Mathematical models let you answer questions that would be expensive or impossible to address directly. When NASA sends a probe to Mars, they use mathematical models to plan the trajectory; they don’t just send multiple probes in different directions until one of them makes it. Drug companies try new drugs in computer simulations before trying them in people or even animals. Oil companies use mathematical models to find the best place to explore, and to estimate the value of that they’ll recover, before going to the expense of drilling a hole.
Models help you draw information from the data you already have, and suggest what data would be most valuable to acquire next. Many companies collect data indiscriminately, and never look at it. With proper analysis, your company can make the best use of your data resources and be strategic about gathering data.
Mathematical models are not magical, though sometimes they do work astonishingly well. Because models require assumptions and simplifications, it is important to understand these assumptions and their effects. It is also important to understand how much confidence you should have in a model’s predictions.
I’ve helped numerous companies create, implement, and interpret mathematical models. For my PhD work I developed models using partial differential equations. Later in my career I developed models using Bayesian analysis. More recently I’ve worked on projects that combine differential equations and Bayesian analysis to accurately model more complex systems.
If you’d like to discuss how analysis and mathematical modeling could benefit your business, please let me know.