{
  "math_check": {
    "analytic_EY_given_M1": {
      "1.0": 1.5,
      "2.0": 1.8
    },
    "empirical_EY_given_M1": {
      "sigma1": 1.5005521774291992,
      "sigma2": 1.7640395164489746
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    "marginal_Y_variance_formula": {
      "1.0": 6.0,
      "2.0": 18.0
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  },
  "neural_experiment": {
    "test_shift_sigma2_nll": {
      "baseline_m_only": 1.9675318002700806,
      "joint": 1.6474906206130981,
      "joint_minus_baseline": -0.3200411796569824
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    "selected_M1_predicted_mean": {
      "baseline": 1.6588640213012695,
      "joint_conditional": 2.0122196674346924,
      "true_sigma2": 1.8
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    "joint_marginal_predicted_Y_variance_sigma2": 13.315326690673828,
    "device": "cuda"
  }
}