Statistical Sampling Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Statistical Sampling Ontology within the Kireth Research Semantic Library. Statistical sampling concerns the selection of observations, units, cases or generated draws from a population or probability distribution in order to estimate characteristics, perform inference, construct experiments or support simulation. This ontology supports probability and nonprobability sampling, simple random sampling, stratified, cluster, systematic and multistage designs, sampling frames, inclusion probabilities, weights, finite-population correction, design effects, unequal-probability sampling, survey sampling, resampling relationships, distribution sampling, bias, variance, sample-size determination, diagnostics, reproducibility and computational execution.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = StatisticalSampling
 ENTITY_CLASS = PopulationAndDistributionSamplingFramework
 PRIMARY_CONTEXT = ComputationalStatistics
 DEFINITION = "Statistical sampling is the selection of units or random draws from a population or probability distribution according to a declared sampling design or stochastic mechanism."
 SYMBOLIC_FORMS = [
  "S subset_of U",
  "pi_i = P(i in S)",
  "w_i = 1/pi_i",
  "theta_hat = estimator(sample,weights,design)"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for sampling populations, frames, inclusion probabilities, sample designs, weights, random draws, design-based estimation, bias, variance, sample size and reproducibility."
}

SCOPE {
 INCLUDE = [
  StatisticalSampling,Sampling,SampleSelection,
  PopulationSampling,ProbabilitySampling,
  NonProbabilitySampling,SurveySampling,
  SamplingDesign,SampleDesign,
  TargetPopulation,StudyPopulation,
  FinitePopulation,Superpopulation,
  PopulationUnit,SamplingUnit,ObservationUnit,
  PrimarySamplingUnit,PSU,
  SecondarySamplingUnit,SSU,
  TertiarySamplingUnit,
  SamplingFrame,FramePopulation,
  FrameCoverage,CoverageError,
  Undercoverage,Overcoverage,
  DuplicateFrameUnit,
  Sample,SampleUnit,SampleSize,
  Census,PartialEnumeration,
  SimpleRandomSampling,SRS,
  SimpleRandomSamplingWithReplacement,
  SimpleRandomSamplingWithoutReplacement,
  SRSWR,SRSWOR,
  BernoulliSampling,
  PoissonSampling,
  SystematicSampling,
  RandomStart,SystematicInterval,
  StratifiedSampling,
  Stratum,Stratification,
  ProportionalAllocation,
  DisproportionalAllocation,
  NeymanAllocation,OptimalAllocation,
  PostStratificationRelationship,
  ClusterSampling,Cluster,
  OneStageClusterSampling,
  TwoStageClusterSampling,
  MultistageSampling,
  AreaSampling,
  SpatialSampling,
  PPSsampling,ProbabilityProportionalToSize,
  PPSWithReplacement,
  PPSWithoutReplacement,
  UnequalProbabilitySampling,
  InclusionProbability,
  FirstOrderInclusionProbability,
  SecondOrderInclusionProbability,
  JointInclusionProbability,
  SelectionProbability,
  SampleWeight,SamplingWeight,
  DesignWeight,InverseProbabilityWeight,
  BaseWeight,FinalWeight,
  WeightAdjustment,
  NonresponseAdjustment,
  CalibrationWeightRelationship,
  RakingRelationship,
  HorvitzThompsonEstimator,
  HansenHurwitzEstimator,
  RatioEstimator,
  RegressionEstimator,
  DifferenceEstimator,
  GeneralisedRegressionEstimator,GREG,
  DesignBasedInference,
  ModelAssistedInference,
  ModelBasedSamplingRelationship,
  SamplingDistribution,
  SamplingVariance,
  DesignVariance,
  DesignBias,
  SamplingBias,
  SelectionBias,
