Report how well the base coefficients are identified

The base layer (loss, heat, bias) showed values only, so a zone with weeks of
samples looked equally trustworthy whether or not the data ever varied its
inputs. Each base coefficient now reports a confidence from its own posterior
variance, as the extended and ventilation layers already did: it stays at 0
for `heat` while the relay never cycles and below 0.8 for `loss` and `bias`
while the indoor-outdoor difference is steady. Readiness is unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

custom_components/heating_mpc/coordinator.py

@@ -431,8 +431,10 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
             model = ZoneModel(self.learners[key], self.extended.get(key), self.ventilation.get(key))
             inputs = {"outside": outside, "lag": lag, "internal": internal[key], "temps": temps,
                       "ventilation": vent_inputs.get(key) or {}}
-            a, b, c = self.learners[key].theta
-            coefficients = {"base": {"loss": round(a, 6), "heat": round(b, 6), "bias": round(c, 6)}}
+            base = self.learners[key]
+            confidence = base.confidence()
+            coefficients = {"base": {name: {"value": round(value, 6), "confidence": confidence[name]}
+                                     for name, value in zip(("loss", "heat", "bias"), base.theta)}}
             for layer, learner in (("extended", model.extended), ("ventilation", model.ventilation)):
                 if learner is not None:
                     coefficients[layer] = {name: {k: info[k] for k in ("value", "std", "confidence", "identified")}
@@ -740,6 +742,8 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
                        "loss": round(model.theta[0], 6),
                        "heat": round(model.theta[1], 6),
                        "bias": round(model.theta[2], 6),
+                       # How well the data pins each coefficient down, not how many samples.
+                       "confidence": model.confidence(),
                        "samples": model.count,
                        "on_samples": model.on_count, "off_samples": model.off_count,
                        "rejected_samples": model.rejected_count,

custom_components/heating_mpc/physics.py

@@ -134,6 +134,17 @@ class Learner:
     def mae(self) -> float | None:
         return self.error_sum / self.count if self.count else None
 
+    def confidence(self) -> dict[str, float]:
+        """Per coefficient, the share of its information that comes from data (0 = prior only).
+
+        Taken from the coefficient's own uncertainty, not from the sample count: it
+        only grows while the data varies that coefficient's input independently of
+        the others. Weeks with the relay always off leave `heat` at 0; a steady
+        indoor-outdoor difference cannot separate `loss` from `bias`.
+        """
+        return {name: round(1 - min(prior, max(0.0, self.p[i][i])) / prior, 3)
+                for i, (name, prior) in enumerate(zip(("loss", "heat", "bias"), PRIOR_VARIANCE))}
+
     def as_dict(self) -> dict[str, Any]:
         return {"theta": self.theta, "p": self.p, "count": self.count, "error_sum": self.error_sum,
                 "on_count": self.on_count, "off_count": self.off_count,