feat: add fANOVA parameter importance via random forest

Implement functional ANOVA decomposition behind the `fanova` feature
flag. A self-contained random forest is trained on trial data, then
marginal predictions are used to compute per-parameter main effects
and pairwise interaction effects, normalized to sum to 1.0.

Adds Study::fanova() / fanova_with_config(), FanovaResult, and
FanovaConfig. Includes unit and integration tests covering dominant
parameters, interaction detection, consistency with correlation-based
importance, and error handling.

tests/fanova_tests.rs

@@ -0,0 +1,88 @@
+//! Integration tests for fANOVA parameter importance.
+
+#![cfg(feature = "fanova")]
+
+use optimizer::prelude::*;
+
+#[test]
+fn fanova_dominant_parameter() {
+    // f(x, y) = x^2 — x should dominate
+    let x = FloatParam::new(0.0, 10.0).name("x");
+    let y = FloatParam::new(0.0, 10.0).name("y");
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(42));
+    study
+        .optimize(50, |trial| {
+            let xv = x.suggest(trial)?;
+            let _yv = y.suggest(trial)?;
+            Ok::<_, Error>(xv * xv)
+        })
+        .unwrap();
+
+    let result = study.fanova().unwrap();
+    assert_eq!(result.main_effects[0].0, "x");
+    assert!(
+        result.main_effects[0].1 > 0.7,
+        "x importance = {}",
+        result.main_effects[0].1
+    );
+}
+
+#[test]
+fn fanova_interaction() {
+    // f(x, y) = x * y — both matter and interact
+    let x = FloatParam::new(0.0, 10.0).name("x");
+    let y = FloatParam::new(0.0, 10.0).name("y");
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(7));
+    study
+        .optimize(100, |trial| {
+            let xv = x.suggest(trial)?;
+            let yv = y.suggest(trial)?;
+            Ok::<_, Error>(xv * yv)
+        })
+        .unwrap();
+
+    let config = FanovaConfig {
+        n_trees: 128,
+        ..FanovaConfig::default()
+    };
+    let result = study.fanova_with_config(&config).unwrap();
+
+    // Should detect interaction
+    assert!(
+        !result.interactions.is_empty(),
+        "should detect x*y interaction"
+    );
+}
+
+#[test]
+fn fanova_consistent_with_correlation() {
+    // f(x, y) = 3*x + 0.5*y — x should rank higher in both methods
+    let x = FloatParam::new(0.0, 10.0).name("x");
+    let y = FloatParam::new(0.0, 10.0).name("y");
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(99));
+    study
+        .optimize(80, |trial| {
+            let xv = x.suggest(trial)?;
+            let yv = y.suggest(trial)?;
+            Ok::<_, Error>(3.0 * xv + 0.5 * yv)
+        })
+        .unwrap();
+
+    let corr = study.param_importance();
+    let fanova = study.fanova().unwrap();
+
+    // Both methods should rank x above y
+    assert_eq!(corr[0].0, "x", "correlation should rank x first");
+    assert_eq!(fanova.main_effects[0].0, "x", "fanova should rank x first");
+}
+
+#[test]
+fn fanova_too_few_trials() {
+    let study: Study<f64> = Study::new(Direction::Minimize);
+
+    let result = study.fanova();
+    assert!(result.is_err(), "should error with no trials");
+}