antecedent_model/

do_sampler.rs

//! Do-samplers: weighting, KDE, and MCMC.
//!
//! SPDX-License-Identifier: MIT OR Apache-2.0

#![allow(
    clippy::cast_possible_truncation,
    clippy::cast_precision_loss,
    clippy::cast_sign_loss,
    clippy::many_single_char_names,
    clippy::needless_range_loop,
    clippy::too_many_arguments
)]

use std::sync::Arc;

use antecedent_core::{CausalRng, ExecutionContext, Intervention, VariableId};
use antecedent_data::{TableView, TabularData};
use antecedent_kernels::standard_normal;

use crate::batch::{MechanismWorkspace, ParentBatch};
use crate::compile::CompiledCausalModel;
use crate::error::ModelError;
use crate::mechanism::log_prob_column;
use crate::sample::sample_interventional;

/// Result of a do-sampler run.
#[derive(Clone, Debug)]
pub struct DoSampleResult {
    /// Sampled (or reweighted observational) outcomes for the target variable.
    pub values: Arc<[f64]>,
    /// Optional importance weights (weighting sampler); empty if not used.
    pub weights: Arc<[f64]>,
    /// Sampler id.
    pub method: Arc<str>,
    /// Diagnostics notes.
    pub notes: Vec<Arc<str>>,
    /// MCMC accept rate when applicable.
    pub accept_rate: Option<f64>,
    /// Gaussian KDE bandwidth when the result carries a density estimate.
    pub bandwidth: Option<f64>,
    /// Effective sample size of the (normalized) importance weights, `1 / Σwᵢ²`.
    ///
    /// Populated for the confounded / kernel-weighted branch of [`WeightingDoSampler`],
    /// where post-normalization concentration is otherwise invisible to the caller (the
    /// per-unit `1e6` cap only bounds pre-normalization weights, not how much of the
    /// normalized mass ends up on a handful of units). `None` for branches where every
    /// contributing unit already carries equal weight (root-treatment exact match, KDE
    /// draws) and an ESS would be redundant with `n`.
    pub ess: Option<f64>,
}

/// Weighting do-sampler for hard `do(T=t)`.
///
/// - **Root treatment:** empirical outcomes among units with `T ≈ t`.
/// - **Confounded continuous treatment:** Horvitz–Thompson (1952) with a **shrinking** Gaussian
///   kernel on the treatment margin (Silverman 1986 bandwidth) over the fitted conditional
///   density `f(T∣parents)`: `wᵢ ∝ Kₕ(Tᵢ − t) / f(Tᵢ∣parents)`. Hard interventions have a
///   Dirac interventional law, so the kernel is the localization numerator (there is no
///   separate `lp_do` term).
/// - **Non-density / discrete mechanisms:** kernel localization alone (exact match when the
///   bandwidth collapses on tied support).
#[derive(Clone, Debug)]
pub struct WeightingDoSampler {
    /// Treatment variable.
    pub treatment: VariableId,
    /// Outcome variable.
    pub outcome: VariableId,
}

impl WeightingDoSampler {
    /// Construct.
    #[must_use]
    pub fn new(treatment: VariableId, outcome: VariableId) -> Self {
        Self { treatment, outcome }
    }

    /// Estimate E[Y | do(T=t)] via matching / Horvitz–Thompson (1952) on fitted model densities.
    ///
    /// # Errors
    ///
    /// Missing columns or unfitted treatment mechanism.
    pub fn estimate(
        &self,
        model: &CompiledCausalModel,
        data: &TabularData,
        treatment_value: f64,
        _ctx: &ExecutionContext,
    ) -> Result<DoSampleResult, ModelError> {
        let t_dense = model
            .dense_of(self.treatment)
            .ok_or_else(|| ModelError::Shape { message: "treatment not in model".into() })?;
        let y = data.float64_cow(self.outcome).map_err(ModelError::from)?;
        let t = data.float64_cow(self.treatment).map_err(ModelError::from)?;
        let n = y.len();
        let gather = model
            .gather_for(t_dense)
            .ok_or_else(|| ModelError::Shape { message: "missing gather for treatment".into() })?;

        let mut weights = vec![0.0; n];
        let mut values = Vec::with_capacity(n);
        let mut notes = Vec::new();

        if gather.n_parents() == 0 {
            // Root treatment: empirical outcomes among units with T ≈ t.
            let mut selected = 0usize;
            for i in 0..n {
                if (t[i] - treatment_value).abs() < 1e-9 {
                    values.push(y[i]);
                    weights[selected] = 1.0;
                    selected += 1;
                }
            }
            weights.truncate(selected);
            if selected == 0 {
                return Err(ModelError::Numerical {
                    message: "weighting sampler: no observational units match do-value".into(),
                });
            }
            notes.push(Arc::from("root treatment: exact match reweighting"));
            return Ok(DoSampleResult {
                values: Arc::from(values),
                weights: Arc::from(weights),
                method: Arc::from("do_weighting"),
                notes,
                accept_rate: None,
                bandwidth: None,
                ess: None,
            });
        }

