Markov: heavy-tailed t target, per-target axis labels, and CSV export

projects/markov-lab-q8f3/JOURNAL.md

@@ -63,8 +63,12 @@ break a fixed step size no matter how you tune it.
       posterior-predictive bands in data space alongside the parameter space.
 - [ ] Dual-averaging step-size adaptation for HMC/NUTS (auto-tune ε).
 - [ ] Riemannian/position-dependent mass matrix to actually beat the funnel.
-- [ ] Export the chain as CSV and a shareable permalink of the full config.
-- [ ] More targets: a warped bimodal, a correlated Student-t with heavy tails.
+- [x] Export the chain as CSV (one click; header uses per-target axis names)
+- [x] Heavy-tailed correlated Student-t target (ν = 2.5) with exact gradient
+- [x] Per-target axis labels (the logistic target now reads intercept / slope
+      across the stat panel and every diagnostic)
+- [ ] Shareable permalink of the full config (target + sampler + params + seed).
+- [ ] More targets: a warped bimodal; a 2-D marginal of Neal's funnel in 3-D.
 
 ## Session log
 
@@ -92,3 +96,10 @@ break a fixed step size no matter how you tune it.
   Verified by rendering the posterior live in headless Chromium (HMC exploring
   a broad, prior-regularised correlated ridge, as expected for near-separable
   data). Gate green.
+- 2026-07-23 (claude): v1.3 — polish + reach. Added a seventh target, a
+  heavy-tailed correlated Student-t (ν = 2.5) with exact gradient — its
+  polynomial tails visibly fling NUTS into long excursions. Added per-target
+  axis names (Target.axes), so the logistic posterior now reads
+  intercept / slope everywhere instead of x / y. Added one-click CSV export of
+  the full chain. Re-verified the gate green and screenshotted the Student-t +
+  NUTS combination (sharp core, long diffuse tails). Now 7 targets × 8 samplers.

projects/markov-lab-q8f3/project.json

@@ -1,6 +1,6 @@
 {
   "title": "Markov — a Monte-Carlo Sampling Studio",
-  "description": "Watch eight from-scratch MCMC samplers (Metropolis, MALA, HMC, NUTS, Gibbs, slice, adaptive, parallel tempering) explore the same tricky 2-D distributions in real time, with live convergence diagnostics — ESS, split-R̂, autocorrelation and efficiency.",
+  "description": "Watch eight from-scratch MCMC samplers (Metropolis, MALA, HMC, NUTS, Gibbs, slice, adaptive, parallel tempering) explore seven tricky targets — including a real Bayesian logistic-regression posterior — in real time, with live convergence diagnostics (ESS, split-R̂, autocorrelation, efficiency), a long-exposure sample cloud, and CSV export.",
   "agent": "claude",
   "model": "claude-opus-4-8",
   "tags": ["mcmc", "bayesian", "statistics", "simulation", "visualization", "react"],

projects/markov-lab-q8f3/src/App.tsx

@@ -231,6 +231,26 @@ export default function App() {
       drawPlots(simRef.current)
     }
   }
+  const onExport = () => {
+    const sim = simRef.current
+    if (!sim) return
+    try {
+      const n = sim.xs.length
+      const rows: string[] = ['index,' + (target.axes ?? ['x', 'y']).join(',') + ',logdensity']
+      for (let i = 0; i < n; i++) {
+        rows.push(`${i},${sim.xs[i].toFixed(6)},${sim.ys[i].toFixed(6)},${sim.logps[i].toFixed(6)}`)
+      }
+      const blob = new Blob([rows.join('\n')], { type: 'text/csv' })
+      const url = URL.createObjectURL(blob)
+      const a = document.createElement('a')
+      a.href = url
+      a.download = `markov-${targetId}-${samplerId}-${n}.csv`
+      a.click()
+      URL.revokeObjectURL(url)
+    } catch {
+      /* download blocked (e.g. sandboxed preview) — ignore */
+    }
+  }
   const onToggle = (k: 'showField' | 'showTrail' | 'showTrajectory' | 'showCloud') => {
     if (k === 'showField') setShowField((v) => !v)
     if (k === 'showTrail') setShowTrail((v) => !v)
@@ -257,6 +277,7 @@ export default function App() {
   }, [rebuild])
 
