Bibliographic record
Abstract
Overview 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. The chapter starts with an introduction to Monte Carlo integration and examines how a Markov chain, implemented by the Metropolis–Hastings algorithm, can be employed to concentrate samples to regions with significant probability. Next, tempering improvements are investigated that prevent the MCMC from getting stuck in the region of a local peak in the probability distribution.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.027 | 0.006 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".