Sensitivity: Minor plotting fixes (#819)

## Summary
Minor improvements in the sensitivity posterior-marginal plots

## Detailed description
- **Prior reference instead of the mean:** the continuous panels drop
the posterior-mean line and instead overlay the uniform prior as a flat
reference plus a shaded 5–95% band.
- **Shared y-axis across a vector variation's components:** share a
y-axis so their densities are directly comparable;

---------

Signed-off-by: Clemens Volk <cvolk@nvidia.com>
Co-authored-by: greptile-apps[bot] <165735046+greptile-apps[bot]@users.noreply.github.com>

Author: cvolkcvolk

isaaclab_arena/analysis/sensitivity/plotting.py

@@ -8,6 +8,7 @@
 import math
 import matplotlib.pyplot as plt
 import numpy as np
+import re
 from pathlib import Path
 from scipy.stats import gaussian_kde
 from typing import TYPE_CHECKING
@@ -19,7 +20,7 @@
 
 _CONTINUOUS_COLOR = "steelblue"
 _CATEGORICAL_COLOR = "steelblue"
-_MEAN_COLOR = "firebrick"
+_PRIOR_COLOR = "grey"
 
 
 def plot_marginals(
@@ -32,7 +33,8 @@ def plot_marginals(
 
     A pure renderer: it draws already-sampled posterior draws and does not run inference.
     One panel per factor — a density curve for continuous factors, a probability bar chart
-    for categorical ones, wrapped into a grid.
+    for categorical ones, wrapped into a grid. Panels for components of the same vector
+    variation share a y-axis, so their densities compare directly.
 
     Args:
         samples: ``(num_samples, num_factors)`` posterior draws in the dataset's factor
@@ -52,17 +54,30 @@ def plot_marginals(
     num_rows = math.ceil(len(factors) / num_columns)
     figure, axes = plt.subplots(num_rows, num_columns, figsize=(6.0 * num_columns, 4.5 * num_rows), squeeze=False)
     flat_axes = axes.flatten()
+    continuous_axes_by_variation: dict[str, list] = {}
     for axis_index, factor in enumerate(factors):
         ax = flat_axes[axis_index]
         factor_samples = samples[:, dataset.factor_columns[factor.name]].squeeze(-1)
         if factor.type == "continuous":
             _draw_continuous_marginal(ax, factor, factor_samples)
+            # Components of one vector variation (name[0], name[1], ...) share a scale.
+            variation_name = re.sub(r"\[\d+\]$", "", factor.name)
+            continuous_axes_by_variation.setdefault(variation_name, []).append(ax)
         else:
             _draw_categorical_marginal(ax, factor, factor_samples)
         ax.set_title(factor.name, fontsize=11)
     for unused_index in range(len(factors), len(flat_axes)):
         flat_axes[unused_index].axis("off")
 
+    # Give the components of a vector variation a common y-axis so their densities compare directly.
+    # A standalone scalar factor keeps its own scale, since unrelated factors can differ in magnitude.
+    for grouped_axes in continuous_axes_by_variation.values():
+        if len(grouped_axes) < 2:
+            continue
+        shared_top = max(grouped_ax.get_ylim()[1] for grouped_ax in grouped_axes)
+        for grouped_ax in grouped_axes:
+            grouped_ax.set_ylim(0, shared_top)
+
     observation_label = ", ".join(
         f"{name}={value:g}" for name, value in zip(dataset.outcome_names, observation.tolist())
     )
@@ -80,21 +95,32 @@ def plot_marginals(
 
 
 def _draw_continuous_marginal(ax, factor: FactorSpec, factor_samples: np.ndarray) -> None:
-    """Smooth posterior density (filled KDE curve) of a continuous factor, with a mean line.
+    """Posterior density of a continuous factor over its swept range.
 
-    A KDE line over the posterior samples reads the shape of a continuous posterior better
-    than a binned histogram. Falls back to a single line at the mean when the samples have
-    no spread (KDE bandwidth is then undefined).
+    Draws the KDE of the posterior samples, the uniform prior as a flat reference, and shades
+    the central 5-95% of the posterior. Reading the posterior against the prior shows whether
+    conditioning on the outcome concentrated the factor, which a mean alone would miss for a
+    factor swept symmetrically around its nominal value.
     """
     range_low, range_high = factor.range
-    sample_mean = float(np.mean(factor_samples))
+    span = range_high - range_low
+
     if float(np.std(factor_samples)) >= 1e-9:
         grid = np.linspace(range_low, range_high, 200)
         density = gaussian_kde(factor_samples)(grid)
-        ax.plot(grid, density, color=_CONTINUOUS_COLOR, linewidth=2)
+        ax.plot(grid, density, color=_CONTINUOUS_COLOR, linewidth=2, label="posterior")
         ax.fill_between(grid, 0, density, color=_CONTINUOUS_COLOR, alpha=0.2)
         ax.set_ylim(bottom=0)
-    ax.axvline(sample_mean, color=_MEAN_COLOR, linestyle="--", linewidth=2, label=f"mean = {sample_mean:.3g}")
+        low_percentile, high_percentile = np.percentile(factor_samples, [5, 95])
+        ax.axvspan(low_percentile, high_percentile, color=_CONTINUOUS_COLOR, alpha=0.15, label="5-95%")
+    else:
+        ax.axvline(float(np.mean(factor_samples)), color=_CONTINUOUS_COLOR, linewidth=2, label="constant")
+        ax.set_ylim(bottom=0)
+
+    if span > 0:
+        # The uniform prior is the "no effect" reference the posterior is read against.
+        ax.axhline(1.0 / span, color=_PRIOR_COLOR, linestyle="--", linewidth=1.5, label="prior (uniform)")
+
     ax.set_xlim(range_low, range_high)
     ax.set_xlabel(factor.name)
     ax.set_ylabel("posterior density")