road networks	Data collection for Figure 1 of this paper. URAP and VIGRE.
Tamar Lando (Spring 2008)	Efficient Networks and Enumerations on Forests	Masters thesis. Part will appear as section xxx of xxx.
Julian Shun (Spring 2008)	Optimal spatial networks	Simulations, forming a substantial part of our joint paper.
Robert Huang (Spring 2008)	Exploratory data analysis of amazon.com book review data.	VIGRE.
Eric Chao and Regina Wu (Spring 2009)		This and the next are continuations of the same project. URAP.
Timothy Wong (Spring 2009)	Exploratory Data Analysis of Amazon.com Book Reviews	Undergraduate honors thesis.
Amy Huang and Irvin Liu (Spring 2009)	References to chance in blogs (RW)	What type of things do "ordinary people" attribute to chance? One way to study this is to search through blogs. URAP.
Amy Huang and Irvin Liu (Spring 2009)	The 1.4 trillion dollar project (RW).	A Google search on "1.4 trillion dollars" gets a surprisingly large number of hits, which can be traced back to some smaller number of different appearances of "1.4 trillion dollars" in some authoritative data. The project was to count this "number of different appearances" for a variety of dollar amounts (2.8 trillion; 1.8 billion, etc) to see whether they follow a particular "informationless" distribution. URAP.
Tung Phan (Spring 2009)	Benford's law. (RW)	Data collection, forming a substantial part of our short joint paper When Can One Test an Explanation? Compare and Contrast Benford's Law and the Fuzzy CLT exhibiting a typical undergrad project.
Priscilla Ku and Janet Larwood (Spring 2009)	40,000 coin tosses yield ambiguous evidence for dynamical bias (RW)	Testing a prediction of Persi Diaconis et al that in coin-tossing there is a small bias -- maybe 1/100 - towards the coin landing the same way as it started. URAP.
Alan Choi (Spring 2009)	Statistics of road networks	Data collection, forming a substantial part of our short joint paper A Route-Length Efficiency Statistic for Road Networks .
Wei Zhou and Jonathan Ong (Spring 2009)	Empires and percolation .	Simulations and pictures, used to complement theory in our joint paper Empires and percolation: stochastic merging of adjacent regions.
Bowei Zheng (2008-2009)	Java simulations for a "parking process"	The process was studied analytically in this old paper.
Tung Phan (Fall 2009)	What can you predict about a team's performance next season? (RW)	Quantifies the regression effect for sports teams.
Karthik Ganesan [VIGRE] (Spring 2012)	Empirical Study on Route-Length Efficiency of Road Networks	Data collection for route-length efficiency of road networks. Graphics used in this talk
Hyerim Hong [Independent study] (Spring 2012)	Perception on role of chance in different aspects of life	Via a survey
Bowen Huang [VIGRE] (Spring 2012)	City Growth Model Simulation	Here is a slightly complicated model for city growth in which cities have positions, populations and spheres of influence. It's not hard to simulate the process, but I want some pretty pictures of the spheres of influence.
Willy Lai [VIGRE] (Spring 2012)	Fitting power-law distributions to data	Testing data for fit to power-law distributions. e.g. this data on family names.
Russell Mays [volunteer] (Spring 2012)	Road route networks linking 4 addresses	Take 4 street addresses, whose positions form roughly a square, of side length roughly 5 miles or 50 miles or 500 miles. Use e.g. Google maps to find the routes between each of the 6 pairs of addresses, and draw a map showing these 6 routes together. Mathematically there are about 45 topologically different possibilities for the map; presumably some come up often and others rarely, but which? And does it vary with distance (side-length of square)?
Max Moacanin [volunteer] (Spring 2012)	Lucky vs Unlucky teams	Assuming gambling odds give true probabilities, one can classify a team as having been lucky or unlucky so far. Do results of matches between lucky and unlucky teams fit the gambling odds?
Selene Xu [Independent study] (Spring 2012)	Study of Auction Theory in eBay Data	Collecting and studying data about auction prices.
Amy Zhang [honors thesis] (Spring 2012)	Pairs trading	A simulation study to explore possible relationship and connection between profit and different variables associated with stock selections in pairs trading.
Yiming Zhou [Independent study] (Spring 2012)	Spatial Poisson processes	Draft of possible Wikipedia article
Xiaoyu (Lily) Wang [Volunteer] (Summer 2012)	Design of simulation of efficient road networks	Continuing the theme of heuristic algorithms in this paper to study models with junctions.
Jian Li [Volunteer] (Summer 2012)	Dynamic random Gabriel networks	Computer simulations and graphics.
Morgan Thompson [graduate volunteer] (Fall 2011 - Summer 2012)	Data on dust-to-dust models	Producing data used in Chapter 11 of Draft write-up of 13 lectures.
Karthik Ganesan [Independent study] (Summer-Fall 2012)	math models of road networks	Graphics and simulation data for the "binary hierarchy" model; to be included in next version of this paper
Bowen Huang [Volunteer] (Summer-Fall 2012)	Simulations of a model for city growth	Graphics and simulation data appear in this paper.
Xiaoyu (Lily) Wang [Independent study] (Fall 2012)	Dynamic Gabriel graphs	The file of dynamic simulations of a network model is too large to show, but here is a static snapshot.
Weijian (James) Han [work-study] (Fall 2012)	References to chance in micro-blogs	Examples/analysis posted here.
Weijian (James) Han [work-study] (Fall 2012)	Simulations of the Waves in long lines model	Brief write-up of model description, simulation results and math conjectures.
Weijian (James) Han [work-study] (Fall 2012)	Distribution of Losses Due to Structural Fires	Analysis of data from Berkeley CA.
Weijian (James) Han [work-study] (Spring 2013)	Simulation of a model of Random Particle Motion related to this model.	Description on this page (applet doesn't work on Macs).
Max Moacanin [volunteer] (Spring 2013)	Simulation data	from the iPod process where favorites are played.