Interesting lecture, prof. For me, I would think that the challenge that oftentimes occurs as a result of some significant divergence between a model and reality begins from the point of measurement. In other words, if the measurements do not considerably capture the interacting variables, it becomes difficult to accurately estimate or approximate reality, irrespective of the specified model. There should be serious emphasis on the end-to-end framework of the investigation, which includes the aspect of measurement and that of inferential statistical methods. This even poses the question of whether the model representing the phenomenon of interest should be specified first or the data be obtained first. Regards,
That is super cool, you are right. Several factors can cause significant divergence between a model and reality: Assumptions and Simplifications: Models are often built based on assumptions and simplifications of real-world phenomena. If these assumptions don't hold true in reality or if the simplifications are too crude, the model's predictions may deviate significantly from actual outcomes. Data Quality and Quantity: Models rely on data to make predictions or simulate real-world processes. If the data used to build the model is incomplete, inaccurate, or biased, the model's predictions may not reflect reality accurately. Additionally, if the model is trained on insufficient data, it may not capture the full complexity of the underlying system. Parameter Estimation: Models often involve parameters that need to be estimated from data or expert knowledge. If these parameters are not estimated accurately or if they vary significantly in reality from the values assumed in the model, it can lead to divergence between the model and reality. Dynamic Nature of Systems: Many real-world systems are dynamic and evolve over time in response to various factors. If a model fails to account for this dynamic nature or if it assumes a static environment, its predictions may become inaccurate as time progresses. Unforeseen Factors: Real-world systems can be influenced by a multitude of factors, some of which may not have been accounted for in the model. These unforeseen factors can lead to divergence between the model's predictions and actual outcomes. Feedback Loops and Nonlinearities: Complex systems often exhibit feedback loops and nonlinear relationships between variables. If a model fails to capture these nonlinearities or if it oversimplifies feedback mechanisms, it may produce inaccurate predictions. Model Complexity: Sometimes, models may be overly complex, incorporating unnecessary features or interactions that do not exist in reality. This can lead to overfitting and poor generalization to new data, causing significant divergence between the model and reality. Errors in Implementation: Mistakes in implementing the model, such as coding errors or numerical inaccuracies, can also lead to divergence between the model's predictions and reality. Addressing these factors often requires careful validation and calibration of the model against real-world data, as well as ongoing refinement as new insights are gained and the understanding of the system improves.
