Artificial Intelligence (ai) systems are precious support for decision-making, with many applications also in the medical domain. The interaction between mds and ai enjoys a renewed interest following the increased possibilities of deep learning devices. However, we still have limited evidence-based knowledge of the context, design, and psychological mechanisms that craft an optimal human–ai collaboration. In this multicentric study, 21 endoscopists reviewed 504 videos of lesions prospectively acquired from real colonoscopies. They were asked to provide an optical diagnosis with and without the assistance of an ai support system. Endoscopists were influenced by ai ($$\textsc {or}=3.05$$ O R = 3.05 ), but not erratically: they followed the ai advice more when it was correct ($$\textsc {or}=3.48$$ O R = 3.48 ) than incorrect ($$\textsc {or}=1.85$$ O R = 1.85 ). Endoscopists achieved this outcome through a weighted integration of their and the ai opinions, considering the case-by-case estimations of the two reliabilities. This Bayesian-like rational behavior allowed the human–ai hybrid team to outperform both agents taken alone. We discuss the features of the human–ai interaction that determined this favorable outcome.

Variational Bayes (vb) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions within an exponential family. Models with logit components are an apparently notable exception to this class, due to the absence of conjugacy between the logistic likelihood and the Gaussian priors for the coefficients in the linear predictor. To facilitate approximate inference within this widely used class of models, Jaakkola and Jordan (2000) proposed a simple variational approach which relies on a family of tangent quadratic lower bounds of logistic log-likelihoods, thus restoring conjugacy between these approximate bounds and the Gaussian priors. This strategy is still implemented successfully, but less attempts have been made to formally understand the reasons underlying its excellent performance. To cover this key gap, we provide a formal connection between the above bound and a recent Pólya-gamma data augmentation for logistic regression. Such a result places the computational methods associated with the aforementioned bounds within the framework of variational inference for conditionally conjugate exponential family models, thereby allowing recent advances for this class to be inherited also by the methods relying on Jaakkola and Jordan (2000).

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Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative, but such methods face computational problems and large sensitivity to the choice of kernel. This article proposes a generalized Bayes framework that bridges between these paradigms through the use of Gibbs posteriors. In conducting Bayesian updating, the loglikelihood is replaced by a loss function for clustering, leading to a rich family of clustering methods. The Gibbs posterior represents a coherent updating of Bayesian beliefs without needing to specify a likelihood for the data, and can be used for characterizing uncertainty in clustering. We consider losses based on Bregman divergence and pairwise similarities, and develop efficient deterministic algorithms for point estimation along with sampling algorithms for uncertainty quantification. Several existing clustering algorithms, including k-means, can be interpreted as generalized Bayes estimators under our framework, and hence we provide a method of uncertainty quantification for these approaches; for example, allowing calculation of the probability a data point is well clustered.

Summary Discrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features, such as in clustering, mixtures and curve fitting. They are effective and well-developed tools, though their infinite dimensionality is unsuited to some applications. If one restricts to a finite-dimensional simplex, very little is known beyond the traditional Dirichlet multinomial process, which is mainly motivated by conjugacy. This paper introduces an alternative based on the Pitman–Yor process, which provides greater flexibility while preserving analytical tractability. Urn schemes and posterior characterizations are obtained in closed form, leading to exact sampling methods. In addition, the proposed approach can be used to accurately approximate the infinite-dimensional Pitman–Yor process, yielding improvements over existing truncation-based approaches. An application to convex mixture regression for quantitative risk assessment illustrates the theoretical results and compares our approach with existing methods.