The General Model Equation Plus Noise
The results of the previous chapter already represent progress on the spectral analysis problem because we were able to remove consideration of the amplitude, phase and noise level, and find what probability theory has to say about the frequency alone. In addition, it has given us an indication about how to proceed to more general problems. If we had used a model where the quadratic term in the likelihood function did not simplify, we would have a more complicated analytical solution. Although any multivariate Gaussian integral can be done, the key to being able to remove the nuisance parameters easily, and above all selectively, was that the likelihood factored into independent parts. In the full spectrum analysis problem worked on by Jaynes,  the nuisance parameters were not independent, and the explicit solution required the diagonalization of a matrix that could be quite large.
KeywordsModel Function Nuisance Parameter Chirp Rate Joint Likelihood Intuitive Picture
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