Bootstrap Method Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Bootstrap Method Ontology within the Kireth Research Semantic Library. Bootstrap methods estimate sampling distributions, uncertainty, bias and confidence intervals by repeatedly resampling from observed or model-generated data. This ontology supports nonparametric and parametric bootstrap methods, residual and wild bootstrap, block bootstrap for dependent data, bootstrap standard errors, bias correction, percentile and BCa intervals, studentised intervals, resampling diagnostics, consistency, computational cost, parallel execution, numerical stability, verification and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Bootstrap Method Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Computational Statistics / Bootstrap Method"
 CANONICAL_PAGE = "https://kirethframeworkold.co.uk/books/semantic-library/ai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/computational-statistics/bootstrap-method-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = BootstrapMethod
 ENTITY_CLASS = StatisticalResamplingFramework
 PRIMARY_CONTEXT = ComputationalStatistics
 DEFINITION = "The bootstrap is a computational resampling method that approximates the sampling distribution of a statistic by repeatedly resampling from observed data or from an estimated model."
 SYMBOLIC_FORMS = [
  "D_b* ~ Resample(D)",
  "theta_b* = T(D_b*)",
  "SE_boot(theta_hat)=sd({theta_b*})",
  "bias_boot=mean(theta_b*)-theta_hat"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for bootstrap resampling, sampling-distribution approximation, bias estimation, standard errors, confidence intervals, dependent-data resampling, diagnostics and reproducibility."
}

