Ask Russ Rhinehart - What are the pros for empirical models?

Russ' Response:

I would broadly classify models as empirical or phenomenological.  

Empirical models are developed by matching flexible mathematical functions to data.  The functions might be neural networks, or classic statistical power series for regression.  These approaches are used in Big Data, Machine Learning, and Artificial Intelligence.  They might be termed data-based, or regression, or even model-free models.  Many folks are reporting benefits from such data-based, empirical models.  

Some advantages of empirical models include:

• Simplicity: Empirical models are composed of repeating units of the same structure.  In the Autoregressive-Moving-Average approach, it is the addition of linear time-delayed terms multiplied by a coefficient.  In a power series approach it is the variable raised to an integer power and multiplied by a coefficient.  In neural network models it is the addition of exponential terms (neurons) multiplied by weighting factors.  The simple elements and structure make for easy understanding and coding.
• Versatility: The same model structure is used for every application, regardless of the process.  Even diverse processes associated with health care or education would use the same model structure that might be used for modeling a chemical process.
• Effort: The model structure is defined.  Greater engineering effort and skill are needed to derive first-principles models.
• Guidance: If a process is not mechanistically understood, then empirical modeling can identify possible input/output relationships.  

But use caution...  

1. Caution: Correlation is not causation. Grey hair does not cause facial wrinkles. If that correlation is taken as causation, then dying one’s hair might be hypothesized as a cure for facial wrinkles. Dennis Williams sent to me a link to https://www.tylervigen.com/spurious-correlations, about statistically significant correlations, and too-funny-to-believe explanations that GenAI gave for the connection.  
2. Caution: A mechanism might not be visible (adequately expressed) within the historical data.  Just because you have an empirical model for the data does not mean it is complete.  It may be missing important relationships.

I prefer the use of first-principles models. But expediency might justify empirical modeling.

In subsequent Pods, I’ll introduce how to create your own first-principles models, how to simulate environmental vagaries, how to calibrate and validate models, and how to use the models to evaluate the various economic indicators of transient events.  I hope to visit with you later.  Meanwhile, visit my web site www.r3eda.com to access information about modeling, control, optimization, and statistical analysis.