Description
Return the log-likelihood Hessian with respect to a Bernoulli logit at a supplied probability.
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.
Return the log-likelihood Hessian with respect to a Bernoulli logit at a supplied probability.
When to use this tool
Use Bernoulli Logit Hessian Term 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 probability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read hessian. Use the output convention below.
For probability in zero through one return hessian=-probability*(1-probability).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Dimensionless probability from zero through one. | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| hessian | Log-likelihood second derivative with respect to logit, not probability. | Required. Finite number. |
{
"input": {
"probability": 0.5
},
"output": {
"hessian": -0.25
}
}Limitations and assumptions
- This is one Bernoulli log-likelihood curvature term with respect to the logit. Endpoint values return zero as limits; the tool does not calculate a finite endpoint logit or a multivariable Hessian.
- 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 Observed Information One Trial
For mass strictly between zero and one and binary outcome return information=1/mass^2 for outcome one, otherwise 1/(1-mass)^2.
- Bernoulli Fisher Information One Point
For probability strictly between zero and one return information=1/(probability*(1-probability)).