# Error Propagation Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/error-propagation-ontology.html
FLOW ErrorPropagationOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Error Propagation Ontology
PURPOSE:
Represent the mathematical propagation of measurement errors and, where appropriate, measurement uncertainties through functions, transformations and computational models. The ontology supports first-order differential propagation, covariance and correlation, Jacobian matrix methods, sums, differences, products, quotients, powers, logarithmic and exponential transformations, nonlinear models, Monte Carlo propagation, systematic and random components, unit transformations, chained calculations, sensitivity analysis, uncertainty budgets, provenance, and strict distinctions between propagation of unknown measurement error and propagation of quantified measurement uncertainty.
ENTITY ErrorPropagation {
TYPE: MeasurementModelTransformationProcess
DEFINITION:
error_propagation :=
transformation_of_input_error_components
through_a_measurement_or_computational_model
to_determine_their_effect_on_output_error
PROPERTIES:
depends_on_model
depends_on_input_error_structure
may_use_linearisation
may_include_covariance
may_be_deterministic_or_probabilistic
may_be_local_or_global
must_preserve_provenance
}
ENTITY UncertaintyPropagation {
TYPE: MeasurementUncertaintyTransformationProcess
DEFINITION:
propagation_of_probability_distributions_or_standard_uncertainties
associated_with_input_quantities
through_measurement_model
to_output_quantity
RULE:
uncertainty_propagation != true_error_propagation
though_similar_differential_mathematics_may_be_used
}
ENTITY MeasurementModel {
TYPE: MathematicalMapping
FORM:
Y =
f(X_1,X_2,...,X_n)
ESTIMATE:
y =
f(x_1,x_2,...,x_n)
}
TERMINOLOGY_MODEL {
terms:
error_propagation
uncertainty_propagation
propagation_of_uncertainty
law_of_propagation_of_uncertainty
sensitivity_analysis
covariance_propagation
Monte_Carlo_propagation
RULE:
error_and_uncertainty MUST be_distinguished_semantically
}
DIFFERENTIAL_ERROR_MODEL {
small_input_errors:
delta_x_i
first_order_output_error:
delta_y approximately_equals
sum_i(
partial_f/partial_x_i
* delta_x_i
)
RULE:
differential_error_propagation_is_local_linear_approximation
}
SENSITIVITY_COEFFICIENT_MODEL {
coefficient:
c_i =
partial_f/partial_X_i
evaluated_at:
input_estimates
output_effect:
delta_y_i approximately_equals
c_i*delta_x_i
RULE:
sensitivity_coefficient_sign_matters_for_error_direction
}
JACOBIAN_MODEL {
vector_output:
Y =
f(X)
Jacobian:
J_ij =
partial_f_i/partial_X_j
first_order_error:
delta_Y approximately_equals
J*delta_X
RULE:
Jacobian_dimensions_and_variable_order MUST be preserved
}
COVARIANCE_PROPAGATION_MODEL {
input_covariance:
Sigma_X
first_order_output_covariance:
Sigma_Y =
J*Sigma_X*J_transpose
scalar_output:
u_y^2 =
J*Sigma_X*J_transpose
RULE:
covariance_terms MUST be preserved
}
CORRELATION_MODEL {
covariance:
cov(X_i,X_j)
correlation:
rho_ij =
cov(X_i,X_j)/
(u_i*u_j)
WHEN u_i != 0 AND u_j != 0
RULE:
assuming_independence_when_inputs_share_sources_can_under_or_overestimate_output_uncertainty
}
INDEPENDENT_INPUT_MODEL {
condition:
cov(X_i,X_j)=0
for_i_not_equal_j
scalar:
u_y =
sqrt(
sum_i(c_i^2*u_i^2)
)
RULE:
independence_or_zero_covariance MUST be justified
}
SUM_MODEL {
Y =
A+B
deterministic_error:
delta_Y =
delta_A+delta_B
independent_standard_uncertainty:
u_Y =
sqrt(u_A^2+u_B^2)
correlated:
u_Y^2 =
u_A^2+u_B^2+2cov(A,B)
RULE:
arithmetic_error_addition_and_RSS_uncertainty_combination_are_distinct
