How is a mathematical model verified?

A mathematical model is verified by comparing its predictions with real-world data.

To verify a mathematical model, it is necessary to compare its predictions with real-world data. This can be done by collecting data and using it to test the model's predictions. If the model's predictions match the data, then it is considered to be verified. However, if the predictions do not match the data, then the model needs to be revised.

One way to verify a mathematical model is to use statistical analysis. This involves comparing the model's predictions with the actual data using statistical tests such as the chi-squared test or the t-test. If the statistical tests show that the model's predictions are significantly different from the actual data, then the model needs to be revised.

Another way to verify a mathematical model is to use sensitivity analysis. This involves varying the model's parameters and observing how the predictions change. If the predictions are sensitive to changes in the parameters, then the model is considered to be verified. However, if the predictions are not sensitive to changes in the parameters, then the model needs to be revised.

In conclusion, a mathematical model is verified by comparing its predictions with real-world data using statistical analysis and sensitivity analysis. If the model's predictions match the data and are sensitive to changes in the parameters, then it is considered to be verified.