{
  "hypothesis_bernoulli_probabilities": [
    "1/4",
    "3/4"
  ],
  "assumptions": [
    "finite authored hypothesis set",
    "prior weights supplied by author",
    "observations conditionally iid Bernoulli under the fixed latent hypothesis",
    "same hypothesis for successive observations"
  ],
  "trace": [
    {
      "observations": [],
      "weights": [
        "1/2",
        "1/2"
      ],
      "mean_predictive_probability": "1/2",
      "expected_conditional_variance": "3/16",
      "variance_of_conditional_means": "1/16",
      "predictive_variance_direct_joint": "1/4",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "3/8"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/8"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "1/8"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "3/8"
        }
      ]
    },
    {
      "observations": [
        1
      ],
      "likelihoods": [
        "1/4",
        "3/4"
      ],
      "evidence_probability": "1/2",
      "weights": [
        "1/4",
        "3/4"
      ],
      "mean_predictive_probability": "5/8",
      "expected_conditional_variance": "3/16",
      "variance_of_conditional_means": "3/64",
      "predictive_variance_direct_joint": "15/64",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "3/16"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/16"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "3/16"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "9/16"
        }
      ]
    },
    {
      "observations": [
        1,
        1
      ],
      "likelihoods": [
        "1/4",
        "3/4"
      ],
      "evidence_probability": "5/8",
      "weights": [
        "1/10",
        "9/10"
      ],
      "mean_predictive_probability": "7/10",
      "expected_conditional_variance": "3/16",
      "variance_of_conditional_means": "9/400",
      "predictive_variance_direct_joint": "21/100",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "3/40"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/40"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "9/40"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "27/40"
        }
      ]
    },
    {
      "observations": [
        1,
        1,
        0
      ],
      "likelihoods": [
        "3/4",
        "1/4"
      ],
      "evidence_probability": "3/10",
      "weights": [
        "1/4",
        "3/4"
      ],
      "mean_predictive_probability": "5/8",
      "expected_conditional_variance": "3/16",
      "variance_of_conditional_means": "3/64",
      "predictive_variance_direct_joint": "15/64",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "3/16"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/16"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "3/16"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "9/16"
        }
      ]
    },
    {
      "observations": [
        1,
        1,
        0,
        0
      ],
      "likelihoods": [
        "3/4",
        "1/4"
      ],
      "evidence_probability": "3/8",
      "weights": [
        "1/2",
        "1/2"
      ],
      "mean_predictive_probability": "1/2",
      "expected_conditional_variance": "3/16",
      "variance_of_conditional_means": "1/16",
      "predictive_variance_direct_joint": "1/4",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "3/8"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/8"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "1/8"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "3/8"
        }
      ]
    }
  ],
  "same_predictive_Bernoulli_half_different_splits": {
    "single_known_half": {
      "weights": [
        "1"
      ],
      "mean_predictive_probability": "1/2",
      "expected_conditional_variance": "1/4",
      "variance_of_conditional_means": "0",
      "predictive_variance_direct_joint": "1/4",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "1/2"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "1/2"
        }
      ]
    },
    "two_deterministic_hypotheses": {
      "weights": [
        "1/2",
        "1/2"
      ],
      "mean_predictive_probability": "1/2",
      "expected_conditional_variance": "0",
      "variance_of_conditional_means": "1/4",
      "predictive_variance_direct_joint": "1/4",
      "joint_distribution": [
        {
          "hypothesis": 0,
          "y": 0,
          "mass": "1/2"
        },
        {
          "hypothesis": 0,
          "y": 1,
          "mass": "0"
        },
        {
          "hypothesis": 1,
          "y": 0,
          "mass": "0"
        },
        {
          "hypothesis": 1,
          "y": 1,
          "mass": "1/2"
        }
      ]
    }
  },
  "weights_are_actual_Bayes_updates_not_model_training": true,
  "decomposition_not_identifiable_without_model_assumptions": true,
  "empirical_ensemble_disagreement_or_BNN_training_or_real_data": false
}