Parallel tempering
Algorithms AIMech:ParallelTempering DRAFT
Aliases: Replica exchange Monte Carlo, Metropolis-coupled Markov chain Monte Carlo
A population Monte Carlo method that combines within-temperature target-preserving updates with corrected exchanges between replicas targeting differently tempered densities.
Identity Notes & Concept Scope
The record identifies fixed-temperature parallel tempering, with the source’s adjacent-swap and random-walk realization as an explicit example. The population state includes all replicas; the beta=1 replica targets the original distribution. It differs from a single-chain simulated-temperature state and from adapting the temperature ladder. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 181 prior native IDs/names/aliases. Ignored-inclusive searches of both full checkouts found prior discovery leads, neighboring sampler discussions and unrelated author-name/environment substrings. Existing random-walk Metropolis, delayed-rejection, fixed symmetric delayed-rejection and RAM records were inspected; shared components do not make these procedures equivalent.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Choose a fixed L≥2 and inverse temperatures 1=beta1>...>betaL>0 for which each integral Z_beta=integral pi(x)^beta dx is finite. Initialize replicas in positive target support. The joint target is the product of pi(x_l)^beta_l/Z_beta_l. In the inspected realization, choose j uniformly from adjacent pairs and propose swapping x_j and x_(j+1), with probability min(1,[pi(x_(j+1))/pi(x_j)]^(beta_j−beta_(j+1))). Then apply a Gaussian random-walk Metropolis update at every level using acceptance min(1,[pi(y_l)/pi(x_l)]^beta_l); rejected moves retain their current replica state. Both steps preserve the joint target, so their composition does also; samples at beta1=1 have the desired stationary marginal.
⚠️ Curated Limitations & Negative Results
- All tempered densities must be normalizable; flattening a target by taking a positive power below one need not preserve integrability.
- Target invariance alone does not establish irreducibility, mixing speed, finite-run convergence or independence of cold-replica samples.
- The source calls the composed chain reversible. Composition of two reversible kernels need not be reversible without additional conditions; this record asserts only their directly justified invariance.
- The original distribution is the cold replica’s marginal, not the pooled unweighted population distribution.
- Other valid local kernels and exchange schedules require their own conditions. The record’s explicit Gaussian and adjacent-swap realization is not a claim that all implementations use it.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | At fixed temperatures and proposal settings, the complete replica population follows a Markov transition preserving a product of tempered targets. AIO MarkovChain denotes the stochastic process/model beneath Network. This is a related algorithm-to-process mapping, not equivalence, subclass membership or an assertion of independent cold-replica samples. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Błażej Miasojedow, Eric Moulines, Matti Vihola
|
primary paper
full_text
|
ID: arXiv:1205.1076v1
sha256:4c0f3ba8a5a8…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:40:20Z
Updated: 2026-10-11T07:41:38Z
Source File:
data/curated/ParallelTempering.yaml