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API

Temper samplers

MCMCTempering.tempered — Function
tempered(sampler, inverse_temperatures; kwargs...)
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API
Temper samplers
MCMCTempering.tempered — Function
tempered(sampler, inverse_temperatures; kwargs...)
 OR
 tempered(sampler, num_temps; swap_strategy=ReversibleSwap(), kwargs...)
Return a tempered version of sampler using the provided inverse_temperatures or inverse temperatures generated from num_temps and the swap_strategy.
Arguments
  • sampler is an algorithm or sampler object to be used for underlying sampling and to apply tempering to
  • The temperature schedule can be defined either explicitly or just as an integer number of temperatures, i.e. as:
    • inverse_temperatures containing a sequence of 'inverse temperatures' {β₀, ..., βₙ} where 0 ≤ βₙ < ... < β₁ < β₀ = 1     OR
    • num_temps, specifying the integer number of inverse temperatures to include in a generated inverse_temperatures
Keyword arguments
  • swap_strategy::AbstractSwapStrategy specifies the method for swapping inverse temperatures between chains
  • steps_per_swap::Integer steps are carried out between each attempt at a swap
See also
source
MCMCTempering.TemperedSampler — Type
TemperedSampler <: AbstractMCMC.AbstractSampler
A TemperedSampler struct wraps a sampler upon which to apply the Parallel Tempering algorithm.
Fields
  • sampler: sampler(s) used to target the tempered distributions
  • chain_to_beta: collection of inverse temperatures β; β[i] correponds i-th tempered model
  • swapstrategy: strategy to use for swapping
  • adapt: boolean flag specifying whether or not to adapt
  • adaptation_states: adaptation parameters
source
Under the hood, MCMCTempering.TemperedSampler is actually just a "fancy" representation of a composition (represented using a MCMCTempering.CompositionSampler) of a MCMCTempering.MultiSampler and a MCMCTempering.SwapSampler.
Roughly speaking, the implementation of AbstractMCMC.step for MCMCTempering.TemperedSampler is basically
# 1. Construct the tempered models.
 multimodel = MultiModel([make_tempered_model(model, β) for β in tempered_sampler.chain_to_beta])
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 multi_sampler = sampler1 × sampler2 × sampler3 # or `MultiSampler((sampler1, sampler2, sampler3))`
 # Target the joint model.
 AbstractMCMC.step(rng, multi_model, multi_sampler)
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where the tempered models are represented using a MCMCTempering.MultiModel

The step for a MCMCTempering.MultiSampler and a [MCMCTempering.MultiModel] is a transition of type MCMCTempering.MultipleTransitions and a state of type MCMCTempering.MultipleStates

  • SYED19Syed, S., Bouchard-Côté, Alexandre, Deligiannidis, G., & Doucet, A., Non-reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme, arXiv:1905.02939, (2019).
  • SYED19Syed, S., Bouchard-Côté, Alexandre, Deligiannidis, G., & Doucet, A., Non-reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme, arXiv:1905.02939, (2019).
  • PTPH05Earl, D. J., & Deem, M. W., Parallel tempering: theory, applications, and new perspectives, Physical Chemistry Chemical Physics, 7(23), 3910–3916 (2005).
  • 1Malcolm Sambridge, A Parallel Tempering algorithm for probabilistic sampling and multimodal optimization, Geophysical Journal International, Volume 196, Issue 1, January 2014, Pages 357–374, https://doi.org/10.1093/gji/ggt342
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Getting started: a simple Mixture of Gaussians example

Suppose we have a mixture of Gaussians, e.g. something like

using Distributions
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Getting started: a simple Mixture of Gaussians example
Suppose we have a mixture of Gaussians, e.g. something like
using Distributions
 target_distribution = MixtureModel(
     Normal,
     [(-3, 1.5), (3, 1.5), (20, 1.5)],  # parameters
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 end
 density!(chain_tempered_all[1], color="green", size=figsize)
 plot!(size=figsize)

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-Home · MCMCTempering
GitHub
MCMCTempering.jl
Tempering methods and more for Markov chain Monte Carlo methods.
MCMCTempering provides implementations of different ways to define tempered samplers and models, in addition to other ways of composing and mixing samplers.

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MCMCTempering.jl
Tempering methods and more for Markov chain Monte Carlo methods.
MCMCTempering provides implementations of different ways to define tempered samplers and models, in addition to other ways of composing and mixing samplers.

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