Description
Multiply supplied sequential conditional likelihood ratios; independence is required if ratios were instead computed marginally.
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.
Multiply supplied sequential conditional likelihood ratios; independence is required if ratios were instead computed marginally.
When to use this tool
Use Odds Product Evidence Factor 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 priorOdds, suppliedLikelihoodRatios. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read posteriorOdds, evidenceFactor. Use the output convention below.
Multiply the nonnegative suppliedLikelihoodRatios into evidenceFactor, starting from one; multiply this by nonnegative priorOdds for posteriorOdds.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| priorOdds | Prior Odds | Required. Finite number; minimum 0. |
| suppliedLikelihoodRatios | Supplied Likelihood Ratios | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| posteriorOdds | Posterior Odds | Required. Finite number. |
| evidenceFactor | Evidence Factor | Required. Finite number. |
{
"input": {
"priorOdds": 2,
"suppliedLikelihoodRatios": [
3,
0.5
]
},
"output": {
"posteriorOdds": 3,
"evidenceFactor": 1.5
}
}Limitations and assumptions
- An empty factor list returns one. Combining ratios this way requires the caller to supply a valid evidence decomposition; the tool does not establish conditional independence.
- 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
- Bayes Likelihood Zero Evidence Flag
Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.
- Categorical Atom Odds Factor
Compute one atom’s normalized probability and odds from supplied nonnegative categorical masses.