Description
Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.
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.
Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.
When to use this tool
Use Bayes Likelihood Zero Evidence Flag 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 prior, likelihood, complementLikelihood. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read evidence, posteriorDefined, posterior. Inspect posteriorDefined before interpreting the associated values.
Compute evidence=prior*likelihood+(1-prior)*complementLikelihood for three valid probabilities. Return posteriorDefined=(evidence>0) and posterior=prior*likelihood/evidence when defined, otherwise zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| prior | Prior | Required. Finite number; minimum 0; maximum 1. |
| likelihood | Likelihood | Required. Finite number; minimum 0; maximum 1. |
| complementLikelihood | Complement Likelihood | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| evidence | Evidence | Required. Finite number. |
| posteriorDefined | Posterior Defined | Required. Boolean. |
| posterior | Posterior | Required. Finite number. |
{
"input": {
"prior": 0.5,
"likelihood": 0,
"complementLikelihood": 0
},
"output": {
"evidence": 0,
"posteriorDefined": false,
"posterior": 0
}
}Limitations and assumptions
- The undefined posterior is a placeholder that must be read with posteriorDefined. Unlike a density-weight update, this tool bounds both likelihoods by one and rejects no-evidence inference through a flag rather than an input 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
- Likelihood Ratio Explicit Scale Invariance
For positive first, second, and scale return ratio=first/second and scaledRatio=(first*scale)/(second*scale).
- Odds Product Evidence Factor
Multiply supplied sequential conditional likelihood ratios; independence is required if ratios were instead computed marginally.