name: Conditioned Probability Frame Specification

slug: context

slug: evidence

slug: decision

slug: risk

slug: calibration

components:
Target Event Definition
Conditioning Context Statement
Denominator Population
Renormalization Rule
Probability Type Label
Frame Compatibility Check
Assumption Boundary
Reuse Boundary
Joint Probability Table
Base-Rate Reference
Condition Order Record
Scenario Condition Register
Causal Nonclaim Warning

mechanisms:
Given-That Clause
Two-by-Two Probability Table
Probability Tree
Reference Population Note
Stratified Rate Table
Likelihood-Ratio Frame
Conditional Probability Annotation
Scenario Condition Card
Frame Compatibility Review
Base-Rate Check

essence_one_line: State what is being taken as given before interpreting, comparing, or acting on a probability.

compression_statement: Conditioned probability frame specification turns a naked probability into a scoped claim: identify the event of interest, declare the information context or condition, restrict the denominator to cases compatible with that condition, renormalize probability mass within that restricted frame, and forbid comparisons or updates that silently switch frames.

core_intuition: A probability is not just a number; it is a number under a context. The same event can be rare in the whole population, common inside a subgroup, likely after a signal, or impossible under an assumption. Making the “given that” part explicit prevents people from mixing incompatible denominators and treating conditional claims as unconditional truths.

canonical_formula: P(A | B) = P(A ∩ B) / P(B), with B declared as the operative information context and P(B) > 0

structural_problem: Probability claims are made, compared, or used in decisions without declaring what information, subgroup, scenario, evidence state, or assumption set is being taken as given. The missing conditioning frame lets actors mix marginal and conditional probabilities, compare rates with different denominators, ignore base rates, reuse numbers outside their valid context, or treat an updated probability as if it were unconditional. The arithmetic may be correct inside one frame while the conclusion is wrong because the frame has silently changed.

trigger_conditions: A probability, risk, prevalence, rate, likelihood, forecast, or uncertainty estimate is being stated or compared.

trigger_conditions: The estimate depends on evidence already observed, a subgroup membership, a scenario assumption, a diagnostic signal, a sampling process, or a case-selection rule.

trigger_conditions: Decision-makers might confuse P(A), P(A | B), P(B | A), joint probability, marginal probability, or posterior probability.

trigger_conditions: A probability will be reused downstream by people who may not know the reference population, information state, or assumptions used to produce it.

trigger_conditions: Multiple probability claims are being compared across groups, models, time periods, jurisdictions, experiments, or data slices.

trigger_conditions: The denominator population is smaller than the visible population, or the relevant context excludes some cases.

trigger_conditions: A decision depends on whether evidence should change a prior probability, but the evidence context has not been stated.

trigger_conditions: The cost of a denominator error is high enough that the probability statement needs auditability.

symptoms: Reports give a probability number without saying “given what.”

symptoms: A rate from one subgroup is compared with a marginal rate from another population.

symptoms: A diagnostic test result is treated as the probability of disease without a prevalence frame.

symptoms: Decision-makers invert conditional probabilities, such as treating P(signal | condition) as P(condition | signal).

symptoms: A forecast is moved from one scenario to another without recalculation.

symptoms: Different teams argue with incompatible probabilities because each is conditioning on a different evidence set.

symptoms: A risk estimate appears precise but changes dramatically when the reference class or case-mix is clarified.

symptoms: An aggregate statistic hides subgroup-specific probabilities that matter for action.

root_tension: Probability compresses uncertainty into a number, but the number is only meaningful relative to a probability space and information context that users often omit for speed, persuasion, or simplicity.

anti_signatures: The main task is updating beliefs from priors and evidence over time; use bayesian_belief_updating.

anti_signatures: The main task is ranking actions by likelihood and consequence; use probabilistic_risk_weighting.

anti_signatures: The main task is validating whether uncertainty intervals achieve nominal coverage; use coverage_probability_calibration.

anti_signatures: The main task is estimating hidden state from noisy measurements; use state_estimation.

anti_signatures: The main task is drawing a conditional-independence boundary around variables; use conditional_independence_boundary_mapping.

anti_signatures: The main task is causal identification or estimating an intervention effect; use a causal/counterfactual archetype rather than treating conditioning as causal proof.

anti_signatures: The probability is a purely unconditional frequency and no information context, subgroup, or scenario is being held fixed.

anti_signatures: The problem is only vague communication, with no probability measure or denominator at stake.

structural_intervention: Attach every probability claim to an explicit conditioning frame: define the event, specify the given information or condition, verify the denominator population, restrict the sample/model to cases satisfying the condition, renormalize within that restricted frame, label the resulting claim, and require compatibility checks before comparison, update, or reuse.

action: Define the event, outcome, hypothesis, state, or quantity whose probability is being assessed.

reason: Conditional probability cannot be interpreted if the numerator event is ambiguous.

action: State the evidence, subgroup, scenario, assumption set, time, sampling rule, or information state taken as given.

reason: The condition is the structural boundary that determines which world or case set the probability belongs to.

action: Verify that the conditioning context has positive probability or sufficient empirical support and matches the decision context.

reason: Renormalization fails or becomes misleading if the denominator is empty, tiny, unrepresentative, or irrelevant.

action: Restrict the probability space, sample, table, model, or scenario ensemble to the condition and compute or elicit probability within that restricted set.

reason: The operative probability is the share of conditioned cases in which the event occurs, not the share in the original unconditioned universe.

action: Identify whether the claim is marginal, joint, conditional, posterior, scenario-conditioned, subgroup-conditioned, or counterfactual-condition-specific.

