A Generalized Linear Mixed Model for Data Breaches and Its Application in Cyber Insurance
Bibliographic record
Abstract
Data breach incidents result in severe financial loss and reputational damage, which raises the importance of using insurance to manage and mitigate cyber related risks. We analyze data breach chronology collected by Privacy Rights Clearinghouse (PRC) since 2001 and propose a Bayesian generalized linear mixed model for data breach incidents. Our model captures the dependency between frequency and severity of cyber losses and the behavior of cyber attacks on entities across time. Risk characteristics such as types of breach, types of organization, entity locations in chronology, as well as time trend effects are taken into consideration when investigating breach frequencies. Estimations of model parameters are presented under Bayesian framework using a combination of Gibbs sampler and Metropolis–Hastings algorithm. Predictions and implications of the proposed model in enterprise risk management and cyber insurance rate filing are discussed and illustrated. We find that it is feasible and effective to use our proposed NB-GLMM for analyzing the number of data breach incidents with uniquely identified risk factors. Our results show that both geological location and business type play significant roles in measuring cyber risks. The outcomes of our predictive analytics can be utilized by insurers to price their cyber insurance products, and by corporate information technology (IT) and data security officers to develop risk mitigation strategies according to company’s characteristics.
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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 | 0.017 | 0.029 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".