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,

tests/test_coordinator.py

@@ -785,6 +785,11 @@ class BoundaryTests(unittest.IsolatedAsyncioTestCase):
         self.assertEqual(details['model_in_use'], 'extended')
         self.assertGreater(details['contributions_c_per_h']['internal'], 0.2)
         self.assertTrue(details['coefficients']['extended']['internal']['identified'])
+        # The base layer reports how well each coefficient is pinned down too.
+        base = details['coefficients']['base']
+        self.assertEqual(set(base), {'loss', 'heat', 'bias'})
+        self.assertEqual(base['heat']['confidence'], data['models']['office']['confidence']['heat'])
+        self.assertGreater(base['heat']['confidence'], 0.8)
         # Replayed against what happened, the electrical term removes most of the base error.
         accuracy = data['forecast_accuracy'][60]
         self.assertLess(accuracy['mae'], 0.06)

tests/test_physics.py

@@ -140,6 +140,31 @@ class ModelTests(unittest.TestCase):
         self.assertEqual(restored.count, 30000)
         self.assertEqual(restored.p, learn.p)
 
+    def test_confidence_reflects_excitation_not_sample_count(self):
+        # Two weeks of samples, relay always off, a steady 15 degC difference to outside.
+        steady = m.Learner()
+        for _ in range(4000):
+            steady.learn(20.0, 20.0 + 0.003 * -15 + 0.001, 5.0, 0.0, command=False)
+        confidence = steady.confidence()
+        self.assertEqual(steady.count, 4000)
+        self.assertEqual(confidence['heat'], 0)           # never exercised
+        self.assertLess(confidence['loss'], 0.8)          # not separable from bias
+        self.assertLess(confidence['bias'], 0.8)
+        # Fewer samples, with the relay cycling and a cold and a mild spell each day.
+        varied = m.Learner()
+        t, lag = 20.0, 0.0
+        for step in range(1200):
+            heater = int(step % 96 < 35)
+            lag = lag + m.HEAT_LAG * (heater - lag)
+            outside = -2 + 14 * ((step // 144) % 2)
+            value = t + 0.003 * (outside - t) + 0.055 * lag + 0.001
+            varied.learn(t, value, outside, lag, command=bool(heater))
+            t = value
+        self.assertTrue(all(value > 0.8 for value in varied.confidence().values()), varied.confidence())
+        # Recalibration starts confidence over.
+        varied.recalibrate()
+        self.assertEqual(set(varied.confidence().values()), {0})
+
     def test_restore_tolerates_round_off_and_bounds_wound_up_covariance(self):
         # Shape of a v0.2.1 model after a summer: huge heat variance, tiny asymmetry.
         data = m.Learner(count=40000, off_count=40000).as_dict()