}
DIFFERENCE_MODEL {
Y =
A-B
deterministic_error:
delta_Y =
delta_A-delta_B
uncertainty:
u_Y^2 =
u_A^2+u_B^2-2cov(A,B)
RULE:
common_mode_uncertainty_may_cancel_in_difference
}
PRODUCT_MODEL {
Y =
A*B
differential:
delta_Y approximately_equals
B*delta_A+A*delta_B
relative:
delta_Y/Y approximately_equals
delta_A/A+delta_B/B
WHEN A != 0 AND B != 0
independent_standard_relative_uncertainty:
(u_Y/Y)^2 approximately_equals
(u_A/A)^2+(u_B/B)^2
RULE:
relative_RSS_form_is_first_order_and_requires_appropriate_independence
}
QUOTIENT_MODEL {
Y =
A/B
REQUIRE:
B != 0
differential_relative:
delta_Y/Y approximately_equals
delta_A/A-delta_B/B
independent_standard_relative_uncertainty:
(u_Y/Y)^2 approximately_equals
(u_A/A)^2+(u_B/B)^2
RULE:
denominator_near_zero_can_make_linearisation_invalid
}
POWER_MODEL {
Y =
A^n
differential:
delta_Y/Y approximately_equals
n*delta_A/A
standard_relative:
u_Y/abs(Y) approximately_equals
abs(n)*u_A/abs(A)
REQUIRE:
A != 0
valid_real_domain
}
GENERAL_PRODUCT_POWER_MODEL {
Y =
C*product_i(X_i^a_i)
relative_differential:
delta_Y/Y approximately_equals
sum_i(a_i*delta_X_i/X_i)
independent_standard:
(u_Y/Y)^2 approximately_equals
sum_i(
a_i^2*(u_i/X_i)^2
)
RULE:
correlations_require_cross_terms
}
LOGARITHM_MODEL {
natural:
Y =
ln(X)
sensitivity:
dY/dX =
1/X
uncertainty:
u_Y approximately_equals
u_X/abs(X)
REQUIRE:
X > 0
}
LOG10_MODEL {
Y =
log10(X)
sensitivity:
1/(X*ln(10))
uncertainty:
u_Y approximately_equals
u_X/(abs(X)*ln(10))
REQUIRE:
X > 0
}
EXPONENTIAL_MODEL {
Y =
exp(X)
sensitivity:
dY/dX =
exp(X)=Y
relative_uncertainty:
u_Y/abs(Y) approximately_equals
u_X
RULE:
input_X_is_dimensionless_for_pure_exponential_argument
}
TRIGONOMETRIC_MODEL {
Y =
sin(X)
sensitivity:
cos(X)
RULE:
angular_input MUST be_in_radians_for_standard_derivative_form
Y_cos =
cos(X)
sensitivity_cos:
-sin(X)
}
INVERSE_TRIG_MODEL {
example:
Y =
atan(X)
sensitivity:
1/(1+X^2)
RULE:
domain_and_unit_semantics MUST be preserved
}
UNIT_CONVERSION_MODEL {
exact_linear:
Y =
a*X
error:
delta_Y =
a*delta_X
uncertainty:
u_Y =
abs(a)*u_X
exact_affine:
Y =
a*X+b
uncertainty_if_a_b_exact:
u_Y =
abs(a)*u_X
RULE:
exact_offset_does_not_add_uncertainty
}
UNCERTAIN_CONSTANT_MODEL {
Y =
a*X
IF a_uncertain:
a_is_input_quantity
then:
propagate_u_a_and_covariance
RULE:
uncertain_physical_or_calibration_constants MUST_NOT be_treated_as_exact
}
REPEATED_VARIABLE_MODEL {
example:
Y =
X-X
naive_independent:
would_be_wrong
exact:
Y = 0
covariance:
full_correlation_cancels_uncertainty
RULE:
repeated_use_of_same_input MUST preserve_dependency
}
COMMON_REFERENCE_MODEL {
measurements:
A
B
shared_reference:
R
consequence:
correlated_uncertainty
RULE:
shared_calibration_or_reference MUST generate_covariance_link_when_material
}
CHAIN_PROPAGATION_MODEL {
stage_1:
Z =
f(X)
stage_2:
Y =
g(Z)
derivative:
dY/dX =
dY/dZ*dZ/dX
RULE:
intermediate_covariances MUST be_preserved
and_double_counting_avoided
}
COMPUTATIONAL_GRAPH_MODEL {
nodes:
input_quantities
intermediate_quantities
output_quantities
edges:
functional_dependencies
propagation:
automatic_differentiation_or_symbolic_Jacobian
RULE:
identical_source_nodes MUST remain_shared_not_duplicated_as_independent_inputs
}
LINEARISATION_MODEL {
Taylor_first_order:
f(X) approximately_equals
f(x)+J*(X-x)
validity:
small_input_dispersion
smooth_model
no_strong_boundary_effect
RULE:
linearisation_error SHOULD be_assessed_when_model_is_nonlinear
}
SECOND_ORDER_MODEL {
Taylor:
includes_Hessian_terms
possible_effects:
output_mean_shift
variance_correction
asymmetry
RULE:
