{
 "description": "Conjugate Gaussian SBC. Simulated rank histograms are compared with uniformity and with an independent analytic prediction of their shape.",
 "settings": {
  "seed": 8701,
  "observations": 4,
  "noiseSd": 1.0,
  "replications": 4000,
  "posteriorDraws": 99,
  "bins": 20,
  "shiftInPosteriorSd": 0.5,
  "wideFactor": 1.5,
  "narrowFactor": 0.6,
  "wrongPriorSd": 0.5,
  "coverageLevels": [
   0.5,
   0.9
  ],
  "algorithms": [
   "exact",
   "shifted",
   "too-wide",
   "too-narrow",
   "narrow-prior"
  ],
  "repeatStudyRepeats": 200,
  "repeatStudySeed": 100000
 },
 "uniform99Band": [
  165,
  236
 ],
 "expectedPerBin": 200.0,
 "results": [
  {
   "algorithm": "exact",
   "counts": [
    177,
    195,
    211,
    207,
    190,
    208,
    242,
    183,
    213,
    160,
    193,
    209,
    219,
    218,
    181,
    198,
    227,
    205,
    183,
    181
   ],
   "analyticExpectedCounts": [
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0,
    200.0
   ],
   "binsOutsideUniform99Band": 2,
   "chiSquareVsUniform": 36.47,
   "chiSquareVsUniformPValue": 0.00931,
   "chiSquareVsAnalyticShape": 36.47,
   "chiSquareVsAnalyticShapePValue": 0.0093,
   "centralIntervalCoverage": [
    {
     "level": 0.5,
     "simulated": 0.5095,
     "wilson95": [
      0.494,
      0.525
     ],
     "analytic": 0.5
    },
    {
     "level": 0.9,
     "simulated": 0.914,
     "wilson95": [
      0.9049,
      0.9223
     ],
     "analytic": 0.9
    }
   ]
  },
  {
   "algorithm": "shifted",
   "counts": [
    475,
    384,
    332,
    272,
    254,
    250,
    186,
    205,
    216,
    205,
    180,
    150,
    142,
    141,
    142,
    117,
    115,
    93,
    78,
    63
   ],
   "analyticExpectedCounts": [
    495.59,
    364.92,
    314.8,
    282.35,
    258.06,
    238.46,
    221.88,
    207.39,
    194.39,
    182.5,
    171.42,
    160.94,
    150.87,
    141.04,
    131.28,
    121.37,
    111.01,
    99.72,
    86.33,
    65.66
   ],
   "binsOutsideUniform99Band": 15,
   "chiSquareVsUniform": 1051.66,
   "chiSquareVsUniformPValue": 0.0,
   "chiSquareVsAnalyticShape": 19.04,
   "chiSquareVsAnalyticShapePValue": 0.4545,
   "centralIntervalCoverage": [
    {
     "level": 0.5,
     "simulated": 0.452,
     "wilson95": [
      0.4366,
      0.4675
     ],
     "analytic": 0.4492
    },
    {
     "level": 0.9,
     "simulated": 0.8635,
     "wilson95": [
      0.8525,
      0.8738
     ],
     "analytic": 0.8579
    }
   ]
  },
  {
   "algorithm": "too-wide",
   "counts": [
    28,
    69,
    116,
    206,
    205,
    216,
    292,
    307,
    277,
    275,
    312,
    291,
    276,
    246,
    260,
    232,
    177,
    108,
    69,
    38
   ],
   "analyticExpectedCounts": [
    32.34,
    85.41,
    132.92,
    174.24,
    209.4,
    238.5,
    261.65,
    278.94,
    290.43,
    296.16,
    296.16,
    290.43,
    278.94,
    261.65,
    238.5,
    209.4,
    174.24,
    132.92,
    85.41,
    32.34
   ],
   "binsOutsideUniform99Band": 15,
   "chiSquareVsUniform": 856.62,
   "chiSquareVsUniformPValue": 0.0,
   "chiSquareVsAnalyticShape": 37.42,
   "chiSquareVsAnalyticShapePValue": 0.0071,
   "centralIntervalCoverage": [
    {
     "level": 0.5,
     "simulated": 0.69625,
     "wilson95": [
      0.6818,
      0.7103
     ],
     "analytic": 0.6883
    },
    {
     "level": 0.9,
     "simulated": 0.988,
     "wilson95": [
      0.9841,
      0.9909
     ],
     "analytic": 0.9864
    }
   ]
  },
  {
   "algorithm": "too-narrow",
   "counts": [
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    257,
    181,
    169,
    158,
    141,
    144,
    105,
    123,
    130,
    93,
    121,
    136,
    133,
    153,
    137,
    155,
    199,
    225,
    625
   ],
   "analyticExpectedCounts": [
    633.64,
    241.71,
    186.58,
    160.59,
    145.35,
    135.54,
    129.01,
    124.7,
    122.06,
    120.81,
    120.81,
    122.06,
    124.7,
    129.01,
    135.54,
    145.35,
    160.59,
    186.58,
    241.71,
    633.64
   ],
   "binsOutsideUniform99Band": 16,
   "chiSquareVsUniform": 2103.8,
   "chiSquareVsUniformPValue": 0.0,
   "chiSquareVsAnalyticShape": 21.58,
   "chiSquareVsAnalyticShapePValue": 0.3051,
   "centralIntervalCoverage": [
    {
     "level": 0.5,
     "simulated": 0.30975,
     "wilson95": [
      0.2956,
      0.3243
     ],
     "analytic": 0.3143
    },
    {
     "level": 0.9,
     "simulated": 0.685,
     "wilson95": [
      0.6704,
      0.6992
     ],
     "analytic": 0.6763
    }
   ]
  },
  {
   "algorithm": "narrow-prior",
   "counts": [
    591,
    251,
    185,
    149,
    182,
    145,
    136,
    128,
    139,
    119,
    121,
    116,
    151,
    152,
    134,
    148,
    184,
    180,
    236,
    553
   ],
   "analyticExpectedCounts": [
    583.58,
    243.56,
    191.22,
    166.17,
    151.36,
    141.78,
    135.37,
    131.13,
    128.53,
    127.29,
    127.29,
    128.53,
    131.13,
    135.37,
    141.78,
    151.36,
    166.17,
    191.22,
    243.56,
    583.58
   ],
   "binsOutsideUniform99Band": 15,
   "chiSquareVsUniform": 1664.21,
   "chiSquareVsUniformPValue": 0.0,
   "chiSquareVsAnalyticShape": 21.54,
   "chiSquareVsAnalyticShapePValue": 0.3074,
   "centralIntervalCoverage": [
    {
     "level": 0.5,
     "simulated": 0.34225,
     "wilson95": [
      0.3277,
      0.3571
     ],
     "analytic": 0.3303
    },
    {
     "level": 0.9,
     "simulated": 0.704,
     "wilson95": [
      0.6897,
      0.7179
     ],
     "analytic": 0.7018
    }
   ]
  }
 ],
 "repeatStudy": {
  "exact": {
   "flagged": 2,
   "repeats": 200,
   "fraction": 0.01
  },
  "shifted": {
   "flagged": 200,
   "repeats": 200,
   "fraction": 1.0
  },
  "too-wide": {
   "flagged": 200,
   "repeats": 200,
   "fraction": 1.0
  },
  "too-narrow": {
   "flagged": 200,
   "repeats": 200,
   "fraction": 1.0
  },
  "narrow-prior": {
   "flagged": 200,
   "repeats": 200,
   "fraction": 1.0
  }
 }
}