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:
- Define the problem
- Make some assumptions
- Define your variables
- Build a one or many models
- Analyze your model
- Reporting your results
- 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.