  NonresponseBias,
  CoverageBias,
  ResponseBiasRelationship,
  FinitePopulationCorrection,FPC,
  SamplingFraction,
  DesignEffect,DEFF,
  EffectiveSampleSize,
  IntraclusterCorrelation,ICC,
  ClusterEffect,
  StratificationGain,
  Precision,MarginOfError,
  StandardError,
  RelativeStandardError,
  ConfidenceInterval,
  ConfidenceLevel,
  SampleSizeDetermination,
  PowerBasedSampleSizeRelationship,
  PrecisionBasedSampleSize,
  CostConstrainedSampleSize,
  AllocationProblem,
  PilotSample,PilotStudy,
  DomainEstimation,SubpopulationEstimation,
  SmallAreaEstimationRelationship,
  RarePopulationSampling,
  AdaptiveSampling,
  AdaptiveClusterSampling,
  NetworkSamplingRelationship,
  SnowballSampling,
  RespondentDrivenSamplingRelationship,
  ConvenienceSampling,
  QuotaSampling,
  PurposiveSampling,
  JudgmentSampling,
  VolunteerSampling,
  ConsecutiveSampling,
  NonprobabilityWeightingRelationship,
  MatchingAdjustmentRelationship,
  RandomDigitDiallingRelationship,
  MultiFrameSampling,
  DualFrameSampling,
  CaptureRecaptureRelationship,
  PanelSampling,
  LongitudinalSampling,
  RotatingPanel,
  RepeatedCrossSection,
  ReplacementPanel,
  ReservoirSampling,
  StreamSampling,
  SamplingWithoutReplacement,
  SamplingWithReplacement,
  RandomSubset,
  RandomPermutation,
  FisherYatesShuffle,
  DistributionSampling,
  RandomVariableSampling,
  DirectSampling,
  InverseTransformSampling,
  RejectionSampling,
  AcceptanceRejection,
  CompositionSampling,
  ImportanceSamplingRelationship,
  MonteCarloSampling,
  MarkovChainSamplingRelationship,
  SequentialMonteCarloRelationship,
  BootstrapResamplingRelationship,
  QuasiMonteCarloRelationship,
  RandomNumberGeneration,
  RNG,PRNG,RandomSeed,
  RandomStream,
  IndependentRandomStream,
  ParallelRandomNumberGeneration,
  ReproducibleSampling,
  Randomisation,RandomAssignmentRelationship,
  ExperimentalSamplingRelationship,
  MissingDataRelationship,
  UnitNonresponse,ItemNonresponse,
  ResponseRate,CooperationRateRelationship,
  ContactRateRelationship,
  WeightTrimming,WeightWinsorisationRelationship,
  CalibrationRelationship,
  BenchmarkingWeightsRelationship,
  ReplicateWeights,
  JackknifeReplicateWeights,
  BootstrapReplicateWeights,
  BRRRelationship,
  BalancedRepeatedReplicationRelationship,
  FayMethodRelationship,
  VarianceEstimation,
  TaylorLinearisationRelationship,
  ReplicationVarianceEstimation,
  JackknifeVarianceRelationship,
  BootstrapVarianceRelationship,
  RandomGroupVarianceRelationship,
  MonteCarloError,
  ComputationalSampling,
  ParallelSampling,
  DistributedSampling,
  GPUSamplingRelationship,
  BatchSampling,
  VectorisedSampling,
  ComputationalComplexity,
  TimeComplexity,SpaceComplexity,
  Verification,CodeVerification,
  KnownPopulationTest,
  SimulationStudy,
  ReferenceResult,
  Reproducibility,Repeatability,
  Provenance,Configuration,
  SoftwareVersion,LibraryVersion,
  SeedMetadata
 ]
 EXCLUDE_AS_PRIMARY = [
  ResamplingMethodsWhenOriginalSampleIsRepeatedlyReusedForUncertaintyEstimation,
  MarkovChainMonteCarloWhenDependentMarkovTransitionsArePrimary,
  ExperimentalRandomisationWhenTreatmentAssignmentRatherThanPopulationSelectionIsPrimary,
  DataCollectionWithoutSamplingDesignOrProbabilitySemantics
 ]
 DISAMBIGUATION_RULE = "When units or draws are selected from a population or probability distribution according to a declared design or stochastic selection mechanism, interpret the context as statistical sampling."
}

