MCMC

Purpose

MCMC is the baseline Metropolis-style chain sampler in Jarvis-HEP.

Full Sampling Section Keys

• Sampling.Method (required): must be MCMC.
• Sampling.Variables (required, array):
• name (required)
• description (required)
• distribution.type (required)
• distribution.parameters (required)
• Runtime-safe parameter sets:
  • Flat: min, max
  • Log: min, max
  • Normal: mean, stddev
  • Log-Normal: mean, stddev
  • Logit: location, scale
• Sampling.LogLikelihood (required, array): {name, expression}
• Sampling.selection (optional, string): proposal filter expression.
• Sampling.Bounds (required):
• num_chains (required, integer)
• num_iters (required, integer)
• proposal_scale (required, number or array)

Full Skeleton

Sampling:
  Method: "MCMC"
  Variables:
    - name: p1
      description: parameter 1
      distribution:
        type: Flat
        parameters:
          min: -5
          max: 5
  LogLikelihood:
    - name: L_total
      expression: "-0.5*(p1/1.0)^2"
  selection: "p1 > -4.9"
  Bounds:
    num_chains: 8
    num_iters: 5000
    proposal_scale: 0.08

Example

Sampling:
  Method: "MCMC"
  Variables:
    - name: xx
      description: x
      distribution:
        type: Flat
        parameters:
          min: 0.0
          max: 31.4159
    - name: yy
      description: y
      distribution:
        type: Flat
        parameters:
          min: 0.0
          max: 31.4159
  LogLikelihood:
    - name: L_z
      expression: "-0.5*((z-100.0)/10.0)^2"
  selection: "xx > 0 and yy > 0"
  Bounds:
    num_chains: 8
    num_iters: 5000
    proposal_scale: 0.08