second_order_terms MAY be_needed_for_large_uncertainty_or_curvature
}
HESSIAN_MODEL {
H_ij =
partial^2_f/
partial_X_i_partial_X_j
RULE:
Hessian_order_and_units MUST match_model_variables
}
NONLINEAR_MODEL {
risks:
skewed_output
bounded_output
multimodal_output
singularity
nonmonotonic_mapping
alternatives:
Monte_Carlo
unscented_transform
numerical_quadrature
Bayesian_propagation
RULE:
nonlinear_output_distribution SHOULD not_be_forced_into_symmetric_normal_uncertainty
}
MONTE_CARLO_MODEL {
inputs:
joint_distribution_p_X
algorithm:
sample X^(k)
compute Y^(k)=f(X^(k))
repeat k=1...N
outputs:
mean_or_estimate
standard_deviation
quantiles
coverage_interval
covariance
RULE:
input_dependence_and_distribution_shapes MUST be_preserved
}
MONTE_CARLO_CONVERGENCE_MODEL {
checks:
sample_size
repeated_runs
quantile_stability
standard_error_of_simulation
RULE:
Monte_Carlo_sampling_error SHOULD be_small_relative_to_reported_uncertainty_precision
}
CORRELATED_SAMPLING_MODEL {
methods:
multivariate_normal
copula
Cholesky_factorisation
direct_joint_model
RULE:
independent_sampling_of_correlated_inputs_is_invalid
}
ASYMMETRIC_MODEL {
input:
asymmetric_distribution
output:
may_be_asymmetric
reporting:
lower_upper_uncertainty
quantile_interval
RULE:
asymmetric_uncertainty SHOULD preserve_directional_bounds
}
BOUNDED_MODEL {
examples:
probability_between_0_and_1
concentration_nonnegative
angle_domain
RULE:
propagation_method MUST respect_physical_or_mathematical_bounds
}
RATIO_SINGULARITY_MODEL {
denominator:
approaches_zero
consequence:
heavy_tails
undefined_moments
disconnected_intervals
RULE:
first_order_ratio_propagation_is_unreliable_near_zero_denominator
}
ERROR_BOUND_MODEL {
deterministic_bounds:
abs(delta_X_i) <= b_i
worst_case_first_order:
abs(delta_Y) <=
sum_i(
abs(c_i)*b_i
)
RULE:
worst_case_error_bounds != standard_uncertainty
}
INTERVAL_ARITHMETIC_MODEL {
inputs:
X_i in [L_i,U_i]
propagation:
interval_operations
RULE:
dependency_problem_can_overestimate_bounds_when_same_variable_repeated
}
SYSTEMATIC_ERROR_MODEL {
estimated_systematic_components:
propagate_with_sign_through_model
example:
delta_y_systematic approximately_equals
sum_i(c_i*delta_x_i_systematic)
RULE:
systematic_error_correction_and_uncertainty_of_correction MUST be_distinguished
}
RANDOM_ERROR_MODEL {
random_components:
characterised_by_distribution_or_covariance
propagation:
covariance_method_or_sampling
RULE:
random_and_systematic_semantics MUST remain_separate_even_if_combined_in_total_model
}
BIAS_PROPAGATION_MODEL {
input_bias:
b_X
first_order_output_bias:
b_Y approximately_equals
J*b_X
RULE:
nonlinear_models_can_create_additional_bias_from_curvature
}
CORRECTION_PROPAGATION_MODEL {
corrected_input:
X_corr =
X+C
uncertainty:
includes_u(C)
and_covariance
RULE:
correction_value_propagates_deterministically
while_correction_uncertainty_propagates_probabilistically
}
CALIBRATION_MODEL {
calibration_parameters:
theta
output:
y =
f(x,theta)
RULE:
calibration_parameter_covariance MUST be included_when_material
}
REGRESSION_PARAMETER_MODEL {
fitted_parameters:
beta
covariance:
Sigma_beta
prediction:
y =
f(x,beta)
parameter_uncertainty:
J_beta*Sigma_beta*J_beta_transpose
RULE:
parameter_covariance_must_not_be_replaced_by_independent_standard_errors
}
MEASUREMENT_UNCERTAINTY_MODEL {
standard_uncertainties:
u(x_i)
combined:
u_c(y)
first_order:
u_c^2(y) =
sum_i sum_j(
c_i*c_j*u(x_i,x_j)
)
RULE:
this_is_uncertainty_propagation_not_direct_observation_of_error
}
RELATIVE_UNCERTAINTY_MODEL {
output_relative:
u_r(y) =
u(y)/abs(y)
WHEN y != 0
RULE:
