Zero and One tricks for INLA?

Question

The Zero and One tricks are used to sample from a model not included in the basic functions in BUGS:

http://www.medicine.mcgill.ca/epidemiology/Joseph/courses/common/Tricks.html

I have a general and simple question about INLA: is it possible to use similar tricks for sampling from the posterior of models not included in the basic functions of INLA?

In other words, if I can implement a log posterior for a model (up to a constant) that is not part of the basic functions of INLA, can I use a Zero or Ones trick to use the INLA machinery in this new model?

My question is not about software, but about the possibility of reformulating an INLA sampler into a Poisson or Binomial model as it is done in BUGS.

Answer 1

That is not possible.

INLA can only fit a variety, but still very restrictive, type of models. See for instance

Integrated Nested Laplace Approximations (INLA)

In general

INLA focuses on models that can be expressed as latent Gaussian Markov random fields (GMRF) because of their computational properties (see Rue and Held 2005 for details). Not surprisingly, this covers a wide range of models and recent reviews of INLA and its applications can be found in Rue et al. (2017) and Bakka et al. (2018).

https://becarioprecario.bitbucket.io/spde-gitbook/ch-INLA.html

So, either your model is of this specific type, or you cannot use INLA. Indeed, you will only see INLA being applied to standard classical models, such as GLMs, GAMs, GLMM, and GAMMs. These are wide families of models, but they do not cover many models of interest in modern applications.