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Personal Info

John Bihn is a statistics major at Williams College. He is a member of the Williams Ultimate Frisbee Organization (WUFO), junior leader of the Moocho Macho Moocow Military Marching Band, and staff writer for the Williams Record. His favorite color crayon is Purple Mountains' Majesty.

Research Topic

Using statistical surrogates to estimate the behavior of storm surge during a hurricane or tropical storm. See here for more details.


Weekly milestones can be found on our main project page, located here.

Daily Log

Week 1 (6/1 - 6/5)

Monday, June 1

  • Attended introductory session; learned about REU program
  • Met Dr. Spiller and research group over lunch
  • Toured systems lab; learned about wiki with Dr. Dennis Brylow
  • Filled out pre-REU survey
  • Did preliminary readings before Tuesday’s meeting with Dr. Spiller

Tuesday, June 2

  • Took tour of campus
  • Filed paperwork with HR; received Marquette ID
  • Learned about resources at library with Heather James
  • Met with Dr. Spiller, set objectives to complete before meeting on Thursday
    • Objective: Determine how to predict a given function in Python by only using a sample of data points from the function
    • How to achieve: Use formula that relies on finding the optimal value of our parameter(s) (found using maximum likelihood (ML) equation)
  • Examined the function in R and predicted function using selected values of parameter

Wednesday, June 3

  • Added variance function to prediction in R; corrected mistakes in model
  • Examined random selection of sample points in R
  • Installed required packages for Python
  • Met with Dr. Brylow to learned about Marquette email and time keeping
  • Tested optimization routines in Python
  • Attempted to optimize ML equation in Python

Thursday, June 4

  • Determined routine for plotting in Python
  • Organized code before meeting with Dr. Spiller
  • Engaged in group discussion with Dr. Factor about the theory behind approaching a new problem
  • Met with Dr. Spiller; developed research goals and project timeline
  • Downloaded Liclipse IDE
  • Plotted our function in Python

Friday, June 5

  • Met as research group to review project
  • Worked on understanding optimization routine, using it to find the global optimal point, and ensuring that it works in multiple dimensions
  • Reviewed objectives of project, went step by step through each component of our approximating equation and ML equation
  • Created project milestones and finished daily log
  • Began working log of progress in LaTeX

Week 2 (6/5 - 6/12)

Monday, June 8

  • Reviewed components of approximating equation and ML equation with Tao
  • Identified challenges with performing calculations in Python
  • Met with Dr. Spiller to review plan of attack, discuss how to approach preliminary research
  • Worked on creating methods to create needed components of functions
  • Developed a plot of our approximation in Python

Tuesday, June 9

  • Refined approximation
  • Created maximum likelihood function; made function compatible with optimize method
  • Worked through difficulties with singularity in our matrices
  • Obtained local minimum, plot of maximum likelihood function (though did not appear accurate)
  • Performed introductory research on storm surges

Wednesday, June 10

  • Corrected errors in our calculation of maximum likelihood function
  • Found optimal value of parameter according to maximum likelihood function
  • Adapted model to accommodate estimation of multiple parameters
  • Continued introductory research on storm surges

Thursday, June 11

  • Added variance function to Python code
  • Generalized selection of known points
  • Listened to sample presentation by Dr. Factor
  • Met with Dr. Spiller, updated her on our progress and discussed paper by Westerink et al.

Friday, June 12

  • Ensured variance function worked correctly
  • Adjusted code so our approximation used optimal parameters in multiple dimensions
  • Tested our approximation methods for other functions
  • Polished code
  • Read introduction of Westerink et al.

Week 3

Monday, June 15

  • Worked through research paper (Westerink et al.)
  • Identified important factors in storm surge model
  • Developed questions for Dr. Spiller

Tuesday, June 16

  • Prepared individually and as a group for meeting with Dr. Spiller
  • Met with Dr. Spiller
    • Introduced to additional notes on GaSP
    • Discussed how to adapt our model to use different ML equation from notes
  • Met with Dr. Brylow to discuss distinctions between research talks and research papers
  • Began examining new ML equation; compared new equation with previous ML equation

Wednesday, June 17

  • Continued comparing maximum likelihood equations
  • Incorporated a least squares model into our approximation
  • Met with Dr. Spiller to discuss structure of new ML equation
  • Created project page on wiki
    • Edited description of project and personal page

Thursday, June 18

  • Completed Responsible Conduct of Research (RCR) training
  • Created methods for calculating the new ML equation
  • Developed an approximation for our function using new ML equation

Friday, June 19

  • Changed our approximation to fully incorporate least squares model
  • Experimented with different functions, different number of known points
  • Added reference prior into our ML equation
  • Met with Dr. Spiller to determine potential adjustments to our equation
  • Adapted maximum likelihood equation to be compatible with multiple dimensions
  • Adjusted prior to allow for more than one input variable
  • Explored plotting in three dimensions in Python

Week 4

Monday, June 22

  • Continued adjusting ML equation to permit inputs from more than one variable
  • Completed online portion of RCR training
  • Added daily log to personal wiki page