relative_uncertainty_can_be_misleading_near_zero
}
UNCERTAINTY_BUDGET_MODEL {
each_input:
estimate
unit
standard_uncertainty
distribution
sensitivity_coefficient
contribution
covariance_links
provenance
output:
combined_standard_uncertainty
RULE:
budget MUST avoid_double_counting_correlated_or_shared_sources
}
SENSITIVITY_RANKING_MODEL {
local_contribution:
c_i^2*u_i^2
for_uncorrelated_inputs
RULE:
covariance_can_make_simple_component_ranking_incomplete
}
DIMENSIONAL_MODEL {
sensitivity_coefficient:
output_unit/input_unit
covariance:
unit_i*unit_j
output_variance:
output_unit_squared
RULE:
dimensional_consistency MUST hold_through_propagation
}
NUMERICAL_DERIVATIVE_MODEL {
finite_difference:
c_i approximately_equals
[f(x+h_i)-f(x-h_i)]/(2*h_i)
RULE:
step_size_must_balance_truncation_and_roundoff_error
}
AUTOMATIC_DIFFERENTIATION_MODEL {
derivative:
computed_through_computational_graph
RULE:
AD_can_improve_derivative_accuracy_but_does_not_validate_measurement_model
}
SYMBOLIC_DIFFERENTIATION_MODEL {
derivative:
exact_expression_when_available
RULE:
symbolic_expression_domain_and_singularities MUST be_checked
}
NUMERICAL_UNCERTAINTY_MODEL {
sources:
floating_point
solver_tolerance
discretisation
interpolation
numerical_integration
RULE:
numerical_uncertainty MAY need_propagation_as_additional_input
}
VALIDATION_MODEL {
methods:
compare_linear_vs_Monte_Carlo
perturb_inputs
benchmark_known_solution
dimensional_check
simulation
sensitivity_check
RULE:
propagation_result SHOULD be_validated_when_model_is_complex_or_highly_nonlinear
}
RELATIONSHIPS {
ErrorPropagation -> USES -> MeasurementModel
MeasurementModel -> MAPS -> InputQuantitiesToOutputQuantity
SensitivityCoefficient -> MAPS -> InputErrorToOutputEffect
Jacobian -> PROPAGATES -> ErrorVector
Jacobian -> PROPAGATES -> CovarianceMatrix
Covariance -> REPRESENTS -> InputDependence
MonteCarloMethod -> PROPAGATES -> InputDistributionToOutputDistribution
CalibrationParameter -> CONTRIBUTES_TO -> OutputUncertainty
SystematicError -> PROPAGATES_THROUGH -> MeasurementModel
RandomError -> PROPAGATES_THROUGH -> MeasurementModel
UncertaintyBudget -> RECORDS -> PropagationContributions
}
SEMANTIC_EQUIVALENCE {
"propagation of uncertainty" ~= uncertainty_propagation
"law of propagation of uncertainty" ~= first_order_covariance_uncertainty_propagation WHEN GUM_style_context
error_propagation != measurement_uncertainty
error_propagation != uncertainty_propagation_semantically
deterministic_error_bound != standard_uncertainty
worst_case_bound != confidence_interval
sensitivity_coefficient != uncertainty_contribution
covariance != correlation
random_error != standard_uncertainty
systematic_error != bias_uncertainty
}
CONSTRAINTS {
measurement_model_must_be_defined = true
input_quantities_must_be_identified = true
variable_dependencies_must_be_preserved = true
covariance_must_be_included_when_material = true
first_order_propagation_requires_local_linearity = true
denominator_and_domain_singularities_must_be_checked = true
exact_and_uncertain_constants_must_be_distinguished = true
error_and_uncertainty_propagation_are_not_semantically_equivalent = true
repeated_source_variables_must_not_be_treated_as_independent = true
output_units_must_be_dimensionally_consistent = true
nonlinear_models_should_preserve_distribution_shape_when_material = true
}
MEASUREMENT_MODEL {
RECORD:
output_quantity
output_unit
model_expression
input_quantities
input_values
input_units
input_errors_when_known_or_modelled
standard_uncertainties
probability_distributions
covariance_matrix
correlation_matrix
