probe(nars-bayes): preserve sample size and predictive uncertainty beside CE64

crates/causal-edge/tests/palette_bayes_nars_bnn_probe.rs

@@ -0,0 +1,63 @@
+//! Bayesian predictive uncertainty is not NARS confidence by renaming.
+use causal_edge::CausalEdge64;
+
+#[derive(Clone, Copy)]
+struct Posterior {
+    successes: u32,
+    trials: u32,
+}
+
+impl Posterior {
+    fn mean(self) -> f64 {
+        (self.successes as f64 + 0.5) / (self.trials as f64 + 1.0)
+    }
+    fn variance(self) -> f64 {
+        let a = self.successes as f64 + 0.5;
+        let b = (self.trials - self.successes) as f64 + 0.5;
+        a * b / ((a + b) * (a + b) * (a + b + 1.0))
+    }
+}
+
+#[test]
+fn same_frequency_does_not_imply_same_uncertainty() {
+    let few = Posterior {
+        successes: 7,
+        trials: 10,
+    };
+    let many = Posterior {
+        successes: 700,
+        trials: 1000,
+    };
+    assert!((7.0_f64 / 10.0 - 700.0 / 1000.0).abs() < f64::EPSILON);
+    assert!(many.variance() < few.variance() / 50.0);
+    assert!((few.mean() - many.mean()).abs() < 0.02);
+}
+
+#[test]
+fn ce64_expectation_is_a_quantized_projection_not_the_count_carrier() {
+    let sample = Posterior {
+        successes: 7,
+        trials: 10,
+    };
+    let mut edge = CausalEdge64(0);
+    edge.set_frequency_u8((255.0_f64 * 7.0 / 10.0).round() as u8);
+    edge.set_confidence_u8((255.0_f64 * 10.0 / 11.0).round() as u8);
+    assert!((edge.expectation() as f64 - sample.mean()).abs() < 0.01);
+    assert!(sample.variance() > 0.0);
+    // The sample size must be carried separately; the two u8 codes
+    // cannot recover an arbitrary exact 1000-observation history.
+}
+
+#[test]
+fn polarity_and_evidence_mass_are_independent_axes() {
+    let a = Posterior {
+        successes: 1,
+        trials: 2,
+    };
+    let b = Posterior {
+        successes: 500,
+        trials: 1000,
+    };
+    assert!((a.mean() - b.mean()).abs() < 1e-12);
+    assert!(a.variance() > b.variance() * 100.0);
+}