Computational Statistics Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Computational Statistics Ontology within the Kireth Research Semantic Library. Computational statistics applies numerical algorithms, simulation, optimisation, resampling and matrix computation to statistical estimation, inference, prediction and uncertainty quantification. This ontology supports Monte Carlo methods, bootstrap and permutation procedures, likelihood computation, Bayesian computation, MCMC, sequential Monte Carlo, variational inference, EM algorithms, numerical integration, optimisation, random-number generation, convergence diagnostics, high-dimensional methods, numerical stability, scalable execution, verification and reproducibility.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = ComputationalStatistics
 ENTITY_CLASS = StatisticalAlgorithmExecutionFramework
 PRIMARY_CONTEXT = ComputationalStatisticsParent
 DEFINITION = "Computational statistics is the algorithmic and numerical execution of statistical methods for estimation, inference, prediction, model fitting and uncertainty analysis."
 SYMBOLIC_FORMS = [
  "theta_hat = argmax_theta log L(theta|data)",
  "E[f(X)] approx (1/N) sum_i f(X_i)",
  "p(theta|y) proportional to p(y|theta)p(theta)",
  "T_boot = T(sample_with_replacement(data))"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for statistical models, Monte Carlo methods, resampling, Bayesian computation, likelihood methods, optimisation, diagnostics, numerical stability and reproducibility."
}