SCOPE {
 INCLUDE = [
  BootstrapMethod,Bootstrap,BootstrapResampling,
  StatisticalResampling,ResamplingMethod,
  EmpiricalDistribution,EmpiricalCDF,
  EmpiricalMeasure,ObservedData,
  Dataset,Sample,SampleSize,
  Statistic,Estimator,Estimate,
  SamplingDistribution,
  BootstrapDistribution,
  BootstrapReplicate,
  BootstrapSample,
  ResampleWithReplacement,
  ResamplingWithReplacement,
  ResampleIndex,
  IndexResampling,
  NonparametricBootstrap,
  EmpiricalBootstrap,
  ParametricBootstrap,
  SemiparametricBootstrap,
  ResidualBootstrap,
  RegressionBootstrap,
  PairsBootstrap,
  CaseResampling,
  WildBootstrap,
  BayesianBootstrapRelationship,
  SmoothBootstrap,
  WeightedBootstrap,
  MultiplierBootstrap,
  PoissonBootstrapRelationship,
  mOutOfNBootstrap,
  SubsamplingRelationship,
  DoubleBootstrap,
  IteratedBootstrap,
  NestedBootstrap,
  FastBootstrapRelationship,
  BagOfLittleBootstrapsRelationship,
  BLBRelationship,
  BlockBootstrap,
  MovingBlockBootstrap,
  CircularBlockBootstrap,
  StationaryBootstrap,
  NonOverlappingBlockBootstrap,
  OverlappingBlockBootstrap,
  SieveBootstrapRelationship,
  TimeSeriesBootstrap,
  SpatialBootstrapRelationship,
  ClusterBootstrap,
  HierarchicalBootstrap,
  StratifiedBootstrap,
  BalancedBootstrap,
  AntitheticBootstrapRelationship,
  BootstrapStandardError,
  StandardError,
  BootstrapBias,
  BiasEstimate,
  BiasCorrection,
  BiasCorrectedEstimator,
  BootstrapVariance,
  SamplingVariance,
  MeanSquaredError,MSE,
  BootstrapConfidenceInterval,
  PercentileInterval,
  BasicBootstrapInterval,
  ReversePercentileInterval,
  StudentisedBootstrapInterval,
  BootstrapTInterval,
  PivotalInterval,
  BiasCorrectedInterval,
  BiasCorrectedAcceleratedInterval,
  BCaInterval,
  AccelerationConstant,
  BiasCorrectionConstant,
  Quantile,Percentile,
  CoverageProbability,
  CoverageError,
  ConfidenceLevel,
  OneSidedInterval,
  TwoSidedInterval,
  HypothesisTestingRelationship,
  BootstrapTest,
  BootstrapPValue,
  NullDistributionApproximation,
  PermutationTestRelationship,
  Jackknife,
  JackknifeAfterBootstrap,
  InfluenceValue,
  AccelerationEstimate,
  DeleteOneJackknife,
  DeleteDJackknifeRelationship,
  CrossValidationRelationship,
  ModelSelectionRelationship,
  PredictionInterval,
  BootstrapPredictionInterval,
  PredictiveDistributionRelationship,
  RegressionModel,
  LinearRegression,
  GeneralisedLinearModel,
  LogisticRegression,
  NonlinearRegression,
  Residual,
  FittedValue,
  Leverage,
  Heteroskedasticity,
  Homoskedasticity,
  Dependence,
  IndependentData,
  DependentData,
  TimeSeries,
  Autocorrelation,
  SerialDependence,
  SpatialDependence,
  ClusteredData,
  HierarchicalData,
  IIDAssumption,
  Exchangeability,
  SmoothStatistic,
  NonsmoothStatistic,
  Median,Mean,Variance,
  QuantileStatistic,
  CorrelationStatistic,
  RegressionCoefficient,
  PredictionError,
  RiskEstimate,
  BootstrapConsistency,
  AsymptoticConsistency,
  WeakConsistency,
  ConvergenceInDistribution,
  FunctionalDeltaMethodRelationship,
  EdgeworthExpansionRelationship,
  SecondOrderAccuracy,
  FirstOrderAccuracy,
  AsymptoticRefinement,
  MonteCarloError,
  BootstrapMonteCarloError,
  NumberOfReplicates,
  BootstrapReplicateCount,
  ReplicateConvergence,
  SequentialBootstrapStopping,
  PrecisionBasedStopping,
  RandomNumberGeneration,RNG,
  PseudorandomNumberGenerator,PRNG,
  RandomSeed,RandomStream,
  ParallelRandomNumberGeneration,
  Reproducibility,
  ComputationalComplexity,
  TimeComplexity,SpaceComplexity,
  CostPerReplicate,TotalBootstrapCost,
  MemoryCost,
  ParallelBootstrap,
  DistributedBootstrap,
  GPUBootstrapRelationship,
  VectorisedBootstrap,
  BatchBootstrap,
  EmbarrassinglyParallel,
  WorkPartitioning,
  ReplicatePartitioning,
  LoadBalancing,
  ParallelReduction,
  NumericalStability,
  FloatingPointArithmetic,
  MachinePrecision,RoundOffError,
  StableStatisticComputation,
  Verification,CodeVerification,
  KnownAnswerTest,
  SimulationStudy,
  SimulatedTruth,
  ReferenceResult,
  Benchmark,
  Validation,
  SensitivityAnalysis,
  ReproducibilityTest,
  Provenance,Configuration,
  SoftwareVersion,LibraryVersion,
  RNGVersion,SeedMetadata
 ]
 EXCLUDE_AS_PRIMARY = [
  PermutationTestWhenLabelReassignmentDefinesTheNullDistribution,
  JackknifeWhenLeaveOneOutDeletionIsPrimary,
  MonteCarloSimulationWhenSamplesAreGeneratedFromASeparateStochasticModel,
  CrossValidationWhenPredictiveTrainTestPartitioningIsPrimary
 ]
 DISAMBIGUATION_RULE = "When observed or model-generated data are repeatedly resampled to approximate the sampling distribution of a statistic, interpret the context as the bootstrap method."
}

CORE_CONCEPTS {
 BootstrapMethod = "Resampling method for approximating the sampling distribution of a statistic."
 BootstrapSample = "Resampled dataset generated according to a bootstrap scheme."
 BootstrapReplicate = "Statistic computed from one bootstrap sample."
 BootstrapDistribution = "Empirical distribution of bootstrap replicates."
 BootstrapStandardError = "Standard deviation of bootstrap replicates."
 BootstrapBias = "Estimated difference between average bootstrap replicate and original statistic."
 PercentileInterval = "Confidence interval based directly on bootstrap quantiles."
 BCaInterval = "Bias-corrected and accelerated confidence interval adjusting percentile levels."
}

