Description
Multiply nonnegative priorOdds and likelihoodRatio to obtain posteriorOdds, then return posteriorProbability=posteriorOdds/(1+posteriorOdds).
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 nonnegative priorOdds and likelihoodRatio to obtain posteriorOdds, then return posteriorProbability=posteriorOdds/(1+posteriorOdds).
When to use this tool
Use Two Conditionals Bayes Odds 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, likelihoodRatio. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read posteriorOdds, posteriorProbability. Use the output convention below.
Multiply nonnegative priorOdds and likelihoodRatio to obtain posteriorOdds, then return posteriorProbability=posteriorOdds/(1+posteriorOdds).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| priorOdds | Prior Odds | Required. Finite number. |
| likelihoodRatio | Likelihood Ratio | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| posteriorOdds | Posterior Odds | Required. Finite number. |
| posteriorProbability | Posterior Probability | Required. Finite number. |
{
"input": {
"priorOdds": 1,
"likelihoodRatio": 3
},
"output": {
"posteriorOdds": 3,
"posteriorProbability": 0.75
}
}Limitations and assumptions
- Odds mean probability divided by its complement, not a probability numeral. Infinite odds are unsupported; extreme finite products can cause a result-range error.
- 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
- Probability: Probability Odds Boundary Policy
Report exact probability-to-odds endpoint status without non-JSON infinity; odds zero is unused when finite=false, unlike a clipped probability.
- Odds Product Evidence Factor
Multiply supplied sequential conditional likelihood ratios; independence is required if ratios were instead computed marginally.