SCOPE {
 INCLUDE = [
  ComputationalStatistics,StatisticalComputing,
  NumericalStatistics,SimulationBasedInference,
  StatisticalInference,StatisticalEstimation,
  StatisticalModel,ProbabilisticModel,
  Parameter,Estimator,Estimate,Statistic,
  SufficientStatistic,SamplingDistribution,
  Likelihood,LogLikelihood,
  MaximumLikelihood,MaximumLikelihoodEstimation,MLE,
  PenalisedLikelihood,ProfileLikelihood,
  ScoreFunction,FisherInformation,
  ObservedInformation,ExpectedInformation,
  BayesianInference,BayesianComputation,
  PriorDistribution,PosteriorDistribution,
  PosteriorPredictiveDistribution,
  MarginalLikelihood,Evidence,
  MonteCarlo,MonteCarloSimulation,
  MonteCarloEstimator,MonteCarloError,
  MonteCarloStandardError,MCSE,
  VarianceReduction,ControlVariate,
  AntitheticVariate,StratifiedSampling,
  ImportanceSampling,ImportanceWeight,
  SelfNormalisedImportanceSampling,
  RejectionSampling,AcceptanceRejection,
  MarkovChainMonteCarlo,MCMC,
  MarkovChain,TransitionKernel,
  StationaryDistribution,DetailedBalance,
  Ergodicity,Mixing,
  MetropolisAlgorithm,MetropolisHastings,
  RandomWalkMetropolis,GibbsSampling,
  BlockedGibbs,SliceSampling,
  HamiltonianMonteCarlo,HMC,
  NoUTurnSampler,NUTS,
  LangevinMonteCarlo,
  MetropolisAdjustedLangevinAlgorithm,MALA,
  AdaptiveMCMC,
  SequentialMonteCarlo,SMC,
  SequentialImportanceSampling,
  ParticleFilter,ParticleSmoother,
  WeightedParticle,ParticleWeight,
  Resampling,MultinomialResampling,
  StratifiedResampling,SystematicResampling,
  ResidualResampling,
  EffectiveSampleSize,ESS,
  AnnealedImportanceSampling,AIS,
  Tempering,BridgeSampling,
  Bootstrap,NonparametricBootstrap,
  ParametricBootstrap,ResidualBootstrap,
  BlockBootstrap,MovingBlockBootstrap,
  StationaryBootstrap,WildBootstrap,
  BootstrapConfidenceInterval,
  PercentileBootstrap,BCaInterval,
  Jackknife,DeleteOneJackknife,
  PermutationTest,RandomisationTest,
  ResamplingDistribution,
  CrossValidation,KFoldCrossValidation,
  LeaveOneOutCrossValidation,LOOCV,
  NestedCrossValidation,
  ModelSelection,ModelComparison,
  AIC,BIC,WAICRelationship,
  PredictivePerformance,
  ExpectationMaximisation,EM,
  GeneralisedEM,GEM,
  VariationalInference,VI,
  MeanFieldVariationalInference,
  StructuredVariationalInference,
  EvidenceLowerBound,ELBO,
  LaplaceApproximation,
  ApproximateBayesianComputation,ABC,
  LikelihoodFreeInference,
  SyntheticLikelihood,
  SimulationBasedInference,
  NumericalIntegration,Quadrature,
  GaussianQuadrature,AdaptiveQuadrature,
  MonteCarloIntegration,
  QuasiMonteCarlo,QMC,
  SobolSequence,HaltonSequence,
  NumericalOptimisation,
  GradientDescent,StochasticGradientDescent,
  NewtonMethod,QuasiNewtonMethod,
  BFGS,LBFGS,TrustRegion,LineSearch,
  CoordinateDescent,ProximalGradient,
  RootFinding,NewtonRaphson,
  FisherScoring,IRLS,
  ConstrainedOptimisation,
  LinearRegression,GeneralisedLinearModel,GLM,
  LogisticRegression,PoissonRegression,
  ProbitRegression,
  MixedModel,HierarchicalModel,
  GeneralisedLinearMixedModel,GLMM,
  LatentVariableModel,MixtureModel,
  GaussianMixtureModel,GMM,
  GaussianProcess,GP,
  StateSpaceModel,HiddenMarkovModel,HMM,
  TimeSeriesModel,ARIMA,
  SurvivalModel,CoxModel,
  PrincipalComponentAnalysis,PCA,
  FactorAnalysis,IndependentComponentAnalysis,ICA,
  Clustering,KMeans,HierarchicalClustering,
  SpectralClustering,
  DensityEstimation,KernelDensityEstimation,KDE,
  NonparametricRegression,
  SmoothingSpline,
  HighDimensionalStatistics,
  Regularisation,L1Regularisation,
  L2Regularisation,Lasso,RidgeRegression,
  ElasticNet,SparseEstimation,Sparsity,
  VariableSelection,FeatureSelection,
  MultipleTesting,FalseDiscoveryRate,FDR,
  EmpiricalBayes,ShrinkageEstimator,
  RandomNumberGeneration,RNG,
  PseudorandomNumberGenerator,PRNG,
  RandomSeed,RandomStream,
  CounterBasedRNG,
  ParallelRandomNumberGeneration,
  DistributionSampling,
  InverseTransformSampling,
  NumericalStability,FloatingPointArithmetic,
  MachinePrecision,RoundOffError,
  Underflow,Overflow,CatastrophicCancellation,
  LogSumExp,StableLikelihood,
  Conditioning,IllConditioning,
  MatrixComputation,LinearAlgebra,
  MatrixDecomposition,
  CholeskyDecomposition,QRDecomposition,
  SingularValueDecomposition,SVD,
  EigenvalueComputation,
  SparseMatrix,SparseLinearAlgebra,
  ComputationalComplexity,
  TimeComplexity,SpaceComplexity,
  Convergence,EstimatorConvergence,
  OptimisationConvergence,MCMCConvergence,
  NumericalConvergence,
  BurnIn,Warmup,
  Autocorrelation,AutocorrelationTime,
  IntegratedAutocorrelationTime,
  EffectiveSampleSizeDiagnostic,
  GelmanRubinStatistic,RHat,
  TracePlot,RankPlot,
  DivergenceDiagnostic,
  AcceptanceRate,
  Bias,Variance,MeanSquaredError,MSE,
  StandardError,ConfidenceInterval,
  CredibleInterval,PredictionInterval,
  HypothesisTesting,TestStatistic,
  PValue,Power,TypeIError,TypeIIError,
  CoverageProbability,
  SimulationBasedCalibration,SBC,
  PosteriorPredictiveCheck,PPC,
  Calibration,ModelCalibration,
  SensitivityAnalysis,
  RobustStatistics,RobustEstimator,
  MEstimator,HuberLoss,
  MissingData,Imputation,
  MultipleImputation,
  DataAugmentation,
  ParallelStatistics,
  DistributedStatistics,
  GPUStatistics,
  HighPerformanceStatisticalComputing,
  VectorisedStatistics,
  ParallelMonteCarlo,
  DistributedMCMC,
  ParallelBootstrap,
  HighPerformanceComputing,
  ParallelComputing,
  DistributedComputing,
  GPUComputing,
  Verification,CodeVerification,
  AlgorithmVerification,Validation,
  Benchmarking,KnownAnswerTest,
  SimulatedTruth,ReferenceResult,
  Reproducibility,Repeatability,
  Provenance,SoftwareVersion,
  LibraryVersion,Configuration
 ]
 EXCLUDE_AS_PRIMARY = [
  PureTheoreticalStatisticsWithoutAlgorithmicExecution,
  GenericDataAnalysisWithoutStatisticalInference,
  DeterministicNumericalAnalysisWithoutStatisticalSemantics,
  MachineLearningWithoutExplicitStatisticalComputationContext
 ]
 DISAMBIGUATION_RULE = "When statistical estimation, inference or uncertainty is computed through numerical algorithms, simulation, optimisation or resampling, interpret the context as computational statistics."
}

