Topics
Bayesian Inference for Posterior Probability Misinterpretation in Signal-Based Systems
Prof. Alessio Drivet
GeoGebra Institute of Turin Turin, Italy
Abstract:
Systematic errors in probabilistic reasoning arise whenever observable signals are interpreted
without proper accounting for prior probabilities and likelihoods. A pervasive instance of this error
is the confusion between forward probability P(A∣B) and inverse probability P(B∣A), a
misinterpretation that occurs not only in everyday reasoning, but also in the analysis of engineering
and physical detection systems.
This presentation develops a unified Bayesian framework to analyse this class of inference errors
across multiple domains of increasing technical complexity. Starting from socioeconomic case
studies—such as education outcomes and wealth signalling—the analysis extends to clinical
diagnostics, and further to canonical problems in applied physics and engineering, including radar
target detection and trigger-based event selection in high-energy physics experiments.
In each case, observable indicators are modelled as noisy signals generated by latent states, and
inference is formulated as posterior probability estimation under uncertainty. The relationship
between signal strength, base rates, and posterior probability is examined analytically, with
parameters grounded in empirical data and representative system configurations.
Numerical simulations complement the analytical results, illustrating how posterior probabilities
evolve as functions of prior distributions, likelihoods, and false positive rates. The results highlight
structural parallels between Bayesian inference, imbalanced classification, and signal detection
theory, providing a unified perspective on systematic inference errors.
These findings have direct implications for the design and interpretation of detection systems,
decision-support models, and the communication of uncertainty in applied and experimental
contexts.
Brief Biography of the Speaker:
He graduated from the University of Trento in 1975. Until his retirement in 2011, he served as a tenured
teacher in mathematics, probability, and statistics in commercial schools, where he developed a deep
expertise in pedagogical methodologies. Throughout his career, he has been an author, publishing
numerous books, specialised chapters, and scientific articles on mathematics and computer science with
several publishers. His influence extends into higher education and policymaking through his extensive
contract training activities for the University of Turin and the Ministry of Education, where he helped
implement various National Plans for digital and mathematical literacy. It is a speaker at international and
national conferences. Currently, he serves on the scientific and organisational committees of DI.FI.MA. and
the GeoGebra Institute of Turin. His current work focuses on the innovative dissemination of mathematics,
aiming to inspire curiosity and analytical thinking among secondary school students.