        // Confounded: IPW using Gaussian propensity from fitted treatment mechanism.
        let slot = model.mechanisms.get(t_dense);
        let mut parent_cols = Vec::new();
        for &p in gather.parents.iter() {
            let var = model.output_layout.variables[p.as_usize()];
            parent_cols.push(data.float64_cow(var).map_err(ModelError::from)?);
        }
        let n_par = gather.n_parents();
        let mut parent_mat = vec![0.0; n * n_par];
        for (pi, col) in parent_cols.iter().enumerate() {
            for r in 0..n {
                parent_mat[pi * n + r] = col[r];
            }
        }
        let parents = ParentBatch { n_rows: n, n_parents: n_par, values: &parent_mat };
        let mut lp_obs = vec![0.0; n];
        let has_density = log_prob_column(slot, &t, parents, &mut lp_obs).is_ok();
        let bw = silverman_bandwidth(&t).max(1e-8);
        let inv_norm = 1.0 / (bw * (2.0 * std::f64::consts::PI).sqrt());
        for i in 0..n {
            let z = (t[i] - treatment_value) / bw;
            let kernel = inv_norm * (-0.5 * z * z).exp();
            let w = if has_density && lp_obs[i].is_finite() {
                let dens = lp_obs[i].exp().max(1e-300);
                (kernel / dens).min(1e6)
            } else {
                kernel
            };
            weights[i] = w;
            values.push(y[i]);
        }
        let wsum: f64 = weights.iter().sum();
        if wsum.partial_cmp(&0.0) != Some(std::cmp::Ordering::Greater) {
            return Err(ModelError::Numerical {
                message: "weighting sampler: zero weight mass".into(),
            });
        }
        for w in &mut weights {
            *w /= wsum;
        }
        // ESS of the normalized weights, `1 / Σwᵢ²` (Kish 1965), same convention as
        // `antecedent-state::particle_filter::ParticleFilter::ess`. The per-unit `1e6` cap
        // above only bounds each weight *before* normalization; it does nothing to stop the
        // normalized mass from concentrating on one or two units when `treatment_value` sits
        // in the tail of the observed support (global Silverman bandwidth, not locally
        // adaptive). We surface that concentration here rather than staying silent about it,
        // because a caller reading only `weighted_mean` has no other way to tell a
        // well-supported estimate from one that is effectively a single observation.
        let sum_sq: f64 = weights.iter().map(|w| w * w).sum();
        let ess = if sum_sq > 0.0 { 1.0 / sum_sq } else { 0.0 };
        // Flag degeneracy as a note instead of a hard error: this is a diagnostic, not a
        // correctness failure, and different callers have different tolerance for a low-ESS
        // estimate (e.g. exploratory analysis vs. a gated production report). A note keeps
        // `estimate()` infallible for callers that already handle low support, while still
        // making the condition impossible to miss for anyone inspecting `notes`/`ess`.
        let min_ess_floor = (n as f64 * 0.05).max(2.0);
        if ess < min_ess_floor {
            notes.push(Arc::from(format!(
                "degenerate weighting: ess={ess:.3} of n={n} (< floor {min_ess_floor:.3}); \
                 estimate is dominated by a handful of units"
            )));
        }
        notes.push(Arc::from(format!("IPW / Silverman-kernel weighting (bandwidth={bw:.6})")));
        Ok(DoSampleResult {
            values: Arc::from(values),
            weights: Arc::from(weights),
            method: Arc::from("do_weighting"),
            notes,
            accept_rate: None,
            bandwidth: Some(bw),
            ess: Some(ess),
        })
    }

    /// Weighted mean of the sampler result.
    #[must_use]
    pub fn weighted_mean(result: &DoSampleResult) -> f64 {
        if result.values.is_empty() {
            return f64::NAN;
        }
        if result.weights.is_empty() {
            return result.values.iter().sum::<f64>() / result.values.len() as f64;
        }
        let wsum: f64 = result.weights.iter().sum();
        if wsum.partial_cmp(&0.0) != Some(std::cmp::Ordering::Greater) {
            return f64::NAN;
        }
        result.values.iter().zip(result.weights.iter()).map(|(v, w)| v * w).sum::<f64>() / wsum
    }
}

