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I’ve written an in depth article about nonlinear least squares fitting from a Bayesian perspective. In there, I derive the best fit parameters, their covariance, and credible bands around the best fit model from scratch. I am using only elementary linear algebra and calculus. I also try to shine a light on the influence of priors.

None of this is rocket science or novel, but I still feel there’s value to this, since it helps to understand what the method of least squares means from a Bayesian POV.