Description
Return one importance-sampling contribution.
A dimensionless time-step ratio, free-diffusion scale or sampling weight assumes a particular model and data basis. Local bounds and factors can help diagnose a method, but accuracy, stability and statistical uncertainty depend on the complete algorithm and its assumptions.
Return one importance-sampling contribution.
When to use this tool
Use Monte Carlo One Sample Importance Term when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter integrand, proposalDensity, targetDensity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read importanceWeight, contribution. Use the output convention below.
Return one importance-sampling contribution. Require proposalDensity > 0 and targetDensity >= 0; importanceWeight = target/proposal, contribution = integrand*weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| integrand | Integrand | Required. Finite number. |
| proposalDensity | Proposal Density | Required. Finite number; strictly above 0. |
| targetDensity | Target Density | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| importanceWeight | Importance Weight | Required. Finite number. |
| contribution | Contribution | Required. Finite number. |
{
"input": {
"integrand": 3,
"proposalDensity": 0.2,
"targetDensity": 0.4
},
"output": {
"importanceWeight": 2,
"contribution": 6
}
}Limitations and assumptions
- Densities use the same measure; support, normalization, random sampling and an estimator's uncertainty are not verified.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Analyze the full numerical or stochastic method, its support and error behavior before treating a local factor as a reliability guarantee.
References
Similar or alternative tools
- statistics/weighted-mean
Calculate an arithmetic mean using nonnegative observation weights.
- Poisson Stencil One Source Term Tool
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