{
 "description": "Independent checks of the AC87 exact grid posterior (Fisher limit, Metropolis cross-check, grid SBC, linear misspecification bias).",
 "settings": {
  "seed": 8702,
  "fisher": {
   "frequencyHz": 250,
   "dampingTimeMs": 6,
   "sigmas": [
    0.6,
    0.2,
    0.05,
    0.02
   ],
   "realizations": 40
  },
  "metropolis": {
   "steps": 60000,
   "burnIn": 5000,
   "cases": [
    {
     "frequencyHz": 250,
     "dampingTimeMs": 6,
     "sigma": 0.2
    },
    {
     "frequencyHz": 215,
     "dampingTimeMs": 3,
     "sigma": 0.5
    }
   ]
  },
  "sbc": {
   "replications": 2000,
   "posteriorDraws": 99,
   "bins": 20,
   "coverageLevels": [
    0.5,
    0.68,
    0.9,
    0.95
   ]
  },
  "bias": {
   "frequencyHz": 250,
   "dampingTimeMs": 6,
   "strengths": [
    0.02,
    0.05,
    0.1,
    0.2
   ],
   "sharpSigma": 0.01,
   "scalingStrength": 0.3,
   "scalingSigmas": [
    0.6,
    0.3,
    0.15,
    0.05
   ]
  }
 },
 "fisherLimit": [
  {
   "sigma": 0.6,
   "optimalSnr": 4.32,
   "gridFrequencySd": 13.5934,
   "fisherFrequencySd": 9.0878,
   "gridDampingSd": 1.6851,
   "fisherDampingSd": 2.0565,
   "frequencyRatio": 1.4958,
   "dampingRatio": 0.8194
  },
  {
   "sigma": 0.2,
   "optimalSnr": 12.96,
   "gridFrequencySd": 3.3035,
   "fisherFrequencySd": 3.0293,
   "gridDampingSd": 0.6854,
   "fisherDampingSd": 0.6855,
   "frequencyRatio": 1.0905,
   "dampingRatio": 0.9999
  },
  {
   "sigma": 0.05,
   "optimalSnr": 51.84,
   "gridFrequencySd": 0.7563,
   "fisherFrequencySd": 0.7573,
   "gridDampingSd": 0.172,
   "fisherDampingSd": 0.1714,
   "frequencyRatio": 0.9986,
   "dampingRatio": 1.0035
  },
  {
   "sigma": 0.02,
   "optimalSnr": 129.61,
   "gridFrequencySd": 0.3017,
   "fisherFrequencySd": 0.3029,
   "gridDampingSd": 0.0687,
   "fisherDampingSd": 0.0685,
   "frequencyRatio": 0.9958,
   "dampingRatio": 1.0024
  }
 ],
 "metropolis": [
  {
   "case": {
    "frequencyHz": 250,
    "dampingTimeMs": 6,
    "sigma": 0.2
   },
   "acceptanceRate": 0.481,
   "grid": {
    "frequencyMean": 249.9944,
    "dampingMean": 6.0652,
    "frequencySd": 3.2827,
    "dampingSd": 0.6505,
    "covariance": 0.1275
   },
   "metropolis": {
    "frequencyMean": 249.9927,
    "dampingMean": 6.0589,
    "frequencySd": 3.3161,
    "dampingSd": 0.6525
   }
  },
  {
   "case": {
    "frequencyHz": 215,
    "dampingTimeMs": 3,
    "sigma": 0.5
   },
   "acceptanceRate": 0.216,
   "grid": {
    "frequencyMean": 210.9591,
    "dampingMean": 4.4054,
    "frequencySd": 13.7708,
    "dampingSd": 1.7607,
    "covariance": -10.5094
   },
   "metropolis": {
    "frequencyMean": 211.0597,
    "dampingMean": 4.4038,
    "frequencySd": 14.1685,
    "dampingSd": 1.7688
   }
  }
 ],
 "gridSbc": {
  "replications": 2000,
  "posteriorDraws": 99,
  "bins": 20,
  "uniform99Band": [
   76,
   126
  ],
  "parameters": {
   "frequency": {
    "counts": [
     104,
     84,
     97,
     102,
     74,
     117,
     113,
     105,
     94,
     102,
     97,
     105,
     101,
     90,
     100,
     99,
     94,
     121,
     102,
     99
    ],
    "binsOutsideBand": 1,
    "chiSquarePValue": 0.3355
   },
   "dampingTime": {
    "counts": [
     107,
     110,
     93,
     107,
     114,
     98,
     112,
     95,
     86,
     110,
     105,
     112,
     96,
     105,
     112,
     70,
     104,
     95,
     75,
     94
    ],
    "binsOutsideBand": 2,
    "chiSquarePValue": 0.071
   }
  },
  "expectedCoverage": [
   {
    "level": 0.5,
    "empirical": 0.512,
    "wilson95": [
     0.4901,
     0.5339
    ]
   },
   {
    "level": 0.68,
    "empirical": 0.6915,
    "wilson95": [
     0.6709,
     0.7114
    ]
   },
   {
    "level": 0.9,
    "empirical": 0.8965,
    "wilson95": [
     0.8824,
     0.9091
    ]
   },
   {
    "level": 0.95,
    "empirical": 0.9525,
    "wilson95": [
     0.9423,
     0.961
    ]
   }
  ]
 },
 "misspecificationBias": {
  "linearPrediction": [
   {
    "strength": 0.02,
    "predictedFrequencyShiftHz": 0.0888,
    "gridFrequencyShiftHz": 0.0882,
    "predictedDampingShiftMs": 0.0208,
    "gridDampingShiftMs": 0.0207
   },
   {
    "strength": 0.05,
    "predictedFrequencyShiftHz": 0.2219,
    "gridFrequencyShiftHz": 0.2187,
    "predictedDampingShiftMs": 0.052,
    "gridDampingShiftMs": 0.0515
   },
   {
    "strength": 0.1,
    "predictedFrequencyShiftHz": 0.4438,
    "gridFrequencyShiftHz": 0.4313,
    "predictedDampingShiftMs": 0.1039,
    "gridDampingShiftMs": 0.1022
   },
   {
    "strength": 0.2,
    "predictedFrequencyShiftHz": 0.8876,
    "gridFrequencyShiftHz": 0.8396,
    "predictedDampingShiftMs": 0.2079,
    "gridDampingShiftMs": 0.2013
   }
  ],
  "noiseFreeShiftVersusSigma": [
   {
    "sigma": 0.6,
    "frequencyShiftHz": 1.7563,
    "frequencySd": 11.1049,
    "shiftInPosteriorSd": 0.158
   },
   {
    "sigma": 0.3,
    "frequencyShiftHz": 1.3258,
    "frequencySd": 4.5648,
    "shiftInPosteriorSd": 0.29
   },
   {
    "sigma": 0.15,
    "frequencyShiftHz": 1.2498,
    "frequencySd": 2.1926,
    "shiftInPosteriorSd": 0.57
   },
   {
    "sigma": 0.05,
    "frequencyShiftHz": 1.2298,
    "frequencySd": 0.723,
    "shiftInPosteriorSd": 1.701
   }
  ]
 },
 "wallClockSeconds": 14.8
}