Parametric inference for time‐to‐failure in multi‐state semi‐Markov models: A comparison of marginal and process approaches
Bibliographic record
Abstract
Abstract In many applications, the time to some event of interest (generically called “failure”) is the end point of an underlying stochastic process. This article considers processes that can be characterized by multi‐state models, specifically progressive semi‐Markov processes. Under this framework, the authors examine estimation and prediction efficiencies of two approaches for making inference about the time‐to‐failure (TTF) distribution. The first is the traditional approach based on just TTF data. The second uses all the information in the multi‐state data to estimate the underlying parameters and then makes inference about the TTF. The latter inference can be complex with panel data (involving interval and right censoring), so it is important to quantify the efficiency gains to determine if the additional complexity is worth the effort. The authors focus mostly on gamma distributions for state sojourn times because they are closed under convolution. Results for the inverse Gaussian case which shares this property are also briefly discussed. The Canadian Journal of Statistics 39: 537–555; 2011 © 2011 Statistical Society of Canada
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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 | 0.025 | 0.098 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".