/// KDE do-sampler: sample from interventional SCM then smooth the outcome with a Gaussian KDE.
#[derive(Clone, Debug)]
pub struct KdeDoSampler {
    /// Outcome variable.
    pub outcome: VariableId,
    /// Bandwidth (Silverman's (1986) rule if None).
    pub bandwidth: Option<f64>,
}

impl KdeDoSampler {
    /// Construct.
    #[must_use]
    pub fn new(outcome: VariableId) -> Self {
        Self { outcome, bandwidth: None }
    }

    /// Draw interventional samples and return KDE-ready values (+ bandwidth note).
    ///
    /// # Errors
    ///
    /// Sampling failures.
    pub fn sample(
        &self,
        model: &CompiledCausalModel,
        interventions: &[Intervention],
        n_draws: usize,
        rng: &mut CausalRng,
        ws: &mut MechanismWorkspace,
        ctx: &ExecutionContext,
    ) -> Result<DoSampleResult, ModelError> {
        let batch = sample_interventional(model, interventions, n_draws, rng, ws, ctx)?;
        let dense = model
            .dense_of(self.outcome)
            .ok_or_else(|| ModelError::Shape { message: "outcome not in model".into() })?;
        let col = batch.column(dense.as_usize())?;
        let bw = self.bandwidth.unwrap_or_else(|| silverman_bandwidth(col));
        Ok(DoSampleResult {
            values: Arc::from(col.to_vec()),
            weights: Arc::from(vec![1.0 / n_draws as f64; n_draws]),
            method: Arc::from("do_kde"),
            notes: Vec::new(),
            accept_rate: None,
            bandwidth: Some(bw),
            ess: None,
        })
    }

    /// Evaluate KDE density at `x` given sampler values.
    #[must_use]
    pub fn density(result: &DoSampleResult, x: f64) -> f64 {
        let bw = result.bandwidth.unwrap_or(1.0).max(1e-8);
        let n = result.values.len() as f64;
        let inv = 1.0 / (bw * (2.0 * std::f64::consts::PI).sqrt());
        let mut dens = 0.0;
        for &v in result.values.iter() {
            let z = (x - v) / bw;
            dens += inv * (-0.5 * z * z).exp();
        }
        dens / n.max(1.0)
    }
}

fn silverman_bandwidth(x: &[f64]) -> f64 {
    let n = x.len() as f64;
    if n < 2.0 {
        return 1.0;
    }
    let mean = x.iter().sum::<f64>() / n;
    let var = x.iter().map(|v| (v - mean).powi(2)).sum::<f64>() / (n - 1.0);
    let sd = var.sqrt().max(1e-8);
    1.06 * sd * n.powf(-0.2)
}

/// Random-walk Metropolis–Hastings on the **outcome margin**.
///
/// The chain targets a Silverman (1986) Gaussian KDE fitted to a pilot batch of interventional
/// ancestral draws — a smoothed proxy of the interventional law of `outcome`, not the
/// joint mechanism density. Proposals are Gaussian random walks (`proposal_sd`); this is
/// **not** independent MH, and is exact for the interventional law only in the large-pilot
/// / vanishing-bandwidth limit of that KDE proxy.
#[derive(Clone, Debug)]
pub struct McmcDoSampler {
    /// Outcome variable to record.
    pub outcome: VariableId,
    /// Proposal standard deviation.
    pub proposal_sd: f64,
    /// Burn-in iterations.
    pub burn_in: usize,
    /// Thinning.
    pub thin: usize,
}

impl Default for McmcDoSampler {
    fn default() -> Self {
        Self { outcome: VariableId::from_raw(0), proposal_sd: 0.5, burn_in: 100, thin: 2 }
    }
}

impl McmcDoSampler {
    /// Construct targeting `outcome`.
    #[must_use]
    pub fn new(outcome: VariableId) -> Self {
        Self { outcome, ..Self::default() }
    }

