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Record W2496191157 · doi:10.1017/cbo9780511791277.013

Markov chain Monte Carlo

2005· book-chapter· en· W2496191157 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.

Bibliographic record

VenueCambridge University Press eBooks · 2005
Typebook-chapter
Languageen
FieldMathematics
TopicMarkov Chains and Monte Carlo Methods
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsMarkov chain Monte CarloMonte Carlo methodComputer scienceHybrid Monte CarloMonte Carlo molecular modelingMonte Carlo method in statistical physicsStatistical physicsMetropolis–Hastings algorithmBayesian probabilityMonte Carlo integrationApplied mathematicsQuasi-Monte Carlo methodMathematical optimizationComputationApproximate Bayesian computationAlgorithmMathematicsArtificial intelligencePhysicsStatistics

Abstract

fetched live from OpenAlex

In the last chapter, we discussed a variety of approaches to estimate the most probable set of parameters for nonlinear models. The primary rationale for these approaches is that they circumvent the need to carry out the multi-dimensional integrals required in a full Bayesian computation of the desired marginal posteriors. This chapter provides an introduction to a very efficient mathematical tool to estimate the desired posterior distributions for high-dimensional models that has been receiving a lot of attention recently. The method is known as Markov Chain Monte Carlo (MCMC). MCMC was first introduced in the early 1950s by statistical physicists (N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller) as a method for the simulation of simple fluids. Monte Carlo methods are now widely employed in all areas of science and economics to simulate complex systems and to evaluate integrals in many dimensions. Among all Monte Carlo methods, MCMC provides an enormous scope for dealing with very complicated systems. In this chapter we will focus on its use in evaluating the multi-dimensional integrals required in a Bayesian analysis of models with many parameters.

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)0.000
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: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.850
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
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 head0.049
GPT teacher head0.256
Teacher spread0.207 · 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