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Statistical Scenario Modelling and Lookalike Distributions for Multi-Variate AI Risk

Elija Perrier

TL;DR

The paper develops a statistical framework to quantify AI risk in multi-stage workflows by decomposing a process into sub-events $X_i \sim F_i$ and evaluating AI-augmented variants $F_i^{(AI)}$ through dependency models (Markov chains or copulas) and Monte Carlo simulation to obtain the distribution of $X_{total}$, where $X_{total}=\sum_{i=1}^n X_i$ or $X_{total}=g(X_1,...,X_n)$. It addresses data scarcity with lookalike distributions, including AI-tail adjustments and iterative parameter updating guided by goodness-of-fit checks, enabling practical benchmarking of baseline, partial AI, and full AI configurations. The framework computes risk metrics such as Value at Risk $\text{VaR}_{\alpha}(X_{total})$ and Expected Shortfall $\text{ES}_{\alpha}(X_{total})$ to compare how AI affects mean performance versus tail risk. Through a hypothetical three-stage logistics example, the approach demonstrates that partial AI can reduce average performance but may increase tail risk, while full AI often improves medians yet amplifies extreme-event risk, highlighting important trade-offs for deployment. The contribution lies in integrating mature risk-analysis tools with AI risk concepts to provide a replicable method for industry practitioners to quantify and monitor system-wide AI risk in a data-informed, continuously updated manner.

Abstract

Evaluating AI safety requires statistically rigorous methods and risk metrics for understanding how the use of AI affects aggregated risk. However, much AI safety literature focuses upon risks arising from AI models in isolation, lacking consideration of how modular use of AI affects risk distribution of workflow components or overall risk metrics. There is also a lack of statistical grounding enabling sensitisation of risk models in the presence of absence of AI to estimate causal contributions of AI. This is in part due to the dearth of AI impact data upon which to fit distributions. In this work, we address these gaps in two ways. First, we demonstrate how scenario modelling (grounded in established statistical techniques such as Markov chains, copulas and Monte Carlo simulation) can be used to model AI risk holistically. Second, we show how lookalike distributions from phenomena analogous to AI can be used to estimate AI impacts in the absence of directly observable data. We demonstrate the utility of our methods for benchmarking cumulative AI risk via risk analysis of a logistic scenario simulations.

Statistical Scenario Modelling and Lookalike Distributions for Multi-Variate AI Risk

TL;DR

The paper develops a statistical framework to quantify AI risk in multi-stage workflows by decomposing a process into sub-events and evaluating AI-augmented variants through dependency models (Markov chains or copulas) and Monte Carlo simulation to obtain the distribution of , where or . It addresses data scarcity with lookalike distributions, including AI-tail adjustments and iterative parameter updating guided by goodness-of-fit checks, enabling practical benchmarking of baseline, partial AI, and full AI configurations. The framework computes risk metrics such as Value at Risk and Expected Shortfall to compare how AI affects mean performance versus tail risk. Through a hypothetical three-stage logistics example, the approach demonstrates that partial AI can reduce average performance but may increase tail risk, while full AI often improves medians yet amplifies extreme-event risk, highlighting important trade-offs for deployment. The contribution lies in integrating mature risk-analysis tools with AI risk concepts to provide a replicable method for industry practitioners to quantify and monitor system-wide AI risk in a data-informed, continuously updated manner.

Abstract

Evaluating AI safety requires statistically rigorous methods and risk metrics for understanding how the use of AI affects aggregated risk. However, much AI safety literature focuses upon risks arising from AI models in isolation, lacking consideration of how modular use of AI affects risk distribution of workflow components or overall risk metrics. There is also a lack of statistical grounding enabling sensitisation of risk models in the presence of absence of AI to estimate causal contributions of AI. This is in part due to the dearth of AI impact data upon which to fit distributions. In this work, we address these gaps in two ways. First, we demonstrate how scenario modelling (grounded in established statistical techniques such as Markov chains, copulas and Monte Carlo simulation) can be used to model AI risk holistically. Second, we show how lookalike distributions from phenomena analogous to AI can be used to estimate AI impacts in the absence of directly observable data. We demonstrate the utility of our methods for benchmarking cumulative AI risk via risk analysis of a logistic scenario simulations.

Paper Structure

This paper contains 45 sections, 27 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Background
  4. Related Work
  5. Statistical Scenario Modelling
  6. Event Sequencing
  7. Data scarcity
  8. AI-specific tail adjustments.
  9. Lookalike plus goodness-of-fit updates
  10. Dependency Structures
  11. Markov Chains
  12. Copulas
  13. Monte-Carlo Simulations
  14. Risk Measures
  15. Value at Risk (VaR)
  16. ...and 30 more sections

Figures (1)

  • Figure 1: (a) Distribution of $X_{\mathrm{total}}$ under Non-AI, Partial-AI, and Full-AI scenarios using a Gaussian copula model. (b) Distribution of $X_{\mathrm{total}}$ under Non-AI, Partial-AI, and Full-AI scenarios using the Markov chain approach.