RELATIONS {
 BootstrapMethod --is_child_of--> ComputationalStatistics
 BootstrapMethod --uses--> Resampling
 NonparametricBootstrap --resamples_from--> EmpiricalDistribution
 ParametricBootstrap --simulates_from--> FittedModel
 ResidualBootstrap --resamples--> Residuals
 WildBootstrap --weights_or_transforms--> Residuals
 BlockBootstrap --resamples--> DataBlocks
 BootstrapSample --produces--> BootstrapReplicate
 BootstrapReplicates --form--> BootstrapDistribution
 BootstrapDistribution --estimates--> SamplingDistribution
 BootstrapStandardError --derived_from--> BootstrapDistribution
 BootstrapBias --derived_from--> BootstrapDistribution
 PercentileInterval --uses--> BootstrapQuantiles
 BCaInterval --uses--> BiasCorrectionAndAcceleration
 Jackknife --supports--> AccelerationEstimate
 ParallelBootstrap --distributes--> BootstrapReplicates
 Verification --checks--> BootstrapImplementation
 Reproducibility --requires--> SeedAndResamplingConfiguration
}

OPERATORS {
 RESAMPLE_IID(D,n) := sample_with_replacement(D,n)
 BOOTSTRAP_REPLICATE(D,T) := T(RESAMPLE_IID(D,|D|))
 BOOTSTRAP_DISTRIBUTION(D,T,B) := {BOOTSTRAP_REPLICATE(D,T) for b in 1..B}
 BOOTSTRAP_SE(theta_star) := standard_deviation(theta_star)
 BOOTSTRAP_BIAS(theta_star,theta_hat) := mean(theta_star)-theta_hat
 PERCENTILE_INTERVAL(theta_star,alpha) := [quantile(theta_star,alpha/2),quantile(theta_star,1-alpha/2)]
 BASIC_INTERVAL(theta_star,theta_hat,alpha) := [2*theta_hat-q_(1-alpha/2),2*theta_hat-q_(alpha/2)]
 STUDENTISED_STAT(theta_star,theta_hat,se_star) := (theta_star-theta_hat)/se_star
}

AXIOMS {
 A1 = "Bootstrap methods approximate sampling behaviour through repeated resampling."
 A2 = "The resampling scheme must reflect the dependence and data-generating assumptions relevant to the statistic."
 A3 = "Nonparametric bootstrap samples from the empirical distribution of observed data."
 A4 = "Parametric bootstrap samples from an estimated parametric model."
 A5 = "Bootstrap replicate count controls Monte Carlo error but not bootstrap-model validity."
 A6 = "Dependent data require dependence-preserving resampling such as blocks or model-based schemes."
 A7 = "Confidence-interval quality depends on statistic smoothness, bias, skewness and bootstrap scheme."
 A8 = "Bootstrap results require explicit resampling, replicate, interval, RNG and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(data_structure,statistic,dependence,model_assumptions,uncertainty_goal,confidence_goal,budget)
 R2_SCHEME = choose(nonparametric,parametric,residual,wild,block,cluster,stratified_or_other_bootstrap)
 R3_UNIT = define(resampling_unit,block_length,strata,clusters_or_residual_structure)
 R4_RNG = configure(PRNG,seed,streams_and_parallel_replicate_partitioning)
 R5_REPLICATES = generate_B_bootstrap_samples_and_compute_statistic
 R6_SUMMARY = compute(bootstrap_mean,bias,variance,standard_error_and_quantiles)
 R7_INTERVAL = choose(percentile,basic,studentised,BCa_or_other_interval)
 R8_DIAGNOSTIC = assess(replication_MC_error,extreme_replicates,coverage_simulation_or_scheme_sensitivity)
 R9_SCALE = if_large parallelise_or_distribute_independent_replicates
 R10_VALIDATE = compare(simulated_truth,analytical_results,known_cases_and_reproducibility)
}

