LogLikelihood that combines GaussianLogLikelihood and MultiplicativeGaussianLogLikelihood

[DavAug]

In some situations it's beneficial to be able to specify an error model that combines a base-level Gaussian noise and a Gaussian noise that scales with the model output

y_pred = y + (a + b * y^eta) epsilon,

where epsilon is a standard gaussian random variable, and y the model predictions without noise.

In analogy to the existing GaussianLogLikelihood and the MultiplicativeGaussianLogLikelihood, we could introduce a CombinedGaussianLogLikelihood that implements the described error model.

[MichaelClerx]

Which situations?

The question to answer here is "is that general enough to go in PINTS?" It was always the idea that users can create their own likelihood functions

[MichaelClerx]

(If you were really brave, you could make a likelihood that adds two other likelihoods together, or even implement the plus, minus etc. operators for likelihoods, and then work out what that means for the S1 etc... :D) <-- maybe not!

[DavAug]

I would argue that for time series problems (with no correlated noise or well separated measurements) a combined Gaussian error is general enough. I think in almost all measurement processes you have a lower limit of uncertainty which is why a base-level noise would be good to have. But then many measurement devices have an uncertainty that scales with the output which could be captured by a multiplicative Gaussian error.

I know that in the PKPD community such a combined error is quite extensively used.

[MichaelClerx]

Cool! Go for it!