CORE_CONCEPTS {
 ComputationalStatistics = "Algorithmic and numerical implementation of statistical methods."
 MonteCarlo = "Statistical approximation using random samples."
 Bootstrap = "Repeated resampling used to approximate sampling distributions."
 MCMC = "Markov-chain simulation used to approximate difficult target distributions."
 SequentialMonteCarlo = "Weighted-particle approximation updated sequentially over time or tempering levels."
 VariationalInference = "Optimisation-based approximation of a probability distribution."
 MaximumLikelihood = "Estimation by maximising likelihood."
 ConvergenceDiagnostic = "Measure assessing numerical, optimisation or sampling convergence."
}

RELATIONS {
 ComputationalStatistics --is_child_of--> ComputationalStatisticsParent
 ComputationalStatistics --uses--> NumericalMethods
 ComputationalStatistics --uses--> ProbabilityAndStatistics
 MonteCarlo --approximates--> Expectation
 MCMC --samples_from--> TargetDistribution
 SequentialMonteCarlo --represents--> DistributionWithWeightedParticles
 ImportanceSampling --uses--> ProposalDistribution
 Bootstrap --approximates--> SamplingDistribution
 PermutationTest --constructs--> NullDistribution
 MaximumLikelihood --uses--> Optimisation
 EM --optimises--> IncompleteDataLikelihood
 VariationalInference --optimises--> ELBO
 ABC --supports--> LikelihoodFreeInference
 MatrixDecomposition --supports--> StatisticalComputation
 Verification --checks--> StatisticalImplementation
 Reproducibility --requires--> SeedAndVersionMetadata
}

OPERATORS {
 MONTE_CARLO_MEAN(f,X) := (1/N)*sum_i f(X_i)
 LOG_LIKELIHOOD(theta,data) := sum_i log p(data_i|theta)
 MLE(data) := argmax_theta LOG_LIKELIHOOD(theta,data)
 POSTERIOR(theta,data) := likelihood(data|theta)*prior(theta)/evidence(data)
 IMPORTANCE_ESTIMATE(f,w,x) := sum_i w_i*f(x_i)/sum_i w_i
 BOOTSTRAP_STATISTIC(data,T) := T(resample_with_replacement(data))
 MH_ACCEPTANCE(x,x_new) := min(1,target(x_new)*q(x|x_new)/(target(x)*q(x_new|x)))
 ESS(weights) := 1/sum_i(normalised_weight_i^2)
 ELBO(q) := E_q[log p(data,theta)-log q(theta)]
}

