Risk Analysis Ontology

flow "RiskAnalysisOntology" v4.0

# RISK ANALYSIS ONTOLOGY
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/risk-decision-mathematics/risk-analysis-ontology.html"
  title: "Risk Analysis Ontology"
  domain: "Probability and Statistics"
  category: "Risk & Decision Mathematics"
  entity: RISK_ANALYSIS
  entity_type: RISK_DECISION_ONTOLOGY

DEFINE:
  RISK_ANALYSIS :=
    FORMAL_FRAMEWORK(
      HAZARDS,
      EVENTS,
      PROBABILITIES,
      CONSEQUENCES,
      EXPOSURE,
      VULNERABILITY,
      UNCERTAINTY,
      RISK_MEASURES,
      DECISION_RESPONSES
    )

PURPOSE:
  IDENTIFY:
    HAZARDS
    FAILURE_MODES
    UNCERTAIN_EVENTS
  QUANTIFY:
    LIKELIHOOD
    CONSEQUENCE
    EXPECTED_LOSS
    TAIL_RISK
    UNCERTAINTY
  SUPPORT:
    RISK_MANAGEMENT
    DECISION_MAKING
    PRIORITISATION
    MITIGATION
    MONITORING

FOUNDATION:
  EVENT: E
  PROBABILITY: P(E)
  CONSEQUENCE: C(E)
  SIMPLE_EXPECTED_RISK:
    R := SUM_i P(E_i)*C(E_i)
  RANDOM_LOSS: L
  LOSS_DISTRIBUTION:
    F_L(l) := P(L <= l)

ENTITIES:
  RISK: UNCERTAIN_CONSEQUENCE_MEASURE
  HAZARD: POTENTIAL_SOURCE_OF_HARM
  EVENT: POSSIBLE_OCCURRENCE
  THREAT: POTENTIAL_CAUSE_OF_ADVERSE_EVENT
  EXPOSURE: DEGREE_OF_CONTACT_WITH_HAZARD
  VULNERABILITY: SUSCEPTIBILITY_TO_HARM
  CONSEQUENCE: RESULT_OF_EVENT
  LOSS: NEGATIVE_CONSEQUENCE
  LIKELIHOOD: EVENT_PROBABILITY_OR_FREQUENCY
  UNCERTAINTY: IMPERFECT_KNOWLEDGE_OR_RANDOMNESS
  RISK_MEASURE: QUANTITATIVE_RISK_SUMMARY
  MITIGATION: RISK_REDUCTION_ACTION
  RESIDUAL_RISK: RISK_REMAINING_AFTER_CONTROLS

RELATIONSHIPS:
  HAZARD -> MAY_CAUSE -> EVENT
  EVENT -> PRODUCES -> CONSEQUENCE
  EXPOSURE -> MODIFIES -> EVENT_LIKELIHOOD_OR_CONSEQUENCE
  VULNERABILITY -> MODIFIES -> CONSEQUENCE
  PROBABILITY -> WEIGHTS -> CONSEQUENCE
  CONSEQUENCE -> CONTRIBUTES_TO -> RISK
  MITIGATION -> REDUCES -> RISK
  CONTROLS -> LEAVE -> RESIDUAL_RISK
  UNCERTAINTY -> AFFECTS -> RISK_ESTIMATE

RISK_CONCEPT:
  RISK := FUNCTION(LIKELIHOOD,CONSEQUENCE)
  caution:
    RISK != PROBABILITY_ALONE
    RISK != CONSEQUENCE_ALONE

EXPECTED_LOSS:
  E[L] := SUM_l l*P(L=l)
  continuous:
    E[L] := INTEGRAL l*f_L(l) dl

EVENT_RISK:
  R_i := P(E_i)*C(E_i)
  total:
    R := SUM_i R_i
    WHEN:
      ADDITIVE_EXPECTED_CONSEQUENCE_MODEL_APPROPRIATE