Tuesday, June 23

  • Met with Dr. Spiller to discuss difficulty with fitting ML equation
  • Implemented updated conditional mean and variance equations in one dimension
  • Plotted maximum likelihood graph for two input variables

Wednesday, June 24

  • Corrected mistakes in program
  • Tested optimization routines in Python; implemented most reliable routine
  • Continued attempting to adapt our program to work with more than one input variable

Thursday, June 25

  • Prepared questions for Dr. Spiller; tested points along ML equation that includes prior
  • Met with Dr. Spiller
    • Discussed the inclusion of linear regression in our model
    • Dr. Spiller introduced Monte Carlo methods
  • Attended working lunch with example presentation by Dr. Spiller
  • Corrected our linear regression methods
  • Implemented plots of our equation and conditional mean
  • Adjusted our selection of design points to better cover our domain

Friday, June 26

  • Tested our program using different functions and number of design points
  • Adapted our code to work for any number of inputted variables
  • Confirmed that our code works for three inputted variables

Week 5

Monday, June 29

  • Finished automatically plotting conditional mean equation based on number of variables used
  • Continued testing our program
  • Added conditional variance into two-dimensional plot
  • Discussed outline for Thursday's presentation (given to other mentors and REU students)
  • Began reading Bayarri et al. (2006) and Kennedy and O'Hagan

Tuesday, June 30

  • Continued reading Bayarri et al.
  • Met with Dr. Spiller
    • Discussed the accuracy of our program; Dr. Spiller provided suggestions for confirmation
    • Discussed upcoming presentation
  • Completed Bayarri et al., began reading Kennedy and O'Hagan
  • Began working on presentation using Beamer

Wednesday, July 1

  • Developed general outline for our group’s presentations, ensured we each had different focus
  • Completed outline of presentation
  • Met with Dr. Spiller to further discuss presentations
  • Created slides for presentation using Beamer

Thursday, July 2

  • Practiced presentation
  • Presentations
    • Gave talk about progress on project
    • Listened to and provided feedback on other presentations

Week 6

Monday, July 6

  • Met with Dr. Spiller
    • Discussed overall objectives for project
    • Reviewed plans for upcoming week
  • Reviewed notes about GaSP and Bayarri 2006
  • Polished code to send to Dr. Spiller
  • Read through notes about Markov chain Monte Carlo (MCMC) methods

Tuesday, July 7

  • Created code to implement MCMC process
  • Confirmed our process worked by developing plots of our Markov chain
  • Read through additional MCMC notes
  • Completed basic exercise new notes

Wednesday, July 8

  • Worked on harder example using MCMC with more than one parameter
  • Reviewed online RCR materials in preparation for final assessments

Thursday, July 9

  • Completed final tests for RCR training
  • Met with Dr. Spiller
    • Reviewed MCMC methods
    • Discussed next steps in validating model
  • Had working lunch with REU group
  • Successfully implemented harder example of MCMC methods

Friday, July 10

  • Worked on calculating bias function for our model approximation

Week 7

Monday, July 13

  • Met with Dr. Spiller
    • Discussed methods of confirming our code is working properly
    • Talked about goals for our project
  • Attempted to ensure code worked when removing "noise" in our correlation matrix

Tuesday, July 14

  • Created algorithms to simplify verification that our MCMC methods work
  • Searched for errors in our methods to calculate the bias function

Wednesday, July 15

  • Narrowed down sources of error that cause our approximation to be inaccurate in some cases

Thursday, July 16

  • Met with Dr. Spiller to discuss potential reasons for poor approximations in some cases
  • Working lunch
    • Presentation by Dr. Factor about scientific posters
  • Continued searching for errors in our program for developing an accurate approximation

Friday, July 17

  • Identified parameters that must be adjusted to ensure accuracy of our model approximation
  • Met with Dr. Spiller to discuss parameters in exponent of correlation equation
  • Adjusted process of estimating bias in model

Week 8

Monday, July 20

  • Verified code for particular parameters
  • Met with Dr. Spiller
    • Discussed final poster
    • Examined current state of program and next steps
  • Created outline of final poster
  • Reviewed Kennedy and O'Hagan
  • Ran additional tests of model approximation method

Tuesday, July 21

  • Outlined equations from Bayarri et. al.
  • Created outline for poster in LaTeX
  • Found and reviewed online notes relating to preliminary readings
  • Finished plotting maximum likelihood function

Wednesday, July 22

  • Met with Dr. Spiller
    • Planned the implementation of MCMC techniques relating to our project
  • Added a fix to our maximum likelihood method for robustness to parameters
  • Created an MCMC process for a multivariate Gaussian distribution

Thursday, July 23

  • Continued working on poster
  • Working lunch; discussion on graduate school
  • Met with Dr. Spiller
    • Discussed equations needed to complete MCMC process
  • Created MCMC process for distribution centered around bias-corrected prediction

Friday, July 24

  • Attempted to create MCMC process for distribution centered around approximation of model
  • Obtained template for poster
  • Created outline for poster

Week 9

Monday, July 27

  • Continued attempting to fit MCMC processes
  • Wrote text to be used on poster
  • Added images to be used for poster

Tuesday, July 28

  • Reformatted poster and made corrections
  • Created outline for paper