AXIOMS {
 A1 = "Computational statistics combines statistical modelling with numerical or simulation algorithms."
 A2 = "Stochastic computation introduces Monte Carlo variability."
 A3 = "Numerical convergence and statistical validity are distinct."
 A4 = "Posterior or likelihood approximation quality depends on both algorithm and numerical stability."
 A5 = "Resampling estimates sampling behaviour through repeated recomputation."
 A6 = "Random-number generation and stream design affect reproducibility."
 A7 = "Finite precision can alter likelihoods, covariance operations and tail probabilities."
 A8 = "Computational-statistical results require explicit model, algorithm, convergence, uncertainty and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(statistical_question,data_structure,model,estimand,uncertainty_goal,computational_budget)
 R2_METHOD = classify(likelihood,Bayesian,resampling,MonteCarlo,MCMC,SMC,variational_or_optimisation_method)
 R3_MODEL = define(parameters,latent_variables,priors,likelihoods,constraints_and_target_quantities)
 R4_NUMERICS = choose(stable_linear_algebra,log_domain_methods,optimisation,sampling_and_integration_algorithms)
 R5_RANDOMNESS = configure(PRNG,seed,streams_and_parallel_randomness)
 R6_EXECUTION = run(iterations,samples,resamples,optimisation_or_numerical_integration)
 R7_CONVERGENCE = assess(tolerance,mixing,ESS,MCSE,RHat,resampling_stability_or_numerical_convergence)
 R8_DIAGNOSTICS = evaluate(bias,variance,coverage,predictive_fit,posterior_checks_and_failures)
 R9_SCALING = if_large use(vectorised,parallel,distributed_or_GPU_execution)
 R10_VALIDATE = compare(simulated_truth,known_results,reference_implementations_and_reproducibility)
}

CONSTRAINTS {
 C1 = "Monte Carlo error can remain large when effective sample size is small."
 C2 = "MCMC can mix poorly in multimodal, highly correlated or badly scaled targets."
 C3 = "Importance sampling can collapse when proposal and target overlap is poor."
 C4 = "Bootstrap validity depends on the statistic and dependence structure."
 C5 = "Likelihood computations can underflow without stable transformations."
 C6 = "Ill-conditioned covariance or design matrices can destabilise estimates."
 C7 = "Variational methods can produce biased uncertainty estimates."
 C8 = "Optimisation convergence does not guarantee global optimality or inferential adequacy."
 C9 = "Parallel random streams require deliberate independence or counter-based semantics."
 C10 = "High numerical precision does not guarantee correct statistical modelling assumptions."
}

SEMANTIC_EQUIVALENCE {
 "ComputationalStatistics" <=> "StatisticalComputing"
 "MaximumLikelihoodEstimation" <=> "MLE"
 "MarkovChainMonteCarlo" <=> "MCMC"
 "SequentialMonteCarlo" <=> "SMC"
 "VariationalInference" <=> "VI"
 "ApproximateBayesianComputation" <=> "ABC"
 "EffectiveSampleSize" <=> "ESS"
 "MonteCarloStandardError" <=> "MCSE"
}

