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Scan Parameters (Sampler Variables Schema)

Sampling:
  Variables:
    - name: x1
      description: "A flat distributed variable x1"
      distribution:
        type: Flat
        parameters:
          min: 0
          max: 10

    - name: x2
      description: "A log-distributed variable x2"
      distribution:
        type: Log
        parameters:
          min: 0.1
          max: 10

    - name: x3
      description: "A normal-distributed variable x3"
      distribution:
        type: Normal
        parameters:
          mean: 10
          stddev: 5

    - name: x4
      description: "A log-normal variable x4"
      distribution:
        type: Log-Normal
        parameters:
          mean: 10
          stddev: 5

    - name: x5
      description: "A logit-distributed variable x5"
      distribution:
        type: Logit
        parameters:
          location: 10
          scale: 5

Structure (explained)

Sampling.Variables is a list. Each list item defines one input variable.

Fields for each variable

  • name (string)
    • A short identifier for the variable.
    • Keep it unique within the scan.
  • description (string)
    • A short sentence describing what the variable represents.
  • distribution (object)
    • Groups the distribution settings.
    • distribution.type (string)
      • The distribution family to sample from.
    • distribution.parameters (object)
      • The parameter set required by the chosen type.

One-dimensional distributions (definitions)

Below are the definitions (and required parameters) for each supported 1D distribution.

  • Flat (uniform)

    • Parameters: min, max

    • Definition:

      \[ x \sim \mathcal{U}(\mathrm{min},\mathrm{max}) \]

      Meaning: sample uniformly on [min, max].

  • Log (log-uniform)

    • Parameters: min, max (requires min > 0)

    • Definition:

      \[ \ln x \sim \mathcal{U}(\ln(\mathrm{min}),\ln(\mathrm{max})) \]

      Equivalently:

      \[ x = \exp(u),\quad u \sim \mathcal{U}(\ln(\mathrm{min}),\ln(\mathrm{max})) \]

  • Normal (Gaussian)

    • Parameters: mean, stddev

    • Definition:

      \[ x \sim \mathcal{N}(\mathrm{mean},\mathrm{stddev}) \]

      Rule of thumb: approximately 68.3% of the probability mass lies within [mean − stddev, mean + stddev]

  • Log-Normal

    • Parameters: mean, stddev

    • Definition:

      \[ \ln(x) \sim \mathcal{N}(\mathrm{mean},\mathrm{stddev}) \]

      Equivalently:

      \[ x = \exp(u),\quad u \sim \mathcal{N}(\mathrm{mean},\mathrm{stddev}) \]

  • Logit

    • Parameters: location, scale

    • Definition (inverse CDF from a uniform variate):

      \[ u \sim \mathcal{U}(0,1),\quad x = \mathrm{location} + \mathrm{scale}\cdot\ln\left(\frac{u}{1-u}\right) \]

      Equivalent distribution:

      \[ x \sim \mathrm{Logistic}(\mathrm{location},\mathrm{scale}) \]

  • Mapping support

    • The following distributions support mapping from a standard random variable \(u \in [0,1]\): Flat, Log, Normal, Log-Normal, Logit.
    • The following distributions do not support this mapping in the current implementation: Binomial, Poisson, Beta, Exponential, Gamma.