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pymc_extras/inference/INLA/inla.py

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@@ -18,16 +18,16 @@ def fit_INLA(
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r"""
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Performs inference over a linear mixed model using Integrated Nested Laplace Approximations (INLA). Assumes a model of the form:
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\begin{equation}
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\theta \rightarrow x \rightarrow y
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\end{equation}
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.. math::
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Where the prior on the hyperparameters $\pi(\theta)$ is arbitrary, the prior on the latent field is Gaussian (and in precision form): $\pi(x) = N(\mu, Q^{-1})$ and the latent field is linked to the observables $y$ through some linear map.
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\theta \rightarrow x \rightarrow y
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Where the prior on the hyperparameters :math:`\pi(\theta)` is arbitrary, the prior on the latent field is Gaussian (and in precision form): :math:`\pi(x) = N(\mu, Q^{-1})` and the latent field is linked to the observables $y$ through some linear map.
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As it stands, INLA in PyMC Extras has three main limitations:
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- Does not support inference over the latent field, only the hyperparameters.
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- Optimisation for $\mu^*$ is bottlenecked by calling `minimize`, and to a lesser extent, computing the hessian $f^"(x)$.
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- Optimisation for :math:`\mu^*` is bottlenecked by calling `minimize`, and to a lesser extent, computing the hessian :math:`f^"(x)`.
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- Does not offer sparse support which can provide significant speedups.
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Parameters

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