VALIDATION {
 V1 = "Statistical model and target estimand are explicit."
 V2 = "Algorithm and numerical settings are documented."
 V3 = "Random-number generator and seed are documented where relevant."
 V4 = "Sampling or optimisation convergence is assessed."
 V5 = "Monte Carlo, bootstrap or approximation uncertainty is quantified where relevant."
 V6 = "Likelihood and matrix calculations are checked for numerical stability."
 V7 = "Simulated truth or known-answer tests are used where feasible."
 V8 = "Predictive, posterior or resampling diagnostics are documented where applicable."
 V9 = "Parallel or distributed random-stream semantics are documented where used."
 V10 = "Results are reproducible under documented data, seed, software and configuration settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 COMPUTATIONAL_STATISTICS_DEFINITION = 0.99
 MONTE_CARLO_REASONING = 0.99
 MCMC_REASONING = 0.99
 SMC_REASONING = 0.99
 BOOTSTRAP_REASONING = 0.99
 VARIATIONAL_REASONING = 0.98
 NUMERICAL_STABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when model assumptions, convergence, RNG, effective sample size, numerical stability, diagnostics or approximation assumptions are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,ComputationalStatisticsReasoning,
  MonteCarloReasoning,BootstrapReasoning,
  PermutationReasoning,MCMCReasoning,
  SequentialMonteCarloReasoning,
  ImportanceSamplingReasoning,
  LikelihoodReasoning,BayesianComputationReasoning,
  VariationalInferenceReasoning,
  EMReasoning,OptimisationReasoning,
  CrossValidationReasoning,
  RandomNumberGenerationReasoning,
  ConvergenceDiagnosticReasoning,
  NumericalStabilityReasoning,
  StatisticalUncertaintyReasoning,
  ScalableStatisticsReasoning,
  ReproducibilityReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "computational statistics" -> ComputationalStatistics
  "statistical computing" -> ComputationalStatistics
  "MLE" -> MaximumLikelihood
  "MCMC" -> MarkovChainMonteCarlo
  "SMC" -> SequentialMonteCarlo
  "VI" -> VariationalInference
  "ABC" -> ApproximateBayesianComputation
  "ESS" -> EffectiveSampleSize
  "MCSE" -> MonteCarloStandardError
 }
}

EXECUTION_RULES {
 E1 = "If statistical inference is executed through numerical, simulation, optimisation or resampling methods, activate ComputationalStatisticsOntology."
 E2 = "Define the estimand, model, data structure and uncertainty target before computation."
 E3 = "Use numerically stable likelihood and matrix operations."
 E4 = "For stochastic methods, document RNG, seed and stream semantics."
 E5 = "Assess convergence using method-appropriate diagnostics."
 E6 = "Quantify Monte Carlo, resampling or approximation error where material."
 E7 = "For MCMC, use multiple chains or other robust diagnostics where appropriate."
 E8 = "For large workloads, use vector, parallel, distributed or GPU computation with explicit reproducibility semantics."
 E9 = "Validate against simulated truth, known results, reference implementations or independent diagnostics."
}

