Description
For mass strictly between zero and one and binary outcome return information=1/mass^2 for outcome one, otherwise 1/(1-mass)^2.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
For mass strictly between zero and one and binary outcome return information=1/mass^2 for outcome one, otherwise 1/(1-mass)^2.
When to use this tool
Use Bernoulli Observed Information One Trial when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter mass, outcome. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read information. Use the output convention below.
For mass strictly between zero and one and binary outcome return information=1/mass^2 for outcome one, otherwise 1/(1-mass)^2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Mass in a consistent unit for the stated model. | Required. Finite number. |
| outcome | Outcome | Required. Safe integer; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| information | Information | Required. Finite number. |
{
"input": {
"mass": 0.5,
"outcome": 1
},
"output": {
"information": 4
}
}Limitations and assumptions
- This is observed information for the Bernoulli probability parameter, not its expectation or information in the logit parameter. Values near an endpoint can exceed the finite output range.
- 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 full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Bernoulli Fisher Information One Point
For probability strictly between zero and one return information=1/(probability*(1-probability)).
- Bernoulli Logit Hessian Term
Return the log-likelihood Hessian with respect to a Bernoulli logit at a supplied probability.