{
  "experiment": "four iid fictional Bernoulli trials, one observed success",
  "n": 4,
  "k": 1,
  "nominal_level": 0.8,
  "wilson_observed_interval": [
    0.07808074768511777,
    0.5674585496309226
  ],
  "bayesian_flat_prior": {
    "prior_beta": [
      1,
      1
    ],
    "posterior_beta": [
      2,
      4
    ],
    "lower": 0.11223495854585855,
    "upper": 0.583890374619529,
    "posterior_mass": 0.8,
    "equal_tails": [
      0.09999999999999999,
      0.09999999999999998
    ]
  },
  "bayesian_prior_sensitivity": {
    "prior_beta": [
      2,
      2
    ],
    "posterior_beta": [
      3,
      5
    ],
    "lower": 0.16963841739720054,
    "upper": 0.5961797278480441,
    "posterior_mass": 0.8000000000000002,
    "equal_tails": [
      0.09999999999999998,
      0.09999999999999987
    ]
  },
  "all_wilson_intervals": [
    {
      "successes": 0,
      "interval": [
        0.0,
        0.29107859463208074
      ]
    },
    {
      "successes": 1,
      "interval": [
        0.07808074768511777,
        0.5674585496309226
      ]
    },
    {
      "successes": 2,
      "interval": [
        0.2302414993776467,
        0.7697585006223533
      ]
    },
    {
      "successes": 3,
      "interval": [
        0.43254145036907743,
        0.9219192523148823
      ]
    },
    {
      "successes": 4,
      "interval": [
        0.7089214053679194,
        1.0
      ]
    }
  ],
  "exact_binomial_sum_coverage_no_simulation": [
    {
      "fixed_true_p": 0.1,
      "terms": [
        {
          "successes": 0,
          "probability": 0.6561,
          "contains_fixed_p": true
        },
        {
          "successes": 1,
          "probability": 0.2916,
          "contains_fixed_p": true
        },
        {
          "successes": 2,
          "probability": 0.04860000000000001,
          "contains_fixed_p": false
        },
        {
          "successes": 3,
          "probability": 0.0036000000000000008,
          "contains_fixed_p": false
        },
        {
          "successes": 4,
          "probability": 0.00010000000000000002,
          "contains_fixed_p": false
        }
      ],
      "actual_coverage": 0.9477
    },
    {
      "fixed_true_p": 0.25,
      "terms": [
        {
          "successes": 0,
          "probability": 0.31640625,
          "contains_fixed_p": true
        },
        {
          "successes": 1,
          "probability": 0.421875,
          "contains_fixed_p": true
        },
        {
          "successes": 2,
          "probability": 0.2109375,
          "contains_fixed_p": true
        },
        {
          "successes": 3,
          "probability": 0.046875,
          "contains_fixed_p": false
        },
        {
          "successes": 4,
          "probability": 0.00390625,
          "contains_fixed_p": false
        }
      ],
      "actual_coverage": 0.94921875
    },
    {
      "fixed_true_p": 0.5,
      "terms": [
        {
          "successes": 0,
          "probability": 0.0625,
          "contains_fixed_p": false
        },
        {
          "successes": 1,
          "probability": 0.25,
          "contains_fixed_p": true
        },
        {
          "successes": 2,
          "probability": 0.375,
          "contains_fixed_p": true
        },
        {
          "successes": 3,
          "probability": 0.25,
          "contains_fixed_p": true
        },
        {
          "successes": 4,
          "probability": 0.0625,
          "contains_fixed_p": false
        }
      ],
      "actual_coverage": 0.875
    },
    {
      "fixed_true_p": 0.75,
      "terms": [
        {
          "successes": 0,
          "probability": 0.00390625,
          "contains_fixed_p": false
        },
        {
          "successes": 1,
          "probability": 0.046875,
          "contains_fixed_p": false
        },
        {
          "successes": 2,
          "probability": 0.2109375,
          "contains_fixed_p": true
        },
        {
          "successes": 3,
          "probability": 0.421875,
          "contains_fixed_p": true
        },
        {
          "successes": 4,
          "probability": 0.31640625,
          "contains_fixed_p": true
        }
      ],
      "actual_coverage": 0.94921875
    },
    {
      "fixed_true_p": 0.9,
      "terms": [
        {
          "successes": 0,
          "probability": 9.999999999999991e-05,
          "contains_fixed_p": false
        },
        {
          "successes": 1,
          "probability": 0.0035999999999999977,
          "contains_fixed_p": false
        },
        {
          "successes": 2,
          "probability": 0.04859999999999998,
          "contains_fixed_p": false
        },
        {
          "successes": 3,
          "probability": 0.29159999999999997,
          "contains_fixed_p": true
        },
        {
          "successes": 4,
          "probability": 0.6561,
          "contains_fixed_p": true
        }
      ],
      "actual_coverage": 0.9477
    }
  ],
  "quantile_method": "60 bisections of exact finite polynomial integer-Beta CDF; mass tolerance 1e-12",
  "astropy_or_scipy_executed": false
}