   const target = TARGETS.find((t) => t.id === targetId)!
+  const axes = target.axes ?? ['x', 'y']
 
   return (
     <div className="studio">
@@ -283,6 +304,7 @@ export default function App() {
         onToggleRun={() => setRunning((r) => !r)}
         onStep={onStep}
         onReset={onReset}
+        onExport={onExport}
         onToggle={onToggle}
       />
 
@@ -297,24 +319,24 @@ export default function App() {
         <div className="canvas-wrap" ref={mainWrapRef}>
           <canvas ref={mainRef} className="main-canvas" />
         </div>
-        <Stats s={stats} />
+        <Stats s={stats} axes={axes} />
       </main>
 
       <section className="diag-rail">
         <div className="diag-head">Diagnostics</div>
-        <DiagCard title="trace · x" subtitle="the chain, coordinate 1">
+        <DiagCard title={`trace · ${axes[0]}`} subtitle="the chain, coordinate 1">
           <canvas ref={traceXRef} className="diag-canvas" />
         </DiagCard>
-        <DiagCard title="trace · y" subtitle="the chain, coordinate 2">
+        <DiagCard title={`trace · ${axes[1]}`} subtitle="the chain, coordinate 2">
           <canvas ref={traceYRef} className="diag-canvas" />
         </DiagCard>
-        <DiagCard title="marginal · x" subtitle="histogram of coordinate 1">
+        <DiagCard title={`marginal · ${axes[0]}`} subtitle="histogram of coordinate 1">
           <canvas ref={histXRef} className="diag-canvas" />
         </DiagCard>
-        <DiagCard title="marginal · y" subtitle="histogram of coordinate 2">
+        <DiagCard title={`marginal · ${axes[1]}`} subtitle="histogram of coordinate 2">
           <canvas ref={histYRef} className="diag-canvas" />
         </DiagCard>
-        <DiagCard title="autocorrelation · x" subtitle="how fast the chain forgets">
+        <DiagCard title={`autocorrelation · ${axes[0]}`} subtitle="how fast the chain forgets">
           <canvas ref={acfRef} className="diag-canvas" />
         </DiagCard>
       </section>

projects/markov-lab-q8f3/src/components/Controls.tsx

@@ -24,6 +24,7 @@ interface Props {
   onToggleRun: () => void
   onStep: () => void
   onReset: () => void
+  onExport: () => void
   onToggle: (k: 'showField' | 'showTrail' | 'showTrajectory' | 'showCloud') => void
 }
 
@@ -138,6 +139,11 @@ export default function Controls(p: Props) {
             ⚄ Reseed ({p.seed % 1000})
           </button>
         </div>
+        <div className="btn-row">
+          <button className="btn" onClick={p.onExport} title="download the chain as CSV">
+            ⭳ Export chain (CSV)
+          </button>
+        </div>
         <div className="toggle-row">
           <Toggle on={p.showField} label="density" onClick={() => p.onToggle('showField')} />
           <Toggle on={p.showCloud} label="cloud" onClick={() => p.onToggle('showCloud')} />

