{
  "analytic": "causal-confounding",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "bar",
      "labels": [
        "X=0",
        "X=1"
      ],
      "series": [
        {
          "label": "Observational mean",
          "y": [
            1.0,
            6.0
          ]
        },
        {
          "label": "Interventional mean",
          "y": [
            2.5,
            4.5
          ]
        }
      ],
      "ylabel": "Y in constructed units"
    }
  ],
  "title": "Conditioning and intervention select different U distributions",
  "assumptions": "P(U=1)=0.5; P(X=1|U=1)=0.8, |U=0=0.2; Y=2X+5U. Exact enumeration, no population data.",
  "worked": "观察均值为1与6，差5；干预均值为2.5与4.5，差2。后门加权使用总体U分布恢复干预均值，但现实是否可调整仍需因果假设。",
  "source_ids": [
    "arxiv-2102.11107",
    "arxiv-1907.02893",
    "arxiv-2012.07421"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "目标干预与变量定义",
    "结构图 / 混杂假设",
    "识别及支持条件",
    "观察分布与调整",
    "敏感性及外部检验",
    "限定总体的因果结论"
  ]
}