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If you have a parametrized functions that imperfectly models a real phenomenon, of course there are errors. Why assume they are random? A better assumption is t
by patrick451 2y ago
If you have a parametrized functions that imperfectly models a real phenomenon, of course there are errors. Why assume they are random? A better assumption is that your model is just poor. Assuming deterministic modeling errors are due to randomness has always struck me as bizarre.
- exhibit001 2y agoIn the context of MLE, random has a formal definition. What you describe as poor would be included in the mathematics as a factor outside the deterministic parameters that are modeled. E.g. Y = aFactor1 + bFactor2 + ... + constant + 'poor model correction factor'. To solve the equation, we have to make assumptions of the poor correction factor. These assumptions about the error generally have some 'mathematically nice' qualities. For example it's not predictable or has a trend relating to any other factors. An concrete example is having a mean of zero. If it had a non-zero mean, it should be accounted in the constant factor of the model. All these mathematically nice assumptions can be summed up be calling the 'poor model correction' factor as random.
- patrick451 2y agoThis doesn't make sense to me. Any time you want a reduced order model, you will get error. For example: - Say I have data which is perfectly sinusoidal, with an dc bias. I can fit a line a to this data, which will approximate the bias (or be exactly the bias if the data is over an integer number of cycles). - I want to fit a plane to a curved surface - I want to fit a low order transfer function to a high order system. - I want to model a system with friction as a system with no friction. Fitting parameters in all of these situations will result in a non-zero residual. But assuming that is due to randomness is not useful.