RECURSION {
 ENTRY = ComputationalStatistics
 EXPAND(ComputationalStatistics) -> [
  StatisticalComputing,NumericalStatistics,
  SimulationBasedInference,StatisticalInference,
  StatisticalEstimation,StatisticalModel,
  Parameter,Estimator,Statistic,Likelihood,
  LogLikelihood,MaximumLikelihood,MLE,
  ScoreFunction,FisherInformation,
  BayesianInference,PriorDistribution,
  PosteriorDistribution,PosteriorPredictiveDistribution,
  MonteCarlo,MonteCarloEstimator,
  MonteCarloStandardError,MCSE,
  VarianceReduction,ControlVariate,
  ImportanceSampling,RejectionSampling,
  MarkovChainMonteCarlo,MCMC,
  TransitionKernel,StationaryDistribution,
  MetropolisHastings,GibbsSampling,
  SliceSampling,HamiltonianMonteCarlo,HMC,
  NUTS,LangevinMonteCarlo,MALA,
  SequentialMonteCarlo,SMC,
  ParticleFilter,ParticleSmoother,
  Resampling,EffectiveSampleSize,ESS,
  AnnealedImportanceSampling,Bootstrap,
  ParametricBootstrap,BlockBootstrap,
  WildBootstrap,PermutationTest,
  Jackknife,CrossValidation,
  KFoldCrossValidation,ModelSelection,
  AIC,BIC,ExpectationMaximisation,EM,
  VariationalInference,VI,ELBO,
  LaplaceApproximation,
  ApproximateBayesianComputation,ABC,
  NumericalIntegration,Quadrature,
  QuasiMonteCarlo,QMC,
  NumericalOptimisation,GradientDescent,
  StochasticGradientDescent,NewtonMethod,
  BFGS,LBFGS,RootFinding,
  FisherScoring,IRLS,LinearRegression,
  GLM,LogisticRegression,MixedModel,
  HierarchicalModel,GLMM,GaussianProcess,
  StateSpaceModel,HMM,MixtureModel,GMM,
  PCA,Clustering,KDE,
  HighDimensionalStatistics,
  Regularisation,Lasso,RidgeRegression,
  ElasticNet,MultipleTesting,FDR,
  RandomNumberGeneration,PRNG,
  RandomSeed,ParallelRandomNumberGeneration,
  NumericalStability,FloatingPointArithmetic,
  LogSumExp,Conditioning,
  CholeskyDecomposition,QRDecomposition,
  SVD,SparseMatrix,ComputationalComplexity,
  Convergence,MCMCConvergence,
  BurnIn,Mixing,Autocorrelation,
  IntegratedAutocorrelationTime,
  RHat,TracePlot,Bias,Variance,MSE,
  StandardError,ConfidenceInterval,
  CredibleInterval,HypothesisTesting,
  Power,CoverageProbability,
  SimulationBasedCalibration,
  PosteriorPredictiveCheck,
  RobustStatistics,MissingData,
  MultipleImputation,ParallelStatistics,
  DistributedStatistics,GPUStatistics,
  HighPerformanceStatisticalComputing,
  Verification,Validation,Benchmarking,
  Reproducibility,Provenance
 ]
 EXPAND(ComputationalStatisticsFamilies) -> [
  MonteCarloStatisticalMethods,
  ResamplingAndPermutationMethods,
  BayesianComputationalMethods,
  MCMCandSequentialMonteCarlo,
  LikelihoodAndOptimisationMethods,
  ApproximateInferenceMethods,
  HighDimensionalStatisticalComputation,
  ParallelDistributedAndGPUStatistics
 ]
 STOP_CONDITION = "Stop when statistical model, estimand, algorithm, randomness, numerical method, convergence, diagnostics, uncertainty and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Computational Statistics"
 RELATED_ONTOLOGIES = [
  "Computational Statistics",
  "Probability and Statistics Ontologies",
  "Monte Carlo Simulation Ontology",
  "Random Process Ontology",
  "Optimisation Computation",
  "Numerical Methods Ontology 2",
  "Numerical Linear Algebra Ontology 2",
  "Matrix Computation Ontology",
  "Sparse Matrix Ontology 2",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Convergence Ontology",
  "Floating Point Arithmetic Ontology",
  "High Performance Computing Ontology 2",
  "Parallel Computing Ontology",
  "Distributed Computing Ontology",
  "GPU Computing Ontology"
 ]
 ROUTE_RULES = [
  "Computational Statistics Ontology -> Computational Statistics for parent semantics",
  "Computational Statistics Ontology -> Probability and Statistics for statistical foundations",
  "Computational Statistics Ontology -> Monte Carlo Simulation for sampling-based estimation",
  "Computational Statistics Ontology -> Random Process for Markov-chain and stochastic-state methods",
  "Computational Statistics Ontology -> Optimisation Computation for likelihood and variational optimisation",
  "Computational Statistics Ontology -> Numerical Methods for quadrature and root finding",
  "Computational Statistics Ontology -> Numerical Linear Algebra for regression and covariance computation",
  "Computational Statistics Ontology -> Matrix Computation for dense statistical kernels",
  "Computational Statistics Ontology -> Sparse Matrix for high-dimensional sparse models",
  "Computational Statistics Ontology -> Numerical Error, Stability and Convergence for numerical reliability",
  "Computational Statistics Ontology -> Floating Point Arithmetic for underflow, overflow and reduction effects",
  "Computational Statistics Ontology -> High Performance, Parallel, Distributed and GPU Computing for scalable execution"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible computational-statistical methods, diagnostics or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve statistical-model-versus-computational-method distinction.",
  "Preserve stochastic-error-versus-numerical-error distinction.",
  "Preserve convergence-versus-validity distinction.",
  "Preserve prior-versus-likelihood-versus-posterior distinction.",
  "Preserve resampling-versus-generative-simulation distinction.",
  "Preserve exact-versus-approximate inference distinction.",
  "Preserve serial-versus-parallel random-stream semantics.",
  "Preserve machine-readable computational-statistics semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Computational statistics implements statistical estimation and inference through numerical algorithms, simulation, optimisation and resampling."
 MONTE_CARLO_SUMMARY = "Monte Carlo methods approximate expectations, integrals and distributions using random samples."
 RESAMPLING_SUMMARY = "Bootstrap, jackknife and permutation methods estimate sampling behaviour through repeated recomputation."
 BAYESIAN_SUMMARY = "MCMC, SMC, importance sampling, ABC and variational methods approximate Bayesian quantities."
 LIKELIHOOD_SUMMARY = "Maximum-likelihood, EM, Fisher scoring and numerical optimisation fit parameterised statistical models."
 DIAGNOSTIC_SUMMARY = "ESS, MCSE, R-hat, predictive checks, coverage and numerical diagnostics assess computational reliability."
 VALIDATION_SUMMARY = "Computational-statistical results should be checked through simulated truth, known-answer tests, convergence diagnostics, uncertainty quantification, numerical stability and reproducibility."
}