CORE_CONCEPTS {
 StatisticalSampling = "Selection of units or random draws for statistical inference or simulation."
 SamplingFrame = "Operational representation of the population from which units can be selected."
 InclusionProbability = "Probability that a population unit is included in the sample."
 SamplingWeight = "Weight representing the inverse or adjusted inverse of selection probability."
 SimpleRandomSampling = "Probability sample in which eligible samples or units have equal selection probabilities under the declared design."
 StratifiedSampling = "Sampling conducted separately within defined population strata."
 ClusterSampling = "Sampling in which groups of population units are selected as sampling units."
 SampleSize = "Number of selected or generated observations used in the analysis."
}

RELATIONS {
 StatisticalSampling --is_child_of--> ComputationalStatistics
 StatisticalSampling --selects_from--> Population
 SamplingDesign --defines--> SelectionMechanism
 SamplingFrame --represents--> Population
 InclusionProbability --determines--> DesignWeight
 DesignWeight --supports--> DesignBasedEstimator
 SimpleRandomSampling --is_type_of--> ProbabilitySampling
 StratifiedSampling --partitions--> PopulationIntoStrata
 ClusterSampling --selects--> Clusters
 MultistageSampling --contains--> SequentialSamplingStages
 PPSsampling --uses--> SizeMeasure
 HorvitzThompsonEstimator --uses--> InclusionProbabilities
 FinitePopulationCorrection --depends_on--> SamplingFraction
 DesignEffect --compares--> ActualDesignVarianceToSRSVariance
 RandomNumberGeneration --supports--> ComputationalSampling
 Verification --checks--> SamplingImplementation
 Reproducibility --requires--> DesignSeedAndFrameMetadata
}

OPERATORS {
 SRSWOR(U,n) := uniformly_select_n_distinct_units(U)
 SRSWR(U,n) := independently_select_n_units_with_replacement(U)
 STRATIFIED_SAMPLE(U_h,n_h) := union_h SRS(U_h,n_h)
 SYSTEMATIC_SAMPLE(U,k,r) := select_indices(r,r+k,r+2k,...)
 PPS_SELECT(U,size_measure,n) := sample_with_probability_proportional_to_size
 DESIGN_WEIGHT(pi_i) := 1/pi_i
 HORVITZ_THOMPSON(y,pi) := sum_(i in S) y_i/pi_i
 FPC(N,n) := sqrt((N-n)/(N-1))
 DESIGN_EFFECT(var_design,var_srs) := var_design/var_srs
}

AXIOMS {
 A1 = "Probability sampling requires known or computable selection probabilities."
 A2 = "Sampling design and estimator must be interpreted together."
 A3 = "Sampling weights encode unequal selection and adjustment semantics."
 A4 = "Frame imperfections can create coverage bias even under correct random selection."
 A5 = "Cluster sampling can increase variance when units within clusters are positively correlated."
 A6 = "Stratification can reduce variance when strata are internally homogeneous."
 A7 = "Sample size affects precision but does not repair systematic selection bias."
 A8 = "Statistical-sampling results require explicit population, frame, design, weight, uncertainty and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(target_population,frame,estimand,precision_goal,cost_constraints,dependence_and_logistics)
 R2_DESIGN = choose(census,SRS,systematic,stratified,cluster,multistage,PPS,adaptive_or_nonprobability_design)
 R3_UNITS = define(primary_secondary_or_other_sampling_units_and_stage_structure)
 R4_PROBABILITIES = derive(selection_and_inclusion_probabilities)
 R5_WEIGHTS = compute(base_weights_and_adjustments_if_required)
 R6_SIZE = determine(sample_size_and_allocation_using_precision_cost_or_power_constraints)
 R7_SELECTION = configure_RNG_seed_random_start_streams_and_selection_algorithm)
 R8_ESTIMATION = choose(design_based_model_assisted_or_model_based_estimator
 R9_VARIANCE = estimate(design_variance,FPC,DEFF,replicate_or_linearisation_uncertainty)
 R10_VALIDATE = assess(frame_coverage,bias,nonresponse,weighting,simulation_checks_and_reproducibility)
}

