MétaCan
Menu
Back to cohort
Record W1840847274 · doi:10.1201/9781003453420-2

MCMC Using Hamiltonian Dynamics

2011· preprint· en· W1840847274 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

Venuenot available
Typepreprint
Languageen
FieldMathematics
TopicMarkov Chains and Monte Carlo Methods
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsHamiltonian (control theory)Statistical physicsHamiltonian mechanicsComputationDiscretizationHybrid Monte CarloJacobian matrix and determinantApplied mathematicsMonte Carlo methodComputer scienceMathematicsMathematical optimizationMarkov chain Monte CarloAlgorithmPhysicsMathematical analysisPhase spaceQuantum mechanics

Abstract

fetched live from OpenAlex

Despite a few notable uses of simulation of random processes in the pre-computer era (Hammersley and Handscomb, 1964, Section 1.2; Stigler, 2002, Chapter 7), practical widespread use of simulation had to await the invention of computers. Almost as soon as computers were invented, they were used for simulation (Hammersley and Handscomb, 1964, Section 1.2). The name “Monte Carlo” started as cuteness-gambling was then (around 1950) illegal in most places, and the casino at Monte Carlo was the most famous in the world-but it soon became a colorless technical term for simulation of random processes. Markov chain Monte Carlo (MCMC) was invented soon after ordinary Monte Carlo atLos Alamos, one of the few places where computers were available at the time. Metropolis et al. (1953)∗ simulated a liquid in equilibrium with its gas phase. The obvious way to find out about the thermodynamic equilibrium is to simulate the dynamics of the system, and let it run until it reaches equilibrium. The tour de force was their realization that they did not need to simulate the exact dynamics; they only needed to simulate someMarkov chain having the same equilibrium distribution. Simulations following the scheme of Metropolis et al. (1953) are said to use the Metropolis algorithm. As computers became more widely available, the Metropolis algorithm was widely used by chemists and physicists, but it did not become widely known among statisticians until after 1990. Hastings (1970) generalized the Metropolis algorithm, and simulations following his scheme are said to use the Metropolis-Hastings algorithm. A special case of the Metropolis-Hastings algorithm was introduced by Geman and Geman (1984), apparently without knowledge of earlier work. Simulations following their scheme are said to use the Gibbs sampler. Much of Geman and Geman (1984) discusses optimization to find the posterior mode rather than simulation, and it took some time for it to be understood in the spatial statistics community that the Gibbs sampler simulated the posterior distribution, thus enabling full Bayesian inference of all kinds. Amethodology that was later seen to be very similar to the Gibbs sampler was introduced by Tanner and Wong (1987), again apparently without knowledge of earlier work. To this day, some refer to the Gibbs sampler as “data augmentation” following these authors. Gelfand and Smith (1990)made thewider Bayesian community aware of theGibbs sampler, which up to that time had been known only in the spatial statistics community. Then it took off; as of this writing, a search for Gelfand and Smith (1990) on Google Scholar yields 4003 links to other works. It was rapidly realized that most Bayesian inference couldresearchers to properly understand the theory of MCMC (Geyer, 1992; Tierney, 1994) and that all of the aforementionedworkwas a special case of the notion ofMCMC. Green (1995) generalized theMetropolis-Hastings algorithm, asmuch as it can be generalized.Although this terminology is not widely used, we say that simulations following his scheme use the Metropolis-Hastings-Green algorithm. MCMC is not used only for Bayesian inference. Likelihood inference in caseswhere the likelihood cannot be calculated explicitly due tomissing data or complex dependence can also useMCMC (Geyer, 1994, 1999; Geyer and Thompson, 1992, 1995, and references cited therein).

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.360
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.264
GPT teacher head0.407
Teacher spread0.144 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations542
Published2011
Admission routes2
Has abstractyes

Explore more

Same topicMarkov Chains and Monte Carlo MethodsFrench-language works237,207