    /// Run random-walk MH against a KDE of interventional pilot draws (see type docs).
    ///
    /// # Errors
    ///
    /// Sampling / density failures.
    pub fn sample(
        &self,
        model: &CompiledCausalModel,
        interventions: &[Intervention],
        n_samples: usize,
        rng: &mut CausalRng,
        ws: &mut MechanismWorkspace,
        ctx: &ExecutionContext,
    ) -> Result<DoSampleResult, ModelError> {
        let pilot = sample_interventional(model, interventions, n_samples.max(64), rng, ws, ctx)?;
        let dense = model
            .dense_of(self.outcome)
            .ok_or_else(|| ModelError::Shape { message: "outcome not in model".into() })?;
        let pilot_col = pilot.column(dense.as_usize())?;
        let pilot_bw = silverman_bandwidth(pilot_col);
        let kde = DoSampleResult {
            values: Arc::from(pilot_col.to_vec()),
            weights: Arc::from([]),
            method: Arc::from("pilot"),
            notes: Vec::new(),
            accept_rate: None,
            bandwidth: Some(pilot_bw),
            ess: None,
        };

        let mut current = pilot_col[0];
        let mut accepted = 0usize;
        let mut total = 0usize;
        let mut out = Vec::with_capacity(n_samples);
        let iters = self.burn_in + n_samples * self.thin.max(1);
        // Degenerate pilot (near-zero bandwidth) → independent draws from the pilot
        // empirical measure (random-walk MH cannot move).
        let degenerate =
            pilot_bw < 1e-6 || pilot_col.iter().all(|&v| (v - pilot_col[0]).abs() < 1e-12);

        // `current` changes only on accept, so its density is carried across
        // iterations instead of re-summing the O(pilot) KDE twice per step —
        // an exact 2× on the dominant cost of the chain.
        let mut p_cur =
            if degenerate { f64::NAN } else { KdeDoSampler::density(&kde, current).max(1e-300) };
        for i in 0..iters {
            if degenerate {
                let idx = (rng.next_f64() * pilot_col.len() as f64).floor() as usize
                    % pilot_col.len().max(1);
                current = pilot_col[idx];
                accepted += 1;
                total += 1;
            } else {
                let z = standard_normal(rng);
                let prop = current + self.proposal_sd * z;
                let p_prop = KdeDoSampler::density(&kde, prop).max(1e-300);
                let accept = (p_prop / p_cur).min(1.0);
                total += 1;
                if rng.next_f64() < accept {
                    current = prop;
                    p_cur = p_prop;
                    accepted += 1;
                }
            }
            if i >= self.burn_in && (i - self.burn_in) % self.thin.max(1) == 0 {
                out.push(current);
                if out.len() == n_samples {
                    break;
                }
            }
        }
        let rate = accepted as f64 / total.max(1) as f64;
        Ok(DoSampleResult {
            values: Arc::from(out),
            weights: Arc::from([]),
            method: Arc::from("do_mcmc"),
            notes: vec![Arc::from(format!("mh_accept_rate={rate}"))],
            accept_rate: Some(rate),
            bandwidth: kde.bandwidth,
            ess: None,
        })
    }
}

/// Convenience: interventional mean of a variable from ancestral sampling.
///
/// # Errors
///
/// Sampling failures.
pub fn interventional_mean(
    model: &CompiledCausalModel,
    interventions: &[Intervention],
    outcome: VariableId,
    n_draws: usize,
    rng: &mut CausalRng,
    ws: &mut MechanismWorkspace,
    ctx: &ExecutionContext,
) -> Result<f64, ModelError> {
    let batch = sample_interventional(model, interventions, n_draws, rng, ws, ctx)?;
    let dense = model
        .dense_of(outcome)
        .ok_or_else(|| ModelError::Shape { message: "outcome not in model".into() })?;
    let col = batch.column(dense.as_usize())?;
    Ok(col.iter().sum::<f64>() / col.len().max(1) as f64)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::registry::{MechanismRegistry, SelectionPolicy};
    use antecedent_core::{
        CausalSchemaBuilder, MeasurementSpec, RoleHint, SmallRoleSet, Value, ValueType,
    };
    use antecedent_data::column::{Float64Column, ValidityBitmap};
    use antecedent_data::{OwnedColumn, OwnedColumnarStorage};
    use antecedent_graph::{Dag, DenseNodeId};