CONSTRAINTS {
 C1 = "A deficient sampling frame can bias otherwise correct probability sampling."
 C2 = "Ignoring unequal inclusion probabilities can bias population estimates."
 C3 = "Cluster correlation can substantially reduce effective sample size."
 C4 = "Systematic sampling can interact badly with periodic ordering in the frame."
 C5 = "Extreme weights can inflate variance and destabilise estimates."
 C6 = "Nonresponse adjustments depend on assumptions about response mechanisms."
 C7 = "Nonprobability samples generally lack design-based inclusion probabilities."
 C8 = "Very small strata or clusters can create unstable variance estimates."
 C9 = "Parallel sample selection requires reproducible and nonoverlapping random streams."
 C10 = "Large sample size does not eliminate coverage, selection or measurement bias."
}

SEMANTIC_EQUIVALENCE {
 "StatisticalSampling" <=> "Sampling"
 "SimpleRandomSampling" <=> "SRS"
 "SimpleRandomSamplingWithReplacement" <=> "SRSWR"
 "SimpleRandomSamplingWithoutReplacement" <=> "SRSWOR"
 "ProbabilityProportionalToSize" <=> "PPS"
 "FinitePopulationCorrection" <=> "FPC"
 "DesignEffect" <=> "DEFF"
 "IntraclusterCorrelation" <=> "ICC"
}

VALIDATION {
 V1 = "Target population and sampling frame are documented."
 V2 = "Sampling units and stage structure are documented."
 V3 = "Selection and inclusion probabilities are documented for probability designs."
 V4 = "Sampling weights and adjustments are documented."
 V5 = "Randomisation algorithm, seed and stream semantics are documented."
 V6 = "Sample-size and allocation calculations are documented."
 V7 = "Variance estimation method is compatible with the sampling design."
 V8 = "Coverage, nonresponse and selection biases are assessed."
 V9 = "Simulation or known-population tests are used where implementation is complex."
 V10 = "Results are reproducible under documented frame, design, seed, software and configuration settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 STATISTICAL_SAMPLING_DEFINITION = 0.99
 SRS_REASONING = 0.99
 STRATIFIED_REASONING = 0.99
 CLUSTER_REASONING = 0.99
 PPS_REASONING = 0.98
 WEIGHTING_REASONING = 0.99
 SAMPLE_SIZE_REASONING = 0.98
 POLICY = "Reduce confidence when population, frame, inclusion probabilities, weights, design stages, nonresponse or variance-estimation method are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,StatisticalSamplingReasoning,
  PopulationSamplingReasoning,SamplingFrameReasoning,
  InclusionProbabilityReasoning,WeightingReasoning,
  SRSReasoning,SystematicSamplingReasoning,
  StratifiedSamplingReasoning,ClusterSamplingReasoning,
  MultistageSamplingReasoning,PPSReasoning,
  SampleSizeReasoning,DesignEffectReasoning,
  SurveySamplingReasoning,DistributionSamplingReasoning,
  RNGReasoning,ParallelSamplingReasoning,
  VerificationReasoning,ReproducibilityReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "statistical sampling" -> StatisticalSampling
  "sampling" -> StatisticalSampling
  "SRS" -> SimpleRandomSampling
  "SRSWR" -> SimpleRandomSamplingWithReplacement
  "SRSWOR" -> SimpleRandomSamplingWithoutReplacement
  "PPS" -> ProbabilityProportionalToSize
  "FPC" -> FinitePopulationCorrection
  "DEFF" -> DesignEffect
  "ICC" -> IntraclusterCorrelation
 }
}

