Parallel Tempering

Parallel tempering (replica exchange MCMC) runs multiple chains at different temperatures to explore multimodal posteriors. Hot chains explore freely while cold chains sample the target posterior.

Basic Usage

from discoverysamplers.eryn_interface import DiscoveryErynBridge

bridge = DiscoveryErynBridge(model, priors)

# Create sampler with parallel tempering
sampler = bridge.create_sampler(
    nwalkers=32,
    tempering_kwargs=dict(
        ntemps=8,      # Number of temperature levels
        Tmax=20.0,     # Maximum temperature
    )
)

# Run MCMC (initial positions drawn from priors automatically)
bridge.run_sampler(nsteps=10000)

# Extract cold chain samples (default)
samples = bridge.return_all_samples()

Temperature Configuration

# Geometric ladder (default)
sampler = bridge.create_sampler(
    nwalkers=32,
    tempering_kwargs=dict(ntemps=5, Tmax=10.0)
)

# Adaptive ladder
sampler = bridge.create_sampler(
    nwalkers=32,
    tempering_kwargs=dict(ntemps=8, Tmax=None, adaptive=True)
)

# Custom ladder
import numpy as np
custom_temps = np.array([1.0, 2.0, 4.0, 8.0, 16.0])
sampler = bridge.create_sampler(
    nwalkers=32,
    ntemps=len(custom_temps),
    betas=1.0 / custom_temps,
)

Guidelines:

  • Start with ntemps = 4-8

  • Rule of thumb: ntemps ≈ 2 * sqrt(ndim)

  • Typical Tmax = 10-50

Diagnostics

# Check swap acceptance (target: 20-40%)
# After running the sampler:
swap_frac = bridge.sampler.tswap_acceptance_fraction
for i, frac in enumerate(swap_frac):
    print(f"Swap {i} ↔ {i+1}: {frac:.2%}")

  • <10%: Temperatures too far apart → increase ntemps or decrease Tmax

  • >60%: Temperatures too close → decrease ntemps or increase Tmax

With Reversible-Jump

from discoverysamplers.eryn_RJ_interface import DiscoveryErynRJBridge

# rj_model is an RJ_Discovery_model instance
# priors are in Eryn RJ format: {branch: {param_idx: distribution}}
rj_bridge = DiscoveryErynRJBridge(
    rj_model=rj_model,
    priors=rj_priors,
)

sampler = rj_bridge.create_sampler(
    nwalkers=32,
    ntemps=8,  # Parallel tempering
)

See Also