HMC

Purpose

HMC uses leapfrog dynamics for Hamiltonian proposals.

Full Sampling Section Keys

• Sampling.Method (required): must be HMC.
• Sampling.Variables (required):
• name, description, distribution.type, distribution.parameters
• runtime-safe parameter sets: Flat(min,max), Log(min,max), Normal(mean,stddev), Log-Normal(mean,stddev), Logit(location,scale)
• Sampling.LogLikelihood (required): array of {name, expression}
• Sampling.selection (optional, string)
• Sampling.Bounds:
• base keys: num_chains, num_iters, proposal_scale
• HMC keys:
  • hmc_step_size (optional, number, default 0.05)
  • hmc_leapfrog_steps (optional, integer, default 8)
  • step_size (optional, number, alias)
  • leapfrog_steps (optional, integer, alias)

Full Skeleton

Sampling:
  Method: "HMC"
  Variables:
    - name: x
      description: variable x
      distribution:
        type: Flat
        parameters:
          min: -5
          max: 5
  LogLikelihood:
    - name: L_x
      expression: "-0.5*(x/1.0)^2"
  Bounds:
    num_chains: 6
    num_iters: 9000
    proposal_scale: [0.05, 0.05, 0.05, 0.05, 0.05, 0.05]
    hmc_step_size: 0.03
    hmc_leapfrog_steps: 12
    step_size: 0.03
    leapfrog_steps: 12

Example

Sampling:
  Method: "HMC"
  Variables:
    - name: x
      description: variable x
      distribution:
        type: Flat
        parameters:
          min: -5
          max: 5
  LogLikelihood:
    - name: L_x
      expression: "-0.5*(x/1.0)^2"
  Bounds:
    num_chains: 6
    num_iters: 9000
    proposal_scale: [0.05, 0.05, 0.05, 0.05, 0.05, 0.05]
    hmc_step_size: 0.03
    hmc_leapfrog_steps: 12