EXECUTION_RULES {
 E1 = "If units or random draws are selected from a population or distribution for statistical use, activate StatisticalSamplingOntology."
 E2 = "Define target population, sampling frame and estimand before choosing the design."
 E3 = "Use probability designs when design-based inference is required."
 E4 = "Compute and preserve inclusion probabilities and weights for unequal-probability designs."
 E5 = "Match variance estimation to stratified, clustered, multistage or unequal-probability structure."
 E6 = "Assess frame coverage and nonresponse separately from random sampling error."
 E7 = "Use reproducible RNG and stream semantics for computational sample selection."
 E8 = "For parallel selection, prevent duplicate or overlapping stream assignments."
 E9 = "Validate complex designs through known-population or simulation studies."
}

RECURSION {
 ENTRY = StatisticalSampling
 EXPAND(StatisticalSampling) -> [
  Sampling,SampleSelection,PopulationSampling,
  ProbabilitySampling,NonProbabilitySampling,
  SurveySampling,SamplingDesign,
  TargetPopulation,FinitePopulation,
  PopulationUnit,SamplingUnit,
  PrimarySamplingUnit,PSU,
  SecondarySamplingUnit,SSU,
  SamplingFrame,FrameCoverage,
  CoverageError,Sample,SampleSize,
  SimpleRandomSampling,SRS,
  SRSWR,SRSWOR,BernoulliSampling,
  PoissonSampling,SystematicSampling,
  RandomStart,StratifiedSampling,
  Stratum,ProportionalAllocation,
  NeymanAllocation,ClusterSampling,
  OneStageClusterSampling,
  TwoStageClusterSampling,
  MultistageSampling,AreaSampling,
  ProbabilityProportionalToSize,PPS,
  UnequalProbabilitySampling,
  InclusionProbability,JointInclusionProbability,
  SamplingWeight,DesignWeight,
  InverseProbabilityWeight,
  NonresponseAdjustment,
  HorvitzThompsonEstimator,
  HansenHurwitzEstimator,
  RatioEstimator,RegressionEstimator,
  DesignBasedInference,SamplingVariance,
  SamplingBias,SelectionBias,
  FinitePopulationCorrection,FPC,
  SamplingFraction,DesignEffect,DEFF,
  EffectiveSampleSize,
  IntraclusterCorrelation,ICC,
  MarginOfError,SampleSizeDetermination,
  DomainEstimation,AdaptiveSampling,
  SnowballSampling,ConvenienceSampling,
  QuotaSampling,PurposiveSampling,
  MultiFrameSampling,PanelSampling,
  ReservoirSampling,SamplingWithoutReplacement,
  SamplingWithReplacement,RandomPermutation,
  DistributionSampling,InverseTransformSampling,
  RejectionSampling,MonteCarloSampling,
  BootstrapResampling,RandomNumberGeneration,
  RNG,PRNG,RandomSeed,RandomStream,
  UnitNonresponse,ResponseRate,
  WeightTrimming,ReplicateWeights,
  VarianceEstimation,ReplicationVarianceEstimation,
  ComputationalSampling,ParallelSampling,
  DistributedSampling,VectorisedSampling,
  Verification,SimulationStudy,
  KnownPopulationTest,Reproducibility,
  Provenance
 ]
 EXPAND(StatisticalSamplingFamilies) -> [
  SimpleRandomAndSystematicSampling,
  StratifiedSampling,
  ClusterAndMultistageSampling,
  UnequalProbabilityAndPPSSampling,
  SurveyWeightingAndVarianceEstimation,
  NonProbabilitySampling,
  DistributionAndComputationalSampling,
  ParallelAndReproducibleSampling
 ]
 STOP_CONDITION = "Stop when population, frame, units, design, inclusion probabilities, weights, sample size, variance, bias 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",
  "Bootstrap Method Ontology",
  "Random Number Generation Ontology",
  "Probability and Statistics Ontologies",
  "Random Process Ontology",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology"
 ]
 ROUTE_RULES = [
  "Statistical Sampling -> Computational Statistics Ontology for parent semantics",
  "Statistical Sampling -> Monte Carlo Method when independent stochastic draws are used for estimation",
  "Statistical Sampling -> Markov Chain Monte Carlo when sample dependence arises from Markov transitions",
  "Statistical Sampling -> Bootstrap Method when repeated resampling of an observed sample is primary",
  "Statistical Sampling -> Random Number Generation for reproducible random selection",
  "Statistical Sampling -> Probability and Statistics for sampling-distribution and estimator foundations",
  "Statistical Sampling -> Random Process for temporally or spatially dependent sampling relationships",
  "Statistical Sampling -> Numerical Error and Stability for computational weighting and accumulation",
  "Statistical Sampling -> High Performance, Parallel and Distributed Computing for large-scale sampling"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible sampling designs, weighting methods or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve population-versus-sample distinction.",
  "Preserve sampling-frame-versus-target-population distinction.",
  "Preserve probability-versus-nonprobability sampling distinction.",
  "Preserve inclusion-probability-versus-sampling-weight distinction.",
  "Preserve stratification-versus-clustering distinction.",
  "Preserve sampling-error-versus-selection-bias distinction.",
  "Preserve original-sampling-versus-resampling distinction.",
  "Preserve machine-readable statistical-sampling semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Statistical sampling selects units or random draws from a population or probability distribution according to a declared design."
 FRAME_SUMMARY = "Sampling frames operationalise target populations but can introduce coverage error."
 DESIGN_SUMMARY = "Simple random, systematic, stratified, cluster, multistage and PPS designs define different selection probabilities and dependence structures."
 WEIGHTING_SUMMARY = "Sampling weights convert unequal-probability selections into design-consistent population estimation when used appropriately."
 PRECISION_SUMMARY = "Sample size, stratification, clustering, finite-population correction and design effect determine sampling precision."
 BIAS_SUMMARY = "Coverage, selection and nonresponse bias are distinct from random sampling error."
 VALIDATION_SUMMARY = "Sampling procedures should document population, frame, selection probabilities, weights, sample size, variance method, RNG, implementation checks and reproducibility."
}

