Description
Require joint, leftGiven, rightGiven, and conditioningMass individually within zero through one; return residual=joint-conditioningMass*leftGiven*rightGiven.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
Require joint, leftGiven, rightGiven, and conditioningMass individually within zero through one; return residual=joint-conditioningMass*leftGiven*rightGiven.
When to use this tool
Use Conditional Independence One Cell Residual when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter joint, leftGiven, rightGiven, conditioningMass. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require joint, leftGiven, rightGiven, and conditioningMass individually within zero through one; return residual=joint-conditioningMass*leftGiven*rightGiven.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| joint | Joint mass including the conditioning event. | Required. Finite number; minimum 0; maximum 1. |
| leftGiven | First conditional event probability given the conditioning event. | Required. Finite number; minimum 0; maximum 1. |
| rightGiven | Second conditional event probability given the conditioning event. | Required. Finite number; minimum 0; maximum 1. |
| conditioningMass | Conditioning Mass | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Signed observed-minus-implied discrepancy under the stated formula. | Required. Finite number. |
{
"input": {
"joint": 0.125,
"leftGiven": 0.5,
"rightGiven": 0.5,
"conditioningMass": 0.5
},
"output": {
"residual": 0
}
}Limitations and assumptions
- Joint must mean the joint mass including the conditioning event. Cross-field feasibility is not checked, and a zero residual for one cell is not a full conditional-independence test.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Conditional Odds Joint Cell Crosswalk
Require joint and conditioning within zero through one and conditioning strictly greater than joint, then return odds=joint/(conditioning-joint).
- Conditional Event Complement Gap
Return conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.