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This paper seems to basically be max likelihood estimation with a Laplace approximation, but I haven't looked at it closely enough to see where it differs from standard Laplace, either for maximization w.rt. the parameters or for inference for the latents. One difference seems to be that they are deriving derivatives rather than relying on AD.
They compare their approach to glmmTMB and to INLA.
Probably worth one of us taking a look at some point.
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