DDM explorer

Companion to Simulating data from a cognitive model (Day 2, 14:00)

Two sliders, 136 precomputed simulations of 4,000 trials each. Watch what happens to the two response-time distributions as you move drift rate and boundary separation. The area under each curve is that boundary’s share of the trials, so the split you see is the accuracy.

grid = FileAttachment("ddm_grid.json").json()

viewof vSel = Inputs.range([-2, 2], {value: 0.75, step: 0.25, label: "drift v"})

viewof aSel = Inputs.range([0.6, 2.0], {value: 1.2, step: 0.2, label: "boundary a"})

cell = {
  const near = (arr, x) => arr.reduce((p, c) => Math.abs(c - x) < Math.abs(p - x) ? c : p);
  return grid.cells.find(d => d.v === near(grid.v_grid, vSel) &&
                              d.a === near(grid.a_grid, aSel));
}

series = grid.meta.rt_centers.flatMap((t, i) => [
  {rt: t, density: cell.upper[i], boundary: "upper (+1)"},
  {rt: t, density: cell.lower[i], boundary: "lower (-1)"}
])

Plot.plot({
  width: 700, height: 300, marginLeft: 55,
  x: {label: "response time (s)", domain: [0, 4]},
  y: {label: "density", domain: [0, 2.2]},
  color: {domain: ["upper (+1)", "lower (-1)"],
          range: ["#2a78d6", "#4a3aa7"], legend: true},
  marks: [
    Plot.areaY(series, {x: "rt", y: "density", fill: "boundary", fillOpacity: 0.22}),
    Plot.lineY(series, {x: "rt", y: "density", stroke: "boundary", strokeWidth: 2}),
    Plot.ruleY([0], {stroke: "#c3c2b7"})
  ]
})

md`At **v = ${cell.v}**, **a = ${cell.a}**: P(upper) = **${cell.p_upper.toFixed(3)}**, mean RT = **${cell.mean_rt.toFixed(3)} s**, error rate = **${(100 * (1 - cell.p_upper)).toFixed(1)}%**`

Three things worth provoking deliberately

Set v = 0. Both curves become identical and the split goes to 50/50 — drift is the only thing here that breaks the symmetry.
Push v to 2 with a small. Errors nearly vanish and the distribution gets very tight. Remember this setting: it is the pathological design dissected in the next session.
Raise a at fixed v. Accuracy improves and everything slows down. That single trade-off is the speed-accuracy trade-off, in one knob.

Why precomputed rather than live

ssm-simulators is Cython — cssm ships compiled extension modules — so it cannot run in a browser, and this website never executes Python. The sliders therefore select among simulations run ahead of time by _src/precompute_ddm_grid.py (a 17 × 8 grid over drift and boundary separation, 78 KB of JSON). Regenerate with:

cd tutorials && uv run python day2_bayes_toolkit/_src/precompute_ddm_grid.py