Clean up is_fully_bayesian

Summary:
X-link: pytorch/botorch#2108

This attempts to clean up the usage of `is_fully_bayesian` and also separately treat fully Bayesian models from ensemble models.

The main changes in diff are to:
- Add an `_is_fully_bayesian` attribute to `Model`. This is `True` for fully Bayesian models that rely on Pyro/NUTS to be fitted (they need some special handling for fitting and `state_dict` loading/saving.
- Add an `_is_ensemble` attribute to `Model`. This indicates whether the model is a collection of multiple models that are stored in an additional batch dimension. This is hopefully a better classification, but I'm open to a different name here.
- Rename `FullyBayesianPosterior` to `GaussianMixturePosterior` since that is more descriptive and plays better with the other changes.

Reviewed By: esantorella

Differential Revision: D50884342

ax/models/torch/botorch.py

@@ -41,7 +41,7 @@
 from botorch.models import ModelList
 from botorch.models.model import Model
 from botorch.utils.datasets import SupervisedDataset
-from botorch.utils.transforms import is_fully_bayesian
+from botorch.utils.transforms import is_ensemble
 from torch import Tensor
 from torch.nn import ModuleList  # @manual
 
@@ -572,7 +572,7 @@ def get_feature_importances_from_botorch_model(
             )
         if ls.ndim == 2:
             ls = ls.unsqueeze(0)
-        if is_fully_bayesian(m):  # Take the median over the MCMC samples
+        if is_ensemble(m):  # Take the median over the model batch dimension
             ls = torch.quantile(ls, q=0.5, dim=0, keepdim=True)
         lengthscales.append(ls)
     lengthscales = torch.cat(lengthscales, dim=0)

ax/models/torch/utils.py

@@ -51,7 +51,7 @@
 from botorch.acquisition.utils import get_infeasible_cost
 from botorch.models import ModelListGP, SingleTaskGP
 from botorch.models.model import Model
-from botorch.posteriors.fully_bayesian import FullyBayesianPosterior
+from botorch.posteriors.fully_bayesian import GaussianMixturePosterior
 from botorch.posteriors.gpytorch import GPyTorchPosterior
 from botorch.posteriors.posterior_list import PosteriorList
 from botorch.sampling.normal import IIDNormalSampler, SobolQMCNormalSampler
@@ -627,7 +627,7 @@ def predict_from_model(model: Model, X: Tensor) -> Tuple[Tensor, Tensor]:
     with torch.no_grad():
         # TODO: Allow Posterior to (optionally) return the full covariance matrix
         posterior = model.posterior(X)
-        if isinstance(posterior, FullyBayesianPosterior):
+        if isinstance(posterior, GaussianMixturePosterior):
             mean = posterior.mixture_mean.cpu().detach()
             var = posterior.mixture_variance.cpu().detach().clamp_min(0)
         elif isinstance(posterior, (GPyTorchPosterior, PosteriorList)):