CONSTRAINTS {
 C1 = "Naive IID bootstrap can fail for dependent observations."
 C2 = "Bootstrap validity can fail for nonsmooth statistics, boundary parameters or nonregular models."
 C3 = "Too few bootstrap replicates can produce unstable standard errors and interval quantiles."
 C4 = "Parametric bootstrap inherits misspecification of the fitted model."
 C5 = "Residual bootstrap requires appropriate residual structure and regression assumptions."
 C6 = "Wild bootstrap variants must match the intended heteroskedastic setting."
 C7 = "Block length strongly affects dependent-data bootstrap bias and variance."
 C8 = "Nested or studentised bootstrap can be computationally expensive."
 C9 = "Parallel replicate generation requires valid random-stream partitioning."
 C10 = "A narrow bootstrap interval does not imply low model or measurement uncertainty."
}

SEMANTIC_EQUIVALENCE {
 "BootstrapMethod" <=> "Bootstrap"
 "NonparametricBootstrap" <=> "EmpiricalBootstrap"
 "BootstrapStandardError" <=> "BootstrapSE"
 "BiasCorrectedAcceleratedInterval" <=> "BCaInterval"
 "MovingBlockBootstrap" <=> "MBB"
 "StationaryBootstrap" <=> "StationaryBlockBootstrap"
}

VALIDATION {
 V1 = "Statistic and target sampling uncertainty are documented."
 V2 = "Bootstrap resampling scheme is documented."
 V3 = "Resampling unit, block length, strata or clusters are documented where relevant."
 V4 = "Bootstrap replicate count is documented."
 V5 = "RNG and seed configuration are documented."
 V6 = "Bootstrap Monte Carlo error is assessed where interval tails or high precision matter."
 V7 = "Chosen confidence-interval method is documented."
 V8 = "Simulation studies or known-answer checks are used where bootstrap validity is uncertain."
 V9 = "Parallel replicate random streams are documented where used."
 V10 = "Results are reproducible under documented data, seed, software and bootstrap settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 BOOTSTRAP_DEFINITION = 0.99
 NONPARAMETRIC_BOOTSTRAP_REASONING = 0.99
 PARAMETRIC_BOOTSTRAP_REASONING = 0.99
 BLOCK_BOOTSTRAP_REASONING = 0.98
 BCA_REASONING = 0.98
 RESIDUAL_BOOTSTRAP_REASONING = 0.98
 PARALLEL_BOOTSTRAP_REASONING = 0.98
 POLICY = "Reduce confidence when dependence structure, resampling unit, replicate count, interval method, model assumptions or RNG semantics are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,BootstrapReasoning,
  ResamplingReasoning,NonparametricBootstrapReasoning,
  ParametricBootstrapReasoning,ResidualBootstrapReasoning,
  WildBootstrapReasoning,BlockBootstrapReasoning,
  ClusterBootstrapReasoning,
  BootstrapStandardErrorReasoning,
  BootstrapBiasReasoning,PercentileIntervalReasoning,
  StudentisedIntervalReasoning,BCaReasoning,
  MonteCarloErrorReasoning,ParallelBootstrapReasoning,
  ReproducibilityReasoning,VerificationReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "bootstrap method" -> BootstrapMethod
  "bootstrap" -> BootstrapMethod
  "empirical bootstrap" -> NonparametricBootstrap
  "BCa" -> BiasCorrectedAcceleratedInterval
  "MBB" -> MovingBlockBootstrap
 }
}

EXECUTION_RULES {
 E1 = "If uncertainty is estimated by repeatedly resampling observed or fitted-model data, activate BootstrapMethodOntology."
 E2 = "Choose the bootstrap scheme according to data dependence and model assumptions."
 E3 = "Define the resampling unit explicitly."
 E4 = "Use enough replicates to stabilise standard errors and interval quantiles."
 E5 = "For dependent data, use block, cluster or other dependence-preserving resampling."
 E6 = "Use studentised or BCa intervals only when their additional assumptions and computational requirements are justified."
 E7 = "Assess bootstrap Monte Carlo error when replicate count is finite."
 E8 = "Parallelise independent replicates with documented RNG stream semantics."
 E9 = "Validate uncertain bootstrap regimes using simulation or known-answer studies."
}