RISK_MATRIX:
  axes:
    LIKELIHOOD
    CONSEQUENCE
  cells:
    QUALITATIVE_OR_ORDINAL_RISK_LEVEL
  caution:
    ORDINAL_MATRIX_DOES_NOT_PRESERVE_PRECISE_QUANTITATIVE_DIFFERENCES

LIKELIHOOD:
  representations:
    - PROBABILITY
    - FREQUENCY
    - RATE
    - ORDINAL_CATEGORY
  requirement:
    TIME_HORIZON_AND_REFERENCE_POPULATION_MUST_BE_EXPLICIT

CONSEQUENCE:
  dimensions:
    - FINANCIAL
    - SAFETY
    - OPERATIONAL
    - ENVIRONMENTAL
    - TECHNICAL
    - REPUTATIONAL
    - STRATEGIC

RISK_IDENTIFICATION:
  methods:
    - CHECKLIST
    - EXPERT_ELICITATION
    - HISTORICAL_DATA
    - PROCESS_MAPPING
    - HAZARD_ANALYSIS
    - FAILURE_MODE_ANALYSIS
    - SCENARIO_ANALYSIS

QUALITATIVE_RISK_ANALYSIS:
  inputs:
    EXPERT_JUDGEMENT
    ORDINAL_SCALES
    CATEGORIES
  caution:
    ORDINAL_SCORES_SHOULD_NOT_BE_TREATED_AS_INTERVAL_SCALE_WITHOUT_JUSTIFICATION

QUANTITATIVE_RISK_ANALYSIS:
  inputs:
    PROBABILITY_DISTRIBUTIONS
    LOSS_MODELS
    FREQUENCY_MODELS
    DEPENDENCE_MODELS
  outputs:
    - EXPECTED_LOSS
    - LOSS_DISTRIBUTION
    - QUANTILES
    - VALUE_AT_RISK
    - EXPECTED_SHORTFALL
    - EXCEEDANCE_PROBABILITY

FREQUENCY_SEVERITY_MODEL:
  event_count: N
  severities: X_1,...,X_N
  aggregate_loss:
    S := SUM[i=1..N] X_i

EXCEEDANCE_PROBABILITY:
  P_exceed := P(L > l)

RETURN_PERIOD:
  approximate:
    T := 1/p
  caution:
    DOES_NOT_MEAN_EVENT_OCCURS_REGULARLY_EVERY_T_PERIODS

VALUE_AT_RISK:
  alias: VaR
  VaR_alpha(L) := inf{l: P(L <= l) >= alpha}
  caution:
    DOES_NOT_CAPTURE_TAIL_SEVERITY_BEYOND_QUANTILE

EXPECTED_SHORTFALL:
  aliases:
    ES
    CVaR
  role:
    SUMMARISE_EXPECTED_UPPER_TAIL_LOSS

TAIL_RISK:
  measures:
    - HIGH_QUANTILES
    - EXPECTED_SHORTFALL
    - EXCEEDANCE_PROBABILITY
    - EXTREME_VALUE_METHODS

UNCERTAINTY:
  ALEATORIC:
    INHERENT_RANDOM_VARIABILITY
  EPISTEMIC:
    LIMITED_KNOWLEDGE_MODEL_OR_PARAMETER_UNCERTAINTY

UNCERTAINTY_PROPAGATION:
  model:
    Y := g(X)
  methods:
    - ANALYTIC_PROPAGATION
    - MONTE_CARLO_SIMULATION
    - DELTA_METHOD
    - BAYESIAN_POSTERIOR_PREDICTIVE

MONTE_CARLO_RISK_ANALYSIS:
  flow:
    DEFINE_INPUT_DISTRIBUTIONS
      -> SAMPLE_INPUTS
      -> RUN_RISK_MODEL
      -> RECORD_OUTCOME
      -> REPEAT
      -> ESTIMATE_LOSS_DISTRIBUTION
      -> COMPUTE_RISK_MEASURES
  requirement:
    DEPENDENCE_BETWEEN_INPUTS_SHOULD_BE_MODELLED_WHEN_RELEVANT