sensitivity_coefficients
Jacobian
Hessian_when_used
calibration_parameters
corrections
systematic_components
random_components
propagation_method
Monte_Carlo_configuration
numerical_method
output_covariance
combined_standard_uncertainty
coverage_interval_when_requested
validation_results
provenance
RULE:
propagation_result MUST remain_linked_to_model_inputs_dependencies_and_method
}
REASONING_RULES {
IF scalar_model_and_small_input_errors_known
THEN output_error approximately_equals
sum(sensitivity_i*input_error_i)
IF Jacobian_and_input_covariance_known
THEN output_covariance =
Jacobian*input_covariance*transpose(Jacobian)
IF inputs_uncorrelated
THEN output_variance =
sum(sensitivity_i^2*input_variance_i)
IF output_is_sum
THEN deterministic_errors_add_with_sign
AND uncertainty_variance_includes_covariance
IF output_is_difference
THEN common_correlated_components_may_cancel
IF output_is_product_or_quotient
AND relative_uncertainties_small
THEN MAY use_relative_first_order_propagation
IF output_is_power
THEN relative_sensitivity =
exponent
IF exact_unit_conversion
THEN propagate_by_exact_scale_factor
without_adding_false_uncertainty
IF same_input_appears_multiple_times
THEN preserve_identity_and_full_dependency
IF model_is_strongly_nonlinear
OR output_is_bounded_skewed_or_near_singularity
THEN prefer_distribution_propagation_or_Monte_Carlo
IF systematic_bias_vector_known
THEN first_order_output_bias =
Jacobian*input_bias_vector
IF correction_uncertainty_known
THEN include_as_input_uncertainty_with_covariance
IF calibration_parameter_covariance_known
THEN propagate_full_parameter_covariance
IF Monte_Carlo_used
THEN verify_sampling_convergence_before_reporting_quantiles
}
VALIDATION {
CHECK measurement_model
CHECK input_and_output_units
CHECK input_identity
CHECK sensitivity_coefficients
CHECK Jacobian_variable_order
CHECK covariance_matrix
CHECK correlation_assumptions
CHECK exact_vs_uncertain_constants
CHECK sum_difference_signs
CHECK product_quotient_domains
CHECK logarithm_and_power_domains
CHECK angular_units_for_trigonometric_derivatives
CHECK repeated_variable_dependencies
CHECK linearisation_validity
CHECK nonlinear_or_singularity_risk
CHECK Monte_Carlo_input_distributions
CHECK correlated_sampling
CHECK systematic_vs_random_components
CHECK correction_uncertainty
CHECK calibration_parameter_covariance
CHECK dimensional_consistency
CHECK numerical_derivative_stability
CHECK output_distribution_or_uncertainty
CHECK validation_results
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
differential_propagation_confidence: 1.00
covariance_propagation_confidence: 1.00
Jacobian_model_confidence: 1.00
elementary_function_confidence: 1.00
error_uncertainty_distinction_confidence: 1.00
Monte_Carlo_semantics_confidence: 0.99
nonlinear_model_confidence: 0.98
RULE:
confidence decreases when model expression, variable identity,
covariance, domain, nonlinearity, calibration parameters,
distribution assumptions, numerical method or provenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_input_measurement:
identify_input_quantity
update_value_unit_error_or_uncertainty
preserve_distribution_and_covariance_links
recompute_output
recompute_propagated_error_or_uncertainty
preserve_provenance
ON measurement_model_revision:
preserve_previous_model
update_function_and_dependency_graph
recompute_symbolic_or_numeric_sensitivities
reassess_linearisation
recompute_propagation
update_confidence
ON covariance_revision:
preserve_marginal_input_uncertainties
update_covariance_matrix