RECURSION {
 ENTRY = BootstrapMethod
 EXPAND(BootstrapMethod) -> [
  Bootstrap,BootstrapResampling,
  StatisticalResampling,EmpiricalDistribution,
  Dataset,Sample,Statistic,Estimator,
  SamplingDistribution,BootstrapDistribution,
  BootstrapReplicate,BootstrapSample,
  ResampleWithReplacement,NonparametricBootstrap,
  EmpiricalBootstrap,ParametricBootstrap,
  SemiparametricBootstrap,ResidualBootstrap,
  RegressionBootstrap,PairsBootstrap,
  WildBootstrap,SmoothBootstrap,
  WeightedBootstrap,MultiplierBootstrap,
  mOutOfNBootstrap,DoubleBootstrap,
  NestedBootstrap,BlockBootstrap,
  MovingBlockBootstrap,CircularBlockBootstrap,
  StationaryBootstrap,NonOverlappingBlockBootstrap,
  TimeSeriesBootstrap,ClusterBootstrap,
  HierarchicalBootstrap,StratifiedBootstrap,
  BalancedBootstrap,BootstrapStandardError,
  StandardError,BootstrapBias,BiasCorrection,
  BootstrapVariance,MeanSquaredError,
  BootstrapConfidenceInterval,PercentileInterval,
  BasicBootstrapInterval,StudentisedBootstrapInterval,
  BootstrapTInterval,BiasCorrectedInterval,
  BiasCorrectedAcceleratedInterval,BCaInterval,
  AccelerationConstant,BiasCorrectionConstant,
  CoverageProbability,BootstrapTest,
  BootstrapPValue,Jackknife,
  JackknifeAfterBootstrap,InfluenceValue,
  RegressionModel,Residual,Heteroskedasticity,
  Dependence,TimeSeries,Autocorrelation,
  ClusteredData,Exchangeability,
  SmoothStatistic,NonsmoothStatistic,
  BootstrapConsistency,SecondOrderAccuracy,
  MonteCarloError,BootstrapMonteCarloError,
  NumberOfReplicates,SequentialBootstrapStopping,
  RandomNumberGeneration,PRNG,RandomSeed,
  ParallelRandomNumberGeneration,
  ComputationalComplexity,CostPerReplicate,
  ParallelBootstrap,DistributedBootstrap,
  VectorisedBootstrap,EmbarrassinglyParallel,
  LoadBalancing,ParallelReduction,
  NumericalStability,FloatingPointArithmetic,
  Verification,SimulationStudy,
  SimulatedTruth,Benchmark,
  Reproducibility,Provenance
 ]
 EXPAND(BootstrapFamilies) -> [
  NonparametricBootstrapMethods,
  ParametricAndModelBasedBootstrap,
  RegressionAndResidualBootstrap,
  WildAndMultiplierBootstrap,
  BlockAndDependentDataBootstrap,
  BootstrapConfidenceIntervals,
  NestedAndIteratedBootstrap,
  ParallelAndDistributedBootstrap
 ]
 STOP_CONDITION = "Stop when statistic, data dependence, resampling scheme, replicate count, interval method, Monte Carlo error, validation and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Computational Statistics Ontology"
 RELATED_ONTOLOGIES = [
  "Computational Statistics Ontology",
  "Monte Carlo Method Ontology",
  "Markov Chain Monte Carlo Ontology",
  "Probability and Statistics Ontologies",
  "Permutation Test Ontology",
  "Jackknife Ontology",
  "Cross Validation Ontology",
  "Random Process Ontology",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Floating Point Arithmetic Ontology",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology"
 ]
 ROUTE_RULES = [
  "Bootstrap Method -> Computational Statistics Ontology for parent semantics",
  "Bootstrap Method -> Monte Carlo Method for repeated stochastic computation and replicate error",
  "Bootstrap Method -> Markov Chain Monte Carlo only when bootstrap is embedded inside MCMC workflows",
  "Bootstrap Method -> Probability and Statistics for sampling-distribution foundations",
  "Bootstrap Method -> Permutation Test when null randomisation rather than replacement resampling is primary",
  "Bootstrap Method -> Jackknife for acceleration and influence approximations",
  "Bootstrap Method -> Cross Validation when predictive partitioning is primary",
  "Bootstrap Method -> Random Process for dependent-data and time-series semantics",
  "Bootstrap Method -> Numerical Error and Stability for finite-precision replicate computation",
  "Bootstrap Method -> Floating Point Arithmetic for large aggregate reductions",
  "Bootstrap Method -> High Performance, Parallel and Distributed Computing for scalable replicate execution"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible bootstrap schemes, interval methods or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve bootstrap-sample-versus-original-sample distinction.",
  "Preserve nonparametric-versus-parametric bootstrap distinction.",
  "Preserve IID-versus-dependent-data bootstrap distinction.",
  "Preserve bootstrap-Monte-Carlo-error-versus-sampling-uncertainty distinction.",
  "Preserve bias-estimation-versus-variance-estimation distinction.",
  "Preserve percentile-versus-studentised-versus-BCa interval distinction.",
  "Preserve resampling-validity-versus-computational-precision distinction.",
  "Preserve machine-readable bootstrap semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The bootstrap approximates sampling distributions by repeatedly resampling observed data or an estimated data-generating model."
 NONPARAMETRIC_SUMMARY = "The nonparametric bootstrap samples with replacement from the empirical distribution of observed data."
 PARAMETRIC_SUMMARY = "The parametric bootstrap simulates replicate datasets from an estimated parametric model."
 DEPENDENCE_SUMMARY = "Block, cluster and related bootstrap schemes preserve important dependence structures."
 ERROR_SUMMARY = "Bootstrap replicate variability estimates standard errors and bias, while finite replicate count introduces additional Monte Carlo error."
 INTERVAL_SUMMARY = "Percentile, basic, studentised and BCa procedures convert bootstrap distributions into confidence intervals with different accuracy properties."
 VALIDATION_SUMMARY = "Bootstrap analysis should document the resampling scheme, replicate count, interval method, dependence assumptions, simulation checks, RNG and reproducibility."
}

