Description
Return responsibility=weight*likelihood/marginal, requiring weight in zero through one, nonnegative likelihood, positive marginal, and weight*likelihood no greater than marginal.
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.
Return responsibility=weight*likelihood/marginal, requiring weight in zero through one, nonnegative likelihood, positive marginal, and weight*likelihood no greater than marginal.
When to use this tool
Use Mixture Responsibility One Component 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 weight, likelihood, marginal. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read responsibility. Use the output convention below.
Return responsibility=weight*likelihood/marginal, requiring weight in zero through one, nonnegative likelihood, positive marginal, and weight*likelihood no greater than marginal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weight | Supplied nonnegative component weight under the stated model. | Required. Finite number; minimum 0; maximum 1. |
| likelihood | Likelihood | Required. Finite number; minimum 0. |
| marginal | Marginal | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| responsibility | Responsibility | Required. Finite number. |
{
"input": {
"weight": 0.25,
"likelihood": 0.8,
"marginal": 0.4
},
"output": {
"responsibility": 0.5
}
}Limitations and assumptions
- Likelihood and marginal may be densities and need a common measure. The supplied marginal is trusted rather than rebuilt from all mixture components.
- 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
- Conditional Probability Mixture One Component
Multiply weight and conditional, both fractions within zero through one, into jointContribution.
- Bayes Likelihood Zero Evidence Flag
Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.