DEPENDENCE:
  issue:
    RISKS_MAY_BE_CORRELATED_OR_DEPENDENT
  methods:
    - CORRELATION_MODELS
    - COPULAS
    - MULTIVARIATE_DISTRIBUTIONS
    - CONDITIONAL_MODELS

SCENARIO_ANALYSIS:
  purpose:
    EXAMINE_PLAUSIBLE_FUTURES_AND_CONSEQUENCES

STRESS_TESTING:
  scenario:
    EXTREME_BUT_PLAUSIBLE
  purpose:
    TEST_RESILIENCE_SYSTEM_FAILURE_AND_DECISION_ROBUSTNESS

SENSITIVITY_ANALYSIS:
  vary:
    - EVENT_PROBABILITY
    - LOSS_SEVERITY
    - MODEL_PARAMETER
    - DEPENDENCE
    - CONTROL_EFFECTIVENESS
  observe:
    - EXPECTED_LOSS
    - VAR
    - EXPECTED_SHORTFALL
    - RISK_RANKING

FAILURE_MODE_EFFECTS_ANALYSIS:
  alias: FMEA
  components:
    - FAILURE_MODE
    - EFFECT
    - CAUSE
    - SEVERITY
    - OCCURRENCE
    - DETECTABILITY

FAULT_TREE_ANALYSIS:
  top_event:
    SYSTEM_FAILURE
  logic:
    - AND_GATE
    - OR_GATE

EVENT_TREE_ANALYSIS:
  initiating_event:
    E_0
  output:
    SCENARIO_PROBABILITIES_AND_CONSEQUENCES

BOW_TIE_ANALYSIS:
  centre:
    TOP_EVENT
  left_side:
    THREATS_AND_PREVENTIVE_CONTROLS
  right_side:
    CONSEQUENCES_AND_MITIGATING_CONTROLS

CONTROL:
  types:
    - PREVENTIVE
    - DETECTIVE
    - MITIGATING
    - CORRECTIVE

CONTROL_EFFECTIVENESS:
  baseline_risk: R_0
  residual_risk: R_1
  risk_reduction:
    Delta_R := R_0-R_1

INHERENT_RISK:
  definition:
    RISK_BEFORE_SPECIFIED_CONTROLS

RESIDUAL_RISK:
  definition:
    RISK_REMAINING_AFTER_SPECIFIED_CONTROLS
  rule:
    RESIDUAL_RISK != ZERO_BY_DEFAULT

RISK_RESPONSE:
  strategies:
    - AVOID
    - REDUCE
    - TRANSFER
    - SHARE
    - ACCEPT
    - MONITOR

COST_BENEFIT_ANALYSIS:
  mitigation_cost: C_m
  expected_risk_reduction: Delta_R_m
  net_benefit:
    NB_m := Delta_R_m-C_m

BAYESIAN_RISK_ANALYSIS:
  prior: p(theta)
  evidence: D
  posterior: p(theta|D)
  posterior_predictive_loss:
    p(L_future|D)
  risk_measure:
    COMPUTED_FROM_POSTERIOR_PREDICTIVE_DISTRIBUTION

RARE_EVENTS:
  methods:
    - EXTREME_VALUE_THEORY
    - BAYESIAN_MODELS
    - EXPERT_ELICITATION
    - IMPORTANCE_SAMPLING
    - SCENARIO_ANALYSIS
  caution:
    TAIL_ESTIMATES_CAN_HAVE_HIGH_UNCERTAINTY

MODEL_RISK:
  definition:
    RISK_FROM:
      INCORRECT_MODEL_STRUCTURE
      PARAMETER_ERROR
      IMPLEMENTATION_ERROR
      MISUSE
      DISTRIBUTION_SHIFT
  response:
    - VALIDATION
    - BENCHMARKING
    - SENSITIVITY_ANALYSIS
    - STRESS_TESTING
    - GOVERNANCE