    fn binary_treatment_scm() -> (CompiledCausalModel, TabularData) {
        let n = 80usize;
        let mut b = CausalSchemaBuilder::new();
        b.add_variable(
            "t",
            ValueType::Continuous,
            SmallRoleSet::from_hint(RoleHint::TreatmentCandidate),
            None,
            None,
            MeasurementSpec::default(),
        )
        .unwrap();
        b.add_variable(
            "y",
            ValueType::Continuous,
            SmallRoleSet::from_hint(RoleHint::OutcomeCandidate),
            None,
            None,
            MeasurementSpec::default(),
        )
        .unwrap();
        let schema = b.build().unwrap();
        let mut t = vec![0.0; n];
        let mut y = vec![0.0; n];
        for i in 0..n {
            t[i] = if i % 2 == 0 { 1.0 } else { 0.0 };
            y[i] = 2.0 * t[i];
        }
        let validity = ValidityBitmap::all_valid(n);
        let cols = vec![
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(0), Arc::from(t), validity.clone())
                    .unwrap(),
            ),
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(1), Arc::from(y), validity).unwrap(),
            ),
        ];
        let data =
            TabularData::new(OwnedColumnarStorage::try_new(schema, cols, None, None).unwrap());
        let mut g = Dag::with_variables(2);
        g.insert_directed(DenseNodeId::from_raw(0), DenseNodeId::from_raw(1)).unwrap();
        let compiled = CompiledCausalModel::compile(g).unwrap();
        let (store, _) = MechanismRegistry::standard()
            .assign_and_fit(&compiled, &data, SelectionPolicy::BestScore)
            .unwrap();
        (compiled.with_mechanisms(store), data)
    }

    #[test]
    fn weighting_recovers_treated_mean() {
        let (model, data) = binary_treatment_scm();
        let ctx = ExecutionContext::for_tests(1);
        let sampler = WeightingDoSampler::new(VariableId::from_raw(0), VariableId::from_raw(1));
        let res = sampler.estimate(&model, &data, 1.0, &ctx).unwrap();
        let mean = WeightingDoSampler::weighted_mean(&res);
        assert!((mean - 2.0).abs() < 1e-9, "mean={mean}");
    }

    /// `z -> t -> y`, `z -> y`: `t` is a confounded continuous treatment with a fitted
    /// conditional density `f(t | z)`, so `WeightingDoSampler::estimate` takes the
    /// Horvitz-Thompson / kernel branch (`gather.n_parents() > 0`).
    fn confounded_continuous_scm(n: usize) -> (CompiledCausalModel, TabularData) {
        let mut b = CausalSchemaBuilder::new();
        for name in ["z", "t", "y"] {
            b.add_variable(
                name,
                ValueType::Continuous,
                SmallRoleSet::from_hint(RoleHint::OutcomeCandidate),
                None,
                None,
                MeasurementSpec::default(),
            )
            .unwrap();
        }
        let schema = b.build().unwrap();
        let mut z = vec![0.0; n];
        let mut t = vec![0.0; n];
        let mut y = vec![0.0; n];
        for i in 0..n {
            // Confounder spread evenly over roughly [-5, 5]; t is z plus small residual noise
            // (keeps the fitted conditional density non-degenerate); y depends on both.
            z[i] = (i as f64 - (n as f64) / 2.0) * (10.0 / n as f64);
            t[i] = z[i] + 0.1 * (i as f64 * 0.7).sin();
            y[i] = t[i] + 0.5 * z[i] + 0.05 * (i as f64 * 0.3).cos();
        }
        let validity = ValidityBitmap::all_valid(n);
        let cols = vec![
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(0), Arc::from(z), validity.clone())
                    .unwrap(),
            ),
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(1), Arc::from(t), validity.clone())
                    .unwrap(),
            ),
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(2), Arc::from(y), validity).unwrap(),
            ),
        ];
        let data =
            TabularData::new(OwnedColumnarStorage::try_new(schema, cols, None, None).unwrap());
        let mut g = Dag::with_variables(3);
        g.insert_directed(DenseNodeId::from_raw(0), DenseNodeId::from_raw(1)).unwrap();
        g.insert_directed(DenseNodeId::from_raw(0), DenseNodeId::from_raw(2)).unwrap();
        g.insert_directed(DenseNodeId::from_raw(1), DenseNodeId::from_raw(2)).unwrap();
        let compiled = CompiledCausalModel::compile(g).unwrap();
        let (store, _) = MechanismRegistry::standard()
            .assign_and_fit(&compiled, &data, SelectionPolicy::BestScore)
            .unwrap();
        (compiled.with_mechanisms(store), data)
    }

