My Summer of Data Science Part One: Mathematical Modeling #sods17

Chip Oglesby bio photo By Chip Oglesby

First, did you know that the Clay Mathematics Institute has a million dollar prize for anyone who can solve any of their problems?

I’m thinking about trying to solving the famous P vs NP Problem.

But before I figure that one out, I want to start with someone more simple that has a practical application for me: mathematical modeling.

I’m participating in the The Summer of Data Science which is a commitment to learn something this summer to enhance your data science skills, and to share what you learned. This will be so much fun!!

Modeling is a process that uses math to represent, analyze make predictions and provide insight into real-world phenomena.

What would be an example of this? So, for example, a coworker might come to you and ask something simple like “What is the best product I should be ** **selling for this marketing campaign?”

Steps for mathematical modeling may include:

  1. Define the problem
  2. Make some assumptions
  3. Define your variables
  4. Build a one or many models
  5. Analyze your model
  6. Reporting your results

A more concise definition of the process can be found here:

  • Why? What are we looking for? Identify the need for the model.
  • Find? What do we want to know? List the data we are seeking.
  • Given? What do we know? Identify the available relevant data.
  • Assume? What can we assume? Identify the circumstances that apply.
  • How? How should we look at this model? Identify the governing physical principles.
  • Predict? What will our model predict? Identify the equations that will be used, the calculations that will be made, and the answers that will result.
  • Valid? Are the predictions valid? Identify tests that can be made to validate the model, i.e., is it consistent with its principles and assumptions?
  • Verified? Are the predictions good? Identify tests that can be made to verify the model, i.e., is it useful in terms of the initial reason it was done?
  • Improve? Can we improve the model? Identify parameter values that are not adequately known, variables that should have been included, and/or assumptions/restrictions that could be lifted. Implement the iterative loop that we can call “model-validate-verify-improve-predict.”
  • Use? How will we exercise the model? What will we do with the model?

So I plan on spending the summer fine-tuning how I will use this process at work for each piece of analysis that I do. This is something that I normally do, but I know that my assumptions can always be better.