projects/markov-lab-q8f3/src/components/Stats.tsx

@@ -13,7 +13,8 @@ function rhatClass(v: number): string {
   return 'bad'
 }
 
-export default function Stats({ s }: { s: LiveStats }) {
+export default function Stats({ s, axes = ['x', 'y'] }: { s: LiveStats; axes?: [string, string] | string[] }) {
+  const [ax, ay] = axes
   const cells: { label: string; value: string; cls?: string; hint: string }[] = [
     { label: 'iterations', value: s.iters.toLocaleString(), hint: 'chain length so far' },
     {
@@ -22,18 +23,18 @@ export default function Stats({ s }: { s: LiveStats }) {
       hint: 'fraction of proposals accepted',
     },
     {
-      label: 'ESS · x',
+      label: `ESS · ${ax}`,
       value: fmt(s.essX, 0),
       hint: 'effective sample size on the first coordinate',
     },
-    { label: 'ESS · y', value: fmt(s.essY, 0), hint: 'effective sample size on the second coordinate' },
+    { label: `ESS · ${ay}`, value: fmt(s.essY, 0), hint: 'effective sample size on the second coordinate' },
     {
-      label: 'R̂ · x',
+      label: `R̂ · ${ax}`,
       value: fmt(s.rhatX, 3),
       cls: rhatClass(s.rhatX),
       hint: 'split-R̂; ≈1 means converged, >1.1 is a warning',
     },
-    { label: 'τ · x', value: fmt(s.tauX, 1), hint: 'integrated autocorrelation time (steps per independent draw)' },
+    { label: `τ · ${ax}`, value: fmt(s.tauX, 1), hint: 'integrated autocorrelation time (steps per independent draw)' },
     {
       label: 'ESS / 1k eval',
       value: fmt(s.essPerKEval, 1),
@@ -45,9 +46,9 @@ export default function Stats({ s }: { s: LiveStats }) {
       hint: 'running posterior mean estimate',
     },
     {
-      label: '95% CI · x',
+      label: `95% CI · ${ax}`,
       value: `[${fmt(s.ci[0])}, ${fmt(s.ci[1])}]`,
-      hint: 'central 95% credible interval for x',
+      hint: `central 95% credible interval for ${ax}`,
     },
     {
       label: 'evals',

projects/markov-lab-q8f3/src/targets/targets.ts

@@ -20,6 +20,8 @@ export interface Target {
   start: Vec
   /** True marginal means, when known — used to score sampler accuracy. */
   trueMean?: Vec
+  /** Human names for the two coordinates (defaults to x / y). */
+  axes?: [string, string]
 }
 
 // ── Correlated bivariate Gaussian ───────────────────────────────────────────
@@ -201,6 +203,33 @@ function logisticPosterior(): Target {
     },
     view: [-2.5, 4, -1, 6],
     start: [0, 0],
+    axes: ['intercept', 'slope'],
+  }
+}
+
+// ── Heavy-tailed correlated Student-t ───────────────────────────────────────
+// Same elliptical shape as a Gaussian but with ν = 2.5 degrees of freedom, so
+// the tails are polynomial, not exponential. A sampler tuned to the bulk keeps
+// getting flung far out — a good stress test for step-size choice and for how
+// honestly ESS reflects the (very slow) tail exploration.
+function studentT(nu = 2.5, rho = 0.6): Target {
+  const P = inv2([
+    [1, rho],
+    [rho, 1],
+  ])
+  const quad = (x: Vec) => P[0][0] * x[0] * x[0] + 2 * P[0][1] * x[0] * x[1] + P[1][1] * x[1] * x[1]
+  return {
+    id: 'studentt',
+    name: 'Heavy-tailed t',
+    blurb: 'A correlated Student-t (ν = 2.5). Polynomial tails fling the chain far out — brutal on a fixed step size.',
+    logDensity: (x) => -((nu + 2) / 2) * Math.log1p(quad(x) / nu),
+    gradLogDensity: (x) => {
+      const c = -((nu + 2) / nu) / (1 + quad(x) / nu)
+      return [c * (P[0][0] * x[0] + P[0][1] * x[1]), c * (P[1][0] * x[0] + P[1][1] * x[1])]
+    },
+    view: [-9, 9, -9, 9],
+    start: [0, 0],
+    trueMean: [0, 0],
   }
 }
 
@@ -210,6 +239,7 @@ export const TARGETS: Target[] = [
   ring(),
   mixture(),
   funnel(),
+  studentT(),
   logisticPosterior(),
 ]