DRAM

Purpose

DRAM (Delayed Rejection Adaptive Metropolis) adds multi-stage delayed rejection on top of adaptive MCMC.

Full Sampling Section Keys

• Sampling.Method (required): must be DRAM.
• 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): {name, expression} list.
• Sampling.selection (optional, string)
• Sampling.Bounds:
• num_chains (required, integer)
• num_iters (required, integer)
• proposal_scale (required, number)
• adapt_enabled (optional, boolean, default true)
• adapt_start_iter (optional, integer, default 100)
• adapt_window (optional, integer, default 25)
• adapt_eps (optional, number, default 1e-6)
• adapt_scale (optional, number, default 2.38)
• dr_steps (optional, integer, default 2)
• dr_scale_factors (optional, array of numbers, default [1.0, 0.5])

Full Skeleton

Sampling:
  Method: "DRAM"
  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"
  Bounds:
    num_chains: 6
    num_iters: 8000
    proposal_scale: 0.08
    adapt_enabled: true
    adapt_start_iter: 100
    adapt_window: 25
    adapt_eps: 1.0e-6
    adapt_scale: 2.38
    dr_steps: 3
    dr_scale_factors: [1.0, 0.6, 0.3]

Example

Sampling:
  Method: "DRAM"
  Variables:
    - name: xx
      description: x
      distribution:
        type: Flat
        parameters:
          min: 0.0
          max: 31.4159
  LogLikelihood:
    - name: L_z
      expression: "-0.5*((z-100.0)/10.0)^2"
  Bounds:
    num_chains: 6
    num_iters: 8000
    proposal_scale: 0.08
    adapt_enabled: true
    dr_steps: 3
    dr_scale_factors: [1.0, 0.6, 0.3]