FLOW {
 INPUT
 -> detect_bootstrap_method_context
 -> identify_data_structure_statistic_dependence_model_assumptions_uncertainty_goal_confidence_goal_and_budget
 -> choose_nonparametric_parametric_residual_wild_block_cluster_stratified_or_other_bootstrap_scheme
 -> define_resampling_unit_block_length_strata_clusters_or_model_based_generator
 -> configure_PRNG_seed_streams_and_parallel_replicate_partitioning
 -> generate_bootstrap_samples
 -> compute_statistic_for_each_replicate
 -> construct_bootstrap_distribution
 -> compute_bootstrap_bias_variance_standard_error_and_quantiles
 -> choose_percentile_basic_studentised_BCa_or_other_interval_method
 -> assess_replicate_count_Monte_Carlo_error_coverage_and_scheme_sensitivity
 -> if_large_parallelise_or_distribute_independent_replicates
 -> verify_against_simulated_truth_analytical_known_answer_or_reference_results
 -> document_data_scheme_replications_seed_software_versions_and_provenance
 -> route_to_related_computational_statistics_Monte_Carlo_MCMC_probability_permutation_jackknife_cross_validation_random_process_error_stability_floating_point_HPC_parallel_and_distributed_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Bootstrap Method Ontology defines resampling-based approximation of sampling distributions. It supports empirical and parametric bootstrap methods, pairs and residual bootstrap for regression, wild and multiplier bootstrap, smooth and weighted variants, m-out-of-n and nested bootstrap, moving, circular and stationary block bootstrap for dependent data, cluster, hierarchical and stratified resampling, bootstrap standard errors, bias and variance estimation, percentile, basic, studentised and BCa confidence intervals, jackknife-based acceleration, coverage analysis, bootstrap tests and p-values, replicate-count and Monte Carlo error diagnostics, random-number and seed semantics, parallel and distributed replicate execution, numerical stability, simulation-based verification, benchmarking and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-STATISTICS-BOOTSTRAP-METHOD-ONTOLOGY-V1"
}

}

END_FLOW