# A Hierarchical Imprecise Probability Approach to Reliability Assessment of Large Language Models

arXiv: https://arxiv.org/abs/2511.00527 · HTML: https://mlsanity.com/paper/2511.00527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 86 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 30 of 42)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [DS-1000: A Natural and Reliable Benchmark for Data Science Code Generation](https://mlsanity.com/paper/2211.11501/) (2022)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [MM-SafetyBench: A Benchmark for Safety Evaluation of Multimodal Large Language Models](https://mlsanity.com/paper/2311.17600/) (2023)
- [InterCode: Standardizing and Benchmarking Interactive Coding with Execution Feedback](https://mlsanity.com/paper/2306.14898/) (2023)
- [SafetyBench: Evaluating the Safety of Large Language Models](https://mlsanity.com/paper/2309.07045/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [Clio: Privacy-Preserving Insights into Real-World AI Use](https://mlsanity.com/paper/2412.13678/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [SG-Bench: Evaluating LLM Safety Generalization Across Diverse Tasks and Prompt Types](https://mlsanity.com/paper/2410.21965/) (2024)
- [Large Language Model Psychometrics: A Systematic Review of Evaluation, Validation, and Enhancement](https://mlsanity.com/paper/2505.08245/) (2025)
- [LLM-PBE: Assessing Data Privacy in Large Language Models](https://mlsanity.com/paper/2408.12787/) (2024)
- [HumanEval Pro and MBPP Pro: Evaluating Large Language Models on Self-invoking Code Generation](https://mlsanity.com/paper/2412.21199/) (2024)
- [The Scales of Justitia: A Comprehensive Survey on Safety Evaluation of LLMs](https://mlsanity.com/paper/2506.11094/) (2025)
- [HCAST: Human-Calibrated Autonomy Software Tasks](https://mlsanity.com/paper/2503.17354/) (2025)
- [A Safety Framework for Critical Systems Utilising Deep Neural Networks](https://mlsanity.com/paper/2003.05311/) (2020)
- [CEB: Compositional Evaluation Benchmark for Fairness in Large Language Models](https://mlsanity.com/paper/2407.02408/) (2024)
- [HiBayES: A Hierarchical Bayesian Modeling Framework for AI Evaluation Statistics](https://mlsanity.com/paper/2505.05602/) (2025)
- [Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurance](https://mlsanity.com/paper/2112.00646/) (2021)
- [Assessing the Safety and Reliability of Autonomous Vehicles from Road Testing](https://mlsanity.com/paper/1908.06540/) (2019)

## Built on by (most cited first, 2 of 2)

- [Evaluating LLM Safety Under Repeated Inference via Accelerated Prompt Stress Testing](https://mlsanity.com/paper/2602.11786/) (2026)
- [Evaluating Reliability Gaps in Large Language Model Safety via Repeated Prompt Sampling](https://mlsanity.com/paper/2604.09606/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over datasets, providing limited insight into the probabilistic behavior of LLMs under real operational conditions. This paper introduces HIP-LLM, a Hierarchical Imprecise Probability framework for modeling and inferring LLM reliability. Building upon the foundations of software reliability engineering, HIP-LLM defines LLM reliability as the probability of failure-free operation over a specified number of future tasks under a given Operational Profile (OP). HIP-LLM represents dependencies across (sub-)domains hierarchically, enabling multi-level inference from subdomain to system-level reliability. HIP-LLM embeds imprecise priors to capture epistemic uncertainty and incorporates OPs to reflect usage contexts. It derives posterior reliability envelopes that quantify uncertainty across priors and data. Experiments on multiple benchmark datasets demonstrate that HIP-LLM offers a more accurate and standardized reliability characterization than existing benchmark and state-of-the-art approaches. A publicly accessible repository of HIP-LLM is provided.