bootstrapConfidenceIntervals method

Future<Map<String, (num, num)>> bootstrapConfidenceIntervals({ int simulations = 1000, num confidence = 0.95, })

Bootstrap confidence intervals for statistics.

Example:

final petalWidth = petals.numericColumns["petal_width"]!,
  species = petals.categoricColumns["species"]!;

print("Petal width:");
for (final MapEntry(:key, :value) in
  (await petalWidth.bootstrapConfidenceIntervals(
     simulations: 10000,
     confidence: 0.9,
   )).entries) {
  final (lower, upper) = value;
  print("$key: "
    "(${lower.toStringAsFixed(2)}, ${upper.toStringAsFixed(2)})");
}

print("\nSpecies:");
for (final MapEntry(:key, :value) in
  (await species.bootstrapConfidenceIntervals(
     simulations: 10000,
     confidence: 0.9,
   )).entries) {
  final (lower, upper) = value;
  print("$key: "
    "(${lower.toStringAsFixed(2)}, ${upper.toStringAsFixed(2)})");
}

Petal width:
sum: (10.30, 19.40)
sumOfSquares: (15.34, 37.10)
mean: (0.86, 1.62)
variance: (0.32, 0.83)
inferredVariance: (0.35, 0.91)
standardDeviation: (0.57, 0.91)
inferredStandardDeviation: (0.59, 0.95)
skewness: (-0.30, 0.15)
meanAbsoluteDeviation: (0.41, 0.84)
lowerQuartile: (0.20, 1.45)
median: (0.20, 1.80)
upperQuartile: (1.42, 2.10)
interQuartileRange: (0.40, 1.85)
maximum: (1.90, 2.50)
maximumNonOutlier: (1.80, 2.50)
minimum: (0.20, 0.20)
minimumNonOutlier: (0.20, 1.40)
range: (1.70, 2.30)

Species:
impurity: (0.49, 0.67)
entropy: (0.82, 1.10)

Implementation

Future<Map<String, (num, num)>> bootstrapConfidenceIntervals({
  int simulations = 1000,
  num confidence = 0.95,
}) async {
  final sample = {
    for (final key in (this is NumericColumn
        ? NumericStat.values
        : CategoricStat.values))
      key.name: NumericColumn([])
  };
  while (simulations > 0) {
    for (final MapEntry(:key, :value) in bootstrap().summary.entries) {
      sample[key]!.add(value);
    }
    simulations--;
  }
  if (confidence > 1) {
    confidence /= 100;
  }
  if (confidence < 0 || confidence > 1) {
    throw PackhorseError.badArgument("Confidence $confidence expected to be"
        "a proportion in [0, 1] or a percentage in [0, 100]");
  }

  final lower = (1 - confidence) / 2, upper = 1 - lower;
  return {
    for (final MapEntry(:key, :value) in sample.entries)
      key: (value.tile(lower), value.tile(upper)),
  };
}