validate_positive_semidefinite_structure
recompute_output_covariance
ON calibration_revision:
preserve_raw_inputs
update_calibration_parameters_and_covariance
recompute_corrected_inputs_and_output
update_propagated_uncertainty
ON propagation_method_revision:
preserve_model_and_inputs
compare_first_order_second_order_or_Monte_Carlo_result
record_method_selection_reason
update_output_distribution
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: ErrorPropagation
canonical_related_entity: UncertaintyPropagation
interpretation_order:
identify_output_quantity
identify_measurement_model
identify_input_quantities_and_units
identify_input_error_or_uncertainty_semantics
identify_variable_dependencies
identify_covariance_and_correlation
identify_sensitivity_coefficients_or_Jacobian
identify_systematic_random_and_correction_components
identify_calibration_parameters
identify_linear_or_nonlinear_context
identify_propagation_method
identify_Monte_Carlo_or_numerical_configuration
identify_output_distribution_or_covariance
identify_validation
identify_provenance
validate_dimensional_and_semantic_consistency
propagate_model
ambiguity_controls:
distinguish_error_propagation_from_uncertainty_propagation
distinguish_deterministic_error_from_standard_uncertainty
distinguish_worst_case_bound_from_probabilistic_interval
distinguish_sensitivity_coefficient_from_uncertainty_contribution
distinguish_covariance_from_correlation
distinguish_random_error_from_standard_uncertainty
distinguish_systematic_error_from_uncertainty_of_systematic_correction
distinguish_exact_constants_from_uncertain_parameters
preserve_model_variable_identity_dependency_distribution_calibration_method_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_uncertainty_and_error_propagation_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Error Propagation Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
differential_error_model
sensitivity_coefficient_model
Jacobian_model
covariance_propagation_model
correlation_model
independent_input_model
sum_model
difference_model
product_model
quotient_model
power_model
general_product_power_model
logarithm_model
log10_model
exponential_model
trigonometric_model
inverse_trig_model
unit_conversion_model
uncertain_constant_model
repeated_variable_model
common_reference_model
chain_propagation_model
computational_graph_model
linearisation_model
second_order_model
Hessian_model
nonlinear_model
Monte_Carlo_model
Monte_Carlo_convergence_model
correlated_sampling_model
asymmetric_model
bounded_model
ratio_singularity_model
error_bound_model
interval_arithmetic_model
systematic_error_model
random_error_model
bias_propagation_model
correction_propagation_model
calibration_model
regression_parameter_model
measurement_uncertainty_model
relative_uncertainty_model
uncertainty_budget_model
sensitivity_ranking_model
dimensional_model
numerical_derivative_model
automatic_differentiation_model
symbolic_differentiation_model
numerical_uncertainty_model
validation_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
measurement_model_or_dependency_graph_changes
input_error_or_uncertainty_semantics_change
sensitivity_Jacobian_or_Hessian_changes
covariance_or_correlation_changes
elementary_transformation_model_changes
linearisation_or_nonlinear_method_changes
Monte_Carlo_configuration_changes
calibration_or_correction_model_changes
systematic_or_random_component_changes
numerical_method_changes
measurement_record_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW
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