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Bayesian inference with sources of uncertainty: from confidence modelling to sparse estimation

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and regularisation control. Building on this framework, we develop a general approach for inducing sparsity in statistical models and illustrate its use in linear and logistic regression, as well as in Bayesian neural networks.