Description
For positive first, second, and scale return ratio=first/second and scaledRatio=(first*scale)/(second*scale).
A binary probability p corresponds to odds p/(1-p). Evidence updates can multiply prior odds by a likelihood ratio, or normalize likelihood-weighted priors. Likelihood densities can exceed one, while event probabilities cannot; compatible observation definitions and measurement bases matter before combining them.
For positive first, second, and scale return ratio=first/second and scaledRatio=(first*scale)/(second*scale).
When to use this tool
Use Likelihood Ratio Explicit Scale Invariance when you need the stated odds conversion, binary update, or normalization of compatible supplied weights.
How to use the tool and how it works
- Enter first, second, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio, scaledRatio. Use the output convention below.
For positive first, second, and scale return ratio=first/second and scaledRatio=(first*scale)/(second*scale).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number; strictly above 0. |
| second | Second | Required. Finite number; strictly above 0. |
| scale | Scale | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Ratio in the direction and unit convention stated in the formula. | Required. Finite number. |
| scaledRatio | Scaled Ratio | Required. Finite number. |
{
"input": {
"first": 2,
"second": 4,
"scale": 3
},
"output": {
"ratio": 0.5,
"scaledRatio": 0.5
}
}Limitations and assumptions
- The mathematical scale invariance can fail numerically when products overflow or underflow. This calculation compares supplied likelihood-like values without evaluating a model.
- 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 complete likelihood model and an explicit hypothesis space when supplied weights cannot be justified independently. For extreme products, a log-domain calculation can reduce avoidable underflow.
References
Similar or alternative tools
- Binary Observation Log Likelihood Ratio Term
For binary outcome and modelMass and referenceMass strictly between zero and one return ln(modelMass/referenceMass) for outcome one, otherwise ln((1-modelMass)/(1-referenceMass)).
- Bayes Likelihood Zero Evidence Flag
Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.