RISK_AGGREGATION:
  individual_losses:
    L_1,...,L_m
  total:
    L_total := SUM_j L_j
  requirement:
    DEPENDENCE_STRUCTURE_MUST_BE_CONSIDERED

PORTFOLIO_RISK:
  aggregate:
    L := SUM_j w_j X_j
  variance:
    Var(L) := w^T Sigma w
    UNDER:
      FINITE_SECOND_MOMENTS

DECISION_THEORY_CONNECTION:
  risk_estimate:
    INPUT_TO:
      EXPECTED_LOSS
      EXPECTED_UTILITY
      DECISION_RULES
  rule:
    RISK_ESTIMATE_ALONE_DOES_NOT_DEFINE_DECISION_WITHOUT_PREFERENCES_OR_CRITERIA

RISK_MONITORING:
  flow:
    DEFINE_RISK_INDICATORS
      -> COLLECT_DATA
      -> UPDATE_RISK_ESTIMATES
      -> COMPARE_WITH_LIMITS
      -> INVESTIGATE_CHANGE
      -> APPLY_RESPONSE

APPLICATIONS:
  RISK_ANALYSIS -> SUPPORTS -> RISK_MANAGEMENT
  RISK_ANALYSIS -> SUPPORTS -> DECISION_MAKING
  RISK_ANALYSIS -> SUPPORTS -> SAFETY_ANALYSIS
  RISK_ANALYSIS -> SUPPORTS -> FINANCIAL_RISK
  RISK_ANALYSIS -> SUPPORTS -> ENGINEERING_RELIABILITY
  RISK_ANALYSIS -> SUPPORTS -> ENVIRONMENTAL_RISK
  RISK_ANALYSIS -> SUPPORTS -> PROJECT_RISK
  RISK_ANALYSIS -> SUPPORTS -> OPERATIONAL_RISK

MODEL_CONNECTIONS:
  RISK_ANALYSIS -> CONNECTS_TO -> RISK_DECISION_MATHEMATICS
  RISK_ANALYSIS -> CONNECTS_TO -> PROBABILITY_THEORY
  RISK_ANALYSIS -> CONNECTS_TO -> BAYESIAN_STATISTICS
  RISK_ANALYSIS -> CONNECTS_TO -> STOCHASTIC_PROCESSES
  RISK_ANALYSIS -> CONNECTS_TO -> EXTREME_VALUE_THEORY
  RISK_ANALYSIS -> CONNECTS_TO -> DECISION_THEORY
  RISK_ANALYSIS -> CONNECTS_TO -> MONTE_CARLO_SIMULATION

SEMANTIC_EQUIVALENCE:
  "risk analysis"
    ~= "systematic identification and evaluation of risk"

  "expected loss"
    ~= "probability-weighted average loss"

  "residual risk"
    ~= "risk remaining after specified controls"

  EXCLUDE_EQUIVALENCE:
    RISK != PROBABILITY
    RISK != CONSEQUENCE
    HAZARD != RISK
    UNCERTAINTY != RISK
    INHERENT_RISK != RESIDUAL_RISK
    VALUE_AT_RISK != EXPECTED_SHORTFALL
    RISK_FACTOR != CAUSAL_FACTOR_BY_DEFAULT
    ASSOCIATION != CAUSATION

