diff --git a/tests/unit/test_bayesian_optimizer.py b/tests/unit/test_bayesian_optimizer.py
index f6d2596544..cec30bf924 100644
--- a/tests/unit/test_bayesian_optimizer.py
+++ b/tests/unit/test_bayesian_optimizer.py
@@ -517,6 +517,10 @@ def test_bayesian_optimizer_optimize_raises_for_negative_steps(num_steps: int) -
 
 def test_bayesian_optimizer_optimize_is_noop_for_zero_steps() -> None:
     class _UnusableModel(TrainableProbabilisticModel):
+        @property
+        def event_shape(self) -> TensorType:
+            assert False
+
         def predict(self, query_points: TensorType) -> NoReturn:
             assert False
 
diff --git a/tests/util/models/gpflow/models.py b/tests/util/models/gpflow/models.py
index 650fc65f08..c7ea8bf009 100644
--- a/tests/util/models/gpflow/models.py
+++ b/tests/util/models/gpflow/models.py
@@ -91,14 +91,22 @@ def __init__(
         mean_functions: Sequence[Callable[[TensorType], TensorType]],
         kernels: Sequence[tfp.math.psd_kernels.PositiveSemidefiniteKernel],
         noise_variance: float = 1.0,
+        event_shape: Optional[TensorType] = None,
     ):
         self._mean_functions = mean_functions
         self._kernels = kernels
         self._noise_variance = noise_variance
+        self._event_shape = event_shape
 
     def __repr__(self) -> str:
         return f"GaussianProcess({self._mean_functions!r}, {self._kernels!r})"
 
+    @property
+    def event_shape(self) -> TensorType:
+        if self._event_shape is None:
+            raise NotImplementedError("event_shape not specified for this model")
+        return self._event_shape
+
     @inherit_check_shapes
     def predict(self, query_points: TensorType) -> tuple[TensorType, TensorType]:
         mean, cov = self.predict_joint(query_points[..., None, :])
@@ -198,7 +206,7 @@ def __init__(
     ):
         self.kernel = tfp.math.psd_kernels.ExponentiatedQuadratic(kernel_amplitude)
         self.mean_function = lambda x: quadratic(x - tf.cast(x_shift, dtype=x.dtype))
-        super().__init__([self.mean_function], [self.kernel], noise_variance)
+        super().__init__([self.mean_function], [self.kernel], noise_variance, tf.constant([1]))
 
     def __repr__(self) -> str:
         return "QuadraticMeanAndRBFKernel()"
diff --git a/trieste/models/gpflow/interface.py b/trieste/models/gpflow/interface.py
index 5fad89f679..83d63b8347 100644
--- a/trieste/models/gpflow/interface.py
+++ b/trieste/models/gpflow/interface.py
@@ -102,6 +102,10 @@ def update_posterior_cache(self) -> None:
     def model(self) -> GPModel:
         """The underlying GPflow model."""
 
+    @property
+    def event_shape(self) -> TensorType:
+        return tf.constant([self.model.num_latent_gps])
+
     @inherit_check_shapes
     def predict(self, query_points: TensorType) -> tuple[TensorType, TensorType]:
         mean, cov = (self._posterior or self.model).predict_f(query_points)
diff --git a/trieste/models/gpflow/models.py b/trieste/models/gpflow/models.py
index 235325e399..9b41b73da1 100644
--- a/trieste/models/gpflow/models.py
+++ b/trieste/models/gpflow/models.py
@@ -1417,6 +1417,10 @@ def __init__(
     def num_fidelities(self) -> int:
         return self._num_fidelities
 
+    @property
+    def event_shape(self) -> TensorType:
+        return self.lowest_fidelity_signal_model.event_shape
+
     @inherit_check_shapes
     def predict(self, query_points: TensorType) -> tuple[TensorType, TensorType]:
         """
diff --git a/trieste/models/gpflux/models.py b/trieste/models/gpflux/models.py
index 903a01222c..4d1b763a7c 100644
--- a/trieste/models/gpflux/models.py
+++ b/trieste/models/gpflux/models.py
@@ -287,6 +287,10 @@ def model_gpflux(self) -> DeepGP:
     def model_keras(self) -> tf.keras.Model:
         return self._model_keras
 
+    @property
+    def event_shape(self) -> TensorType:
+        raise NotImplementedError  # TODO: ???
+
     @inherit_check_shapes
     def sample(self, query_points: TensorType, num_samples: int) -> TensorType:
         trajectory = self.trajectory_sampler().get_trajectory()
diff --git a/trieste/models/interfaces.py b/trieste/models/interfaces.py
index ae265d4f85..683b444a42 100644
--- a/trieste/models/interfaces.py
+++ b/trieste/models/interfaces.py
@@ -45,6 +45,13 @@ class ProbabilisticModel(Protocol):
     https://github.com/python/typing/issues/213 is implemented.
     """
 
+    @property
+    @abstractmethod
+    def event_shape(self) -> TensorType:
+        """
+        The event shape of the model's predictive distribution.
+        """
+
     @abstractmethod
     @check_shapes(
         "query_points: [batch..., D]",
@@ -367,6 +374,11 @@ def __init__(
     # NB we don't use @inherit_shapes below as some classes break the shape API (👀 fantasizer)
     # instead we rely on the shape checking inside the submodels
 
+    @property
+    def event_shape(self) -> TensorType:
+        shapes = [model.event_shape for model in self._models]
+        return tf.concat([shapes[0][:-1], [sum(shape[-1] for shape in shapes)]], axis=0)
+
     def predict(self, query_points: TensorType) -> tuple[TensorType, TensorType]:
         r"""
         :param query_points: The points at which to make predictions, of shape [..., D].
diff --git a/trieste/models/keras/interface.py b/trieste/models/keras/interface.py
index 96b222cccd..00560aff9e 100644
--- a/trieste/models/keras/interface.py
+++ b/trieste/models/keras/interface.py
@@ -57,6 +57,10 @@ def model(self) -> tf.keras.Model:
         """The compiled Keras model."""
         raise NotImplementedError
 
+    @property
+    def event_shape(self) -> TensorType:
+        return tf.constant([self.model.output_shape[0][-1]])
+
     @property
     def optimizer(self) -> KerasOptimizer:
         """The optimizer wrapper for training the model."""