FLOW {
 INPUT
 -> detect_computational_statistics_context
 -> identify_statistical_question_data_structure_model_estimand_uncertainty_goal_and_computational_budget
 -> classify_likelihood_Bayesian_resampling_Monte_Carlo_MCMC_SMC_variational_or_optimisation_method
 -> define_parameters_latent_variables_priors_likelihood_constraints_and_target_quantities
 -> choose_stable_linear_algebra_log_domain_optimisation_sampling_and_integration_algorithms
 -> configure_PRNG_seed_streams_and_parallel_randomness_if_stochastic
 -> execute_iterations_samples_resamples_optimisation_or_numerical_integration
 -> assess_optimisation_tolerance_mixing_ESS_MCSE_RHat_resampling_stability_or_numerical_convergence
 -> check_bias_variance_coverage_predictive_fit_posterior_diagnostics_and_numerical_failures
 -> if_large_vectorise_parallelise_distribute_or_GPU_accelerate_computation
 -> verify_against_simulated_truth_known_results_reference_implementations_or_benchmarks
 -> quantify_statistical_computational_and_numerical_uncertainty
 -> document_data_seed_software_versions_library_versions_configuration_and_provenance
 -> route_to_related_parent_probability_statistics_Monte_Carlo_random_process_optimisation_numerical_methods_linear_algebra_matrix_sparse_error_stability_convergence_floating_point_HPC_parallel_distributed_and_GPU_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Computational Statistics Ontology defines numerical and algorithmic execution of statistical methods. It supports likelihood and maximum-likelihood computation, Bayesian inference, Monte Carlo estimators and variance reduction, importance and rejection sampling, MCMC including Metropolis-Hastings, Gibbs, HMC, NUTS and Langevin methods, sequential Monte Carlo and particle filtering, bootstrap, block and wild bootstrap, permutation and jackknife methods, cross-validation, EM, variational inference, Laplace and approximate Bayesian computation, numerical integration and quasi-Monte Carlo, gradient, Newton, quasi-Newton and stochastic optimisation, regression, GLMs, mixed and hierarchical models, Gaussian processes, state-space and mixture models, PCA, clustering, density estimation, regularisation and multiple testing, random-number generation, numerical stability, matrix decompositions, convergence and MCMC diagnostics, MCSE, R-hat, simulation-based calibration, posterior predictive checking, missing-data computation, parallel, distributed and GPU execution, verification, validation and reproducibility."
}

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

}

END_FLOW