Smoothed dynamic factor analysis for identifying trends in multivariate time series
Bibliographic record
Abstract
Abstract Ecological processes are rarely directly observable, and inference often relies on estimating hidden or latent processes. State‐space models have become widely used for this task because of their ability to simultaneously estimate the multiple sources of variation (natural variability and variance attributed to observation errors). For multivariate time series, a second aim is often dimension reduction, or estimating a number of latent processes that are smaller than the number of observed time series. Dynamic factor analysis (DFA) has been used for performing time‐series dimension reduction, where latent processes are modelled as random walks. Whereas this may be suitable for some situations, random walks may be too flexible for other cases. Here, we introduce a new class of models, where latent processes are modelled as smooth functions (basis splines, penalized splines or Gaussian process models). We implement these models in our bayesdfa r package, which uses the rstan package for fitting. After evaluating model performance with simulated data, we apply conventional models and our smooth trend models to two long‐term datasets from the west coast of the United States: (a) a 35‐year dataset of pelagic juvenile rockfishes and (b) a 39‐year dataset of fisheries catches. Our simulations demonstrate that models matching the underlying trend smoothness make better out‐of‐sample predictions, but this advantage diminishes with increasing levels of observation error. For both case studies, the best smooth trend models had higher predictive accuracy, and yielded more precise predictions, compared to the conventional approach. The smooth trend factor models introduced here offer a new approach for state‐space dimension reduction of multivariate time series. These flexible Bayesian models may be particularly useful for data that are clumped in time, for data with high signal to noise ratios and generally for data where the underlying trend is assumed to be relatively smooth.
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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 | 0.007 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".