A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle
Bibliographic record
Abstract
In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.005 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".