reason: Labels prevent downstream users from treating one probability type as another.

action: Compare probabilities only if their target events, conditioning frames, denominators, time windows, and sampling rules are compatible or explicitly transformed.

reason: Many probability errors are frame-switching errors disguised as numerical comparisons.

action: Record whether the condition is merely observed information, a selection rule, an intervention, or a causal variable requiring adjustment.

reason: Conditioning can clarify probability without proving that the condition causes the event.

action: State where the probability can and cannot be reused, including excluded populations, absent evidence, model assumptions, and update triggers.

reason: A conditional probability becomes misleading when exported beyond the context that made it valid.

decision_rules: Do not accept a probability claim without an explicit “given what” clause when evidence, subgroup, scenario, or sampling context matters.

decision_rules: Treat any comparison between probabilities as invalid until the conditioning frames and denominators are checked for compatibility.

decision_rules: If the condition is rare, unstable, or poorly observed, mark the conditional probability as fragile and request sensitivity analysis.

decision_rules: When a probability follows a signal, preserve base-rate information unless a valid model explains why it should be excluded.

decision_rules: If users may confuse P(A | B) with P(B | A), require a joint table, tree diagram, likelihood-ratio explanation, or equivalent mechanism.

decision_rules: Do not interpret a conditional association as a causal effect without a causal identification argument.

decision_rules: Require a reuse boundary whenever a conditional probability will be communicated outside the team that produced it.

decision_rules: When conditions are nested, order them explicitly and show whether each condition adds information or merely restates a prior filter.

target_invariants: Every probability claim names its target event and conditioning context.

target_invariants: The denominator population or probability mass is explicit and compatible with the decision context.

target_invariants: Marginal, joint, conditional, posterior, and scenario-conditioned probabilities are not silently interchanged.

target_invariants: Probability comparisons use compatible frames or state the transformation between frames.

target_invariants: Conditioning is not treated as causal proof without additional causal assumptions.

target_invariants: Downstream users can see where the probability is valid, fragile, and invalid to reuse.

target_invariants: Base rates or reference populations are preserved unless explicitly replaced by a justified condition.

target_invariants: The condition has nonzero or empirically supportable probability.

expected_outcomes: Fewer denominator errors, base-rate omissions, and conditional-probability inversions.

expected_outcomes: Clearer probability communication across teams and domains.

expected_outcomes: More valid comparisons between risk estimates, subgroup rates, diagnostic probabilities, and forecasts.

expected_outcomes: Better separation of observed evidence from causal claims.

expected_outcomes: Reduced misuse of probabilities outside their valid context.

expected_outcomes: Improved auditability of probabilistic reasoning and decision thresholds.

expected_outcomes: More transparent handoff from conditional probability framing to Bayesian updating, risk weighting, or causal analysis when those are needed.

prose_tradeoffs: The archetype adds communication overhead. It can also reduce apparent certainty, because once the denominator is visible the number may look more fragile or context-bound. Fine-grained conditioning may improve relevance while shrinking sample size. The goal is not to condition on everything; it is to condition on what the probability claim actually depends on and to say so.

Base-Rate Conditioning Frame

short_definition: A conditioning frame that preserves the relevant reference population before applying evidence or rates.

distinctive_feature: It foregrounds the denominator population before any likelihood or posterior calculation is allowed.

distinct_from_parent: The parent archetype covers any probability conditioned on given information; this variant emphasizes base-rate and reference-class preservation.

still_same_parent_because: Its intervention remains conditioning-context specification and renormalization, not a separate updating workflow.

use_when: A probability claim uses a rate, prevalence, prior frequency, or historical occurrence rate.

use_when: The risk is that people silently replace the relevant population with a salient subset or anecdotal case.

use_when: Bayesian updating, diagnosis, screening, or forecasting depends on the denominator being correct.

example: A diagnostic probability is stated as P(disease | positive test, symptomatic clinic population), not just P(disease | positive test).

domain: forecasting

example: A project risk rate is conditioned on comparable projects, not all projects or only memorable failures.

Subgroup-Conditioned Rate Comparison

short_definition: A conditioning frame for comparing rates only after subgroup, exposure, or case-mix conditions have been stated.

distinctive_feature: It treats the conditioning frame as a guard against denominator drift in comparisons.

distinct_from_parent: The parent applies to any conditioned probability; this variant is specialized for comparisons between groups, treatments, sites, or periods.

still_same_parent_because: The essential move is still declaring and holding fixed the conditioning event/context.

use_when: Aggregate and subgroup comparisons may disagree.

use_when: A rate comparison is vulnerable to case-mix, selection, or confounding differences.

use_when: Decision-makers need to know whether a claim is marginal, conditional, stratified, or adjusted.

example: Treatment success rates are compared within severity strata before being summarized.

example: Support-team resolution rates are conditioned on ticket complexity before teams are ranked.

Evidence-Context Probability Statement

short_definition: A communication form that states probability together with the evidence, assumptions, and information state it is conditional on.

distinctive_feature: It packages the probability number with the information-state label needed to interpret it.

distinct_from_parent: The parent covers the reasoning architecture; this variant focuses on the statement or reporting artifact.

still_same_parent_because: It remains an implementation of conditioning-frame specification.

use_when: A probability estimate will be communicated to non-specialists or downstream decision-makers.

use_when: The same number would mean something different under another evidence context.

use_when: A decision requires knowing whether probability is prior, conditional, posterior, marginal, scenario-specific, or subgroup-specific.

example: A threat estimate is labeled as conditional on current intelligence holdings, not as an unconditional event frequency.