Description
Normalize two nonnegative hypothesis likelihood weights against a supplied binary prior, rejecting zero evidence; likelihoods may be densities above one.
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.
Normalize two nonnegative hypothesis likelihood weights against a supplied binary prior, rejecting zero evidence; likelihoods may be densities above one.
When to use this tool
Use Probability: Two Hypothesis Likelihood Weight Normalizer 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 firstLikelihood, secondLikelihood, firstPrior. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Form a=firstLikelihood*firstPrior and b=secondLikelihood*(1-firstPrior). Require nonnegative likelihoods, a prior within zero through one, and positive a+b; return evidence=a+b and posterior weights a/evidence and b/evidence inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstLikelihood | Nonnegative first-hypothesis likelihood or density; may exceed one. | Required. Finite number. |
| secondLikelihood | Nonnegative second-hypothesis likelihood on the same observation/measure basis. | Required. Finite number. |
| firstPrior | First-hypothesis probability; the second prior is one minus this. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.firstPosterior | First Posterior | Calculated result member: number. |
| result.secondPosterior | Second Posterior | Calculated result member: number. |
| result.evidence | Evidence | Calculated result member: number. |
{
"input": {
"firstLikelihood": 0.8,
"secondLikelihood": 0.2,
"firstPrior": 0.5
},
"output": {
"result": {
"firstPosterior": 0.8,
"secondPosterior": 0.2,
"evidence": 0.5
}
}
}Limitations and assumptions
- Likelihoods can be densities above one; both must use a compatible observation and measure. Zero evidence is an input-domain error, and the two hypotheses are treated as exhaustive.
- Outputs are nested inside result. 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.
- Two Conditionals Bayes Odds Factor
Multiply nonnegative priorOdds and likelihoodRatio to obtain posteriorOdds, then return posteriorProbability=posteriorOdds/(1+posteriorOdds).