arXiv subjects

Tommaso Costa

Publications and source records attributed to Tommaso Costa.

5 recordsLinked to original sources

arXiv2026

A Bayesian Reinterpretation of Cornfield-Type Sensitivity Analysis: From Thresholds to Probabilities

Sensitivity analysis for unmeasured confounding in observational studies is commonly based on threshold quantities, such as the Cornfield condition or the E-value, which quantify how strong a confounder must be to explain away an observed association. However, these approaches do not address a fundamental inferential question: how plausible is it that such a confounder exists? In this work, we propose a Bayesian reformulation of Cornfield-type sensitivity analysis in which the strength of unmeasured confounding is treated as a random variable. Within this framework, the E-value is reinterpreted as a threshold, and the central inferential quantity becomes the posterior probability that confounding exceeds this threshold. This transforms sensitivity analysis from a descriptive diagnostic into a probabilistic assessment of robustness. We develop a simple generative model linking observed effect estimates to true causal effects and confounding bias, and we specify prior distributions reflecting plausible confounding mechanisms. The resulting framework yields posterior measures of evidential vulnerability that are directly interpretable and applicable to summary-level data. Illustrations based on empirical case studies show that the proposed approach preserves the interpretability of the E-value while providing a more nuanced and decision-relevant characterization of robustness. More broadly, the framework aligns sensitivity analysis with Bayesian principles of inference under uncertainty, offering a coherent alternative to purely threshold-based reasoning.

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arXiv2025

Evidence and Elimination: A Bayesian Interpretation of Falsification in Scientific Practice

The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet the relationship between Popper's eliminative view of theory testing and Bayesian model comparison remains insufficiently articulated. This paper develops a unified account in which falsification is reinterpreted as a Bayesian process of model elimination. A theory is not rejected because it contradicts an observation in a logical sense; it is eliminated because it assigns vanishing integrated probability to the data in comparison with an alternative model. This reinterpretation resolves the difficulties raised by the Duhem-Quine thesis, clarifies the status of auxiliary hypotheses, and explains why ad hoc modifications reduce rather than increase theoretical credibility. The analysis is illustrated through two classical episodes in celestial mechanics, the discovery of Neptune and the anomalous precession of Mercury. In the Neptune case, an auxiliary hypothesis internal to Newtonian gravity dramatically increases the marginal likelihood of the theory, preserving it from apparent refutation. In the Mercury case, no permissible auxiliary modification can rescue the Newtonian model, while general relativity assigns high probability to the anomaly without adjustable parameters. The resulting posterior collapse provides a quantitative realisation of Popper's eliminative criterion. Bayesian model comparison therefore supplies the mathematical structure that Popper's philosophy lacked and offers a coherent account of scientific theory change as a process of successive eliminations within a space of competing models.

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arXiv2025

From Hume to Jaynes: Induction as the Logic of Plausible Reasoning

The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace and Jeffreys, who sought to quantify belief through probability, and the critical skepticism of Popper, who replaced confirmation with falsification. Both approaches, however, assume that induction must deliver certainty or its negation. In this paper, I argue that the problem of induction dissolves when recast in terms of logical coherence (understood as internal consistency of credences under updating) rather than truth. Following E. T. Jaynes, probability is interpreted not as frequency or decision rule but as the extension of deductive logic to incomplete information. Under this interpretation, Bayes's theorem is not an empirical statement but a consistency condition that constrains rational belief updating. Induction thus emerges as the special case of deductive reasoning applied to uncertain premises. Falsification appears as the limiting form of Bayesian updating when new data drive posterior plausibility toward zero, while the Bayes Factor quantifies the continuous spectrum of evidential strength. Through analytical examples, including Laplace's sunrise problem, Jeffreys's mixed prior, and confidence-based reformulations, I show that only the logic of plausible reasoning unifies these perspectives without contradiction. Induction, properly understood, is not the leap from past to future but the discipline of maintaining coherence between evidence, belief, and information.

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arXiv2025

Reevaluating Specificity in Neuroimaging: Implications for the Salience Network and Methodological Rigor

The accurate assessment of neuroimaging specificity is critical for advancing our understanding of brain disorders. Current methodologies often rely on frequentist approaches and limited cross-pathology comparisons, leading to potential overestimations of specificity. This study critiques these limitations, highlighting the inherent shortcomings of frequentist methods in specificity calculations and the necessity of comprehensive control conditions. Through a review of the Bayesian framework, we demonstrate its superiority in evaluating specificity by incorporating probabilistic modeling and robust reverse inference. The work also emphasizes the pivotal role of well-defined control conditions in mitigating overlap among brain pathologies, particularly within shared networks like the salience network. By applying Bayesian tools such as BACON (Bayes fACtor mOdeliNg), we validate the ability to derive disease-specific patterns, contrasting these with the narrower findings of frequentist analyses. This paper underscores the importance of Bayesian methodologies and extensive meta-analytic datasets in overcoming existing challenges, ultimately paving the way for more precise neuroimaging studies.

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arXiv2021

A bayesian reanalysis of the phase III aducanumab (ADU) trial

In this article we have conducted a reanalysis of the phase III aducanumab (ADU) summary statistics announced by Biogen, in particular the result of the Clinical Dementia Rating-Sum of Boxes (CDR-SB). The results showed that the evidence on the efficacy of the drug is very low and a more clearer view of the results of clinical trials are presented in the Bayesian framework that can be useful for future development and research in the field.

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