Bayesian Adaptively Updated Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models
Bibliographic record
Abstract
Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a sequence of steps following the Hamiltonian dynamics of the underlying parameter space, often yielding superior mixing properties of the resulting Markov chain. However, its performance can deteriorate sharply with the degree of irregularity of the underlying likelihood due to its lack of local adaptability in the parameter space. Riemann Manifold HMC (RMHMC), a locally adaptive version of HMC, alleviates this problem, but at a substantially increased computational cost that can become prohibitive in high-dimensional scenarios. In this paper we propose the Adaptively Updated HMC (AUHMC), an alternative inferential method based on HMC that is both fast and locally adaptive, combining the advantages of both HMC and RMHMC. The benefits become more pronounced with higher dimensionality of the parameter space and with the degree of irregularity of the underlying likelihood surface. We show that AUHMC satisfies detailed balance for a valid MCMC scheme and provide a comparison with RMHMC in terms of effective sample size, highlighting substantial efficiency gains of AUHMC. Simulation examples and an application of the BEKK GARCH model show the practical usefulness of the new posterior sampler.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
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 teacher head, 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".