FLOW {
 INPUT
 -> detect_statistical_sampling_context
 -> identify_target_population_sampling_frame_estimand_precision_goal_cost_constraints_dependence_and_logistics
 -> choose_census_SRS_systematic_stratified_cluster_multistage_PPS_adaptive_or_nonprobability_design
 -> define_sampling_units_stage_structure_strata_clusters_and_size_measures
 -> derive_selection_and_inclusion_probabilities
 -> compute_base_weights_and_required_adjustments
 -> determine_sample_size_and_allocation
 -> configure_random_start_PRNG_seed_streams_and_selection_algorithm
 -> execute_sample_selection
 -> choose_design_based_model_assisted_or_model_based_estimator
 -> estimate_sampling_variance_FPC_design_effect_and_effective_sample_size
 -> assess_frame_coverage_nonresponse_selection_bias_and_weight_extremes
 -> if_large_parallelise_or_distribute_selection_with_reproducible_streams
 -> verify_against_known_population_simulation_or_reference_results
 -> document_frame_design_weights_seed_versions_and_provenance
 -> route_to_related_computational_statistics_Monte_Carlo_MCMC_bootstrap_RNG_probability_random_process_error_stability_HPC_parallel_and_distributed_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Statistical Sampling Ontology defines selection of units or random draws for statistical inference and computation. It supports target and finite populations, sampling frames and coverage error, primary and secondary sampling units, simple random sampling with and without replacement, Bernoulli and Poisson sampling, systematic sampling, stratification and Neyman allocation, cluster and multistage sampling, area and spatial sampling, probability-proportional-to-size and unequal-probability designs, inclusion probabilities, design and inverse-probability weights, Horvitz-Thompson and Hansen-Hurwitz estimation, finite-population correction, design effects and effective sample size, sample-size determination, adaptive and nonprobability methods, panel and reservoir sampling, distribution sampling, RNG and reproducible random selection, nonresponse adjustment, replicate weights, design-compatible variance estimation, parallel and distributed sampling, verification, simulation testing and reproducibility."
}

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

}

END_FLOW