    /// Regression test for the confounded-continuous-treatment ESS gap: the weighting
    /// sampler must report a small effective sample size when `treatment_value` sits far
    /// into the tail of the observed treatment support (the global Silverman bandwidth
    /// makes the kernel tiny everywhere but relatively largest for the one or two nearest
    /// `T_i`, so the self-normalized weights concentrate almost entirely on them), and a
    /// healthy ESS close to `n` when `treatment_value` is well inside the support.
    #[test]
    fn weighting_ess_flags_tail_degeneracy() {
        let n = 200usize;
        let (model, data) = confounded_continuous_scm(n);
        let ctx = ExecutionContext::for_tests(1);
        let sampler = WeightingDoSampler::new(VariableId::from_raw(1), VariableId::from_raw(2));

        // Well-supported: treatment_value near the center of the observed t range.
        let healthy = sampler.estimate(&model, &data, 0.0, &ctx).unwrap();
        let healthy_ess = healthy.ess.expect("weighted branch must report ess");

        // Tail: treatment_value far beyond the observed t range (~[-5, 5]), but not so far
        // that every kernel weight underflows to zero (which would instead trip the
        // "zero weight mass" error path, not the degeneracy path this test targets).
        let degenerate = sampler.estimate(&model, &data, 20.0, &ctx).unwrap();
        let degenerate_ess = degenerate.ess.expect("weighted branch must report ess");

        assert!(
            healthy_ess > 0.2 * n as f64,
            "expected healthy ess to be a healthy fraction of n={n}, got {healthy_ess}"
        );
        assert!(
            degenerate_ess < 0.05 * n as f64,
            "expected degenerate ess << n={n}, got {degenerate_ess}"
        );
        assert!(
            degenerate_ess < healthy_ess,
            "degenerate ess ({degenerate_ess}) should be far below healthy ess ({healthy_ess})"
        );
        assert!(
            degenerate.notes.iter().any(|n| n.contains("degenerate weighting")),
            "expected a degeneracy note, got {:?}",
            degenerate.notes
        );
        assert!(
            !healthy.notes.iter().any(|n| n.contains("degenerate weighting")),
            "healthy case should not be flagged as degenerate, got {:?}",
            healthy.notes
        );
    }

    #[test]
    fn kde_and_mcmc_run() {
        let n = 40;
        let mut b = CausalSchemaBuilder::new();
        b.add_variable(
            "t",
            ValueType::Continuous,
            SmallRoleSet::from_hint(RoleHint::TreatmentCandidate),
            None,
            None,
            MeasurementSpec::default(),
        )
        .unwrap();
        b.add_variable(
            "y",
            ValueType::Continuous,
            SmallRoleSet::from_hint(RoleHint::OutcomeCandidate),
            None,
            None,
            MeasurementSpec::default(),
        )
        .unwrap();
        let schema = b.build().unwrap();
        let mut t = vec![0.0; n];
        let mut y = vec![0.0; n];
        for i in 0..n {
            t[i] = if i % 2 == 0 { 1.0 } else { 0.0 };
            // Continuous noise keeps Y off the discrete auto-path and gives KDE spread for MH.
            y[i] = 2.0 * t[i] + 0.05 * ((i as f64) - 20.0);
        }
        let validity = ValidityBitmap::all_valid(n);
        let cols = vec![
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(0), Arc::from(t), validity.clone())
                    .unwrap(),
            ),
            OwnedColumn::Float64(
                Float64Column::new(VariableId::from_raw(1), Arc::from(y), validity).unwrap(),
            ),
        ];
        let data =
            TabularData::new(OwnedColumnarStorage::try_new(schema, cols, None, None).unwrap());
        let mut g = Dag::with_variables(2);
        g.insert_directed(DenseNodeId::from_raw(0), DenseNodeId::from_raw(1)).unwrap();
        let compiled = CompiledCausalModel::compile(g).unwrap();
        let (store, _) = MechanismRegistry::standard()
            .assign_and_fit(&compiled, &data, SelectionPolicy::BestScore)
            .unwrap();
        let model = compiled.with_mechanisms(store);

        let ctx = ExecutionContext::for_tests(1);
        let mut rng = CausalRng::from_seed(3);
        let mut ws = MechanismWorkspace::default();
        let iv = [Intervention::set(VariableId::from_raw(0), Value::f64(1.0))];
        let kde = KdeDoSampler::new(VariableId::from_raw(1))
            .sample(&model, &iv, 40, &mut rng, &mut ws, &ctx)
            .unwrap();
        assert_eq!(kde.values.len(), 40);
        let mcmc = McmcDoSampler::new(VariableId::from_raw(1))
            .sample(&model, &iv, 30, &mut rng, &mut ws, &ctx)
            .unwrap();
        assert_eq!(mcmc.values.len(), 30);
        assert!(mcmc.accept_rate.unwrap() > 0.0);
    }
}