VALIDATION_RULES:
  RULE_1:
    HAZARD_EVENT_CONSEQUENCE_AND_TIME_HORIZON_MUST_BE_DEFINED
  RULE_2:
    PROBABILITY_FREQUENCY_AND_RATE_MUST_NOT_BE_CONFLATED
  RULE_3:
    RISK_MEASURE_AND_CONFIDENCE_LEVEL_MUST_BE_EXPLICIT
  RULE_4:
    DEPENDENCE_BETWEEN_RISKS_MUST_BE_MODELLED_WHEN_MATERIAL
  RULE_5:
    PARAMETER_AND_MODEL_UNCERTAINTY_SHOULD_BE_PROPAGATED_WHEN_MATERIAL
  RULE_6:
    ORDINAL_RATINGS_MUST_NOT_BE_TREATED_AS_PRECISE_CARDINAL_VALUES_WITHOUT_JUSTIFICATION
  RULE_7:
    CONTROL_EFFECTIVENESS_AND_RESIDUAL_RISK_MUST_BE_DISTINGUISHED_FROM_INHERENT_RISK
  RULE_8:
    ASSOCIATIONAL_RISK_FACTORS_MUST_NOT_BE_INTERPRETED_AS_CAUSAL_WITHOUT_CAUSAL_ASSUMPTIONS

CONFIDENCE:
  ontology_identity: 0.99
  probability_consequence_structure: 0.99
  loss_distribution_structure: 0.99
  uncertainty_structure: 0.99
  control_residual_risk_structure: 0.99
  tail_risk_structure: 0.99
  semantic_distinctions: 0.99

UPDATE_MODEL:
  IF:
    NEW_EVENT_DATA_ARRIVES
  THEN:
    UPDATE:
      EVENT_FREQUENCIES
      SEVERITY_DISTRIBUTIONS
      DEPENDENCE_ESTIMATES
      LOSS_DISTRIBUTION
      RISK_MEASURES

  IF:
    CONTROL_EFFECTIVENESS_CHANGES
  THEN:
    UPDATE:
      CONTROL_PARAMETERS
      RESIDUAL_RISK
    REASSESS:
      RISK_RESPONSE

  IF:
    MODEL_OR_ASSUMPTIONS_CHANGE
  THEN:
    UPDATE:
      MODEL_VERSION
      PARAMETER_ESTIMATES
      STRUCTURAL_ASSUMPTIONS
    RERUN:
      UNCERTAINTY_PROPAGATION
      SENSITIVITY_ANALYSIS
      STRESS_TESTS

  PRESERVE:
    RISK_IDENTIFIERS
    HAZARD_DEFINITIONS
    EVENT_DEFINITIONS
    CONSEQUENCE_DEFINITIONS
    TIME_HORIZON
    PROBABILITY_MODEL
    LOSS_MODEL
    CONTROL_DEFINITIONS
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_HAZARDS_EVENTS_AND_CONSEQUENCES
    - DEFINE_TIME_HORIZON_AND_EXPOSURE
    - ESTIMATE_LIKELIHOODS
    - ESTIMATE_SEVERITIES_OR_CONSEQUENCES
    - MODEL_DEPENDENCE
    - CONSTRUCT_LOSS_DISTRIBUTION
    - COMPUTE_EXPECTED_AND_TAIL_RISK_MEASURES
    - PROPAGATE_PARAMETER_AND_MODEL_UNCERTAINTY
    - EVALUATE_CONTROLS_AND_RESIDUAL_RISK
    - PERFORM_SENSITIVITY_AND_STRESS_ANALYSIS
    - COMPARE_WITH_RISK_LIMITS_OR_DECISION_CRITERIA
    - RETURN_RISK_ANALYSIS_INTERPRETATION

  constraints:
    - PRESERVE_HAZARD_EVENT_CONSEQUENCE_DISTINCTIONS
    - PRESERVE_TIME_HORIZON
    - DISTINGUISH_PROBABILITY_FROM_RISK
    - DISTINGUISH_INHERENT_FROM_RESIDUAL_RISK
    - DISTINGUISH_VAR_FROM_EXPECTED_SHORTFALL
    - MODEL_DEPENDENCE_WHEN_MATERIAL
    - DISTINGUISH_ASSOCIATION_FROM_CAUSATION
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "risk-analysis"
  namespace: "probability-statistics/risk-decision-mathematics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - HAZARD_EVENT_CONSEQUENCE
    - LOSS_DISTRIBUTION
    - UNCERTAINTY
    - RISK_MEASURES

END_FLOW