arXiv subjects

Rabiu Tsoho Muhammad

Publications and source records attributed to Rabiu Tsoho Muhammad.

3 recordsLinked to original sources

arXiv2026

The Impact of Operational-Data Fidelity when Assessing Safety-Critical Autonomous-Vehicle Software

For safety-critical software, data from the software's operational past (e.g. a sequence of success and failure events experienced by the software) can provide strong statistical support for reliability claims about the software. However, such data might not describe past software failure events in sufficient detail, and this might leave a reliability assessment (based on this data) unable to account for important features of past software failures. In this paper, by extending conservative Bayesian inference (CBI) techniques used in reliability assessment, we illustrate a principled statistical approach for checking the robustness of reliability claims derived from insufficiently detailed operational data. We demonstrate the extent to which insufficient detail in operational data can undermine software reliability claims in autonomous vehicle (AV) safety assessment scenarios. Reliability claims derived from insufficiently fine-grained data might be dangerously optimistic, despite a concerted effort by an assessor to use such data conservatively during the assessment. While these findings are consistent with previous work on the impact of statistical model fidelity in Bayesian software reliability assessments, our work clarifies why attempts to use low-fidelity data conservatively can be naive, and we give the first conservative estimates of the impact of data fidelity on assessments.

cs.RO↗

arXiv2026

Fixed-Point Characterisations of Extremal Distributions under Partial Distributional Constraints

We present a methodological framework for solving robust inference problems with partially specified distributions over measurable subsets of a parameter space. Partial specifications define a set of admissible distributions. The goal is to determine extremal values (over these admissible distributions) for statistical quantities, where these quantities---these objective functions---are ratios of expectations of analytic functions, continuous functions, piecewise continuous functions, and uniform limits of piecewise continuous functions. We show that extremal values are approached by sequences of admissible distributions, whose limiting extremal distributions are characterised by fixed-point conditions on their support locations. This characterises where extremal distributions place probability mass and yields a practical computational framework for solving the corresponding optimisation problems. We establish convergence and asymptotic properties of the resulting extremal distributions and extremal objective function values. This work extends robust inference methods (e.g. robust Bayesian inference) by combining extremal-distribution reduction, fixed-point characterisation, and approximation-based analysis within a unified framework.

math.ST↗

arXiv2025

Conservative Software Reliability Assessments Using Collections of Bayesian Inference Problems

When using Bayesian inference to support conservative software reliability assessments, it is useful to consider a collection of Bayesian inference problems, with the aim of determining the worst-case value (from this collection) for a posterior predictive probability that characterizes how reliable the software is. Using a Bernoulli process to model the occurrence of software failures, we explicitly determine (from collections of Bayesian inference problems) worst-case posterior predictive probabilities of the software operating without failure in the future. We deduce asymptotic properties of these conservative posterior probabilities and their priors, and illustrate how to use these results in assessments of safety-critical software. This work extends robust Bayesian inference results and so-called conservative Bayesian inference methods.

stat.AP↗