Towards conservative inference in credal networks using belief functions: the case of credal chains

This paper explores belief inference in credal networks using Dempster-Shafer theory. By building on previous work, we propose a novel framework for propagating uncertainty through a subclass of credal networks, namely chains. The proposed approach efficiently yields conservative intervals through belief and plausibility functions, combining computational speed with robust uncertainty representation. Key contributions include formalizing belief-based inference methods and comparing belief-based inference against classical sensitivity analysis. Numerical results highlight the advantages and limitations of applying belief inference within this framework, providing insights into its practical utility for chains and for credal networks in general.

An Imprecise Probabilistic Estimator for the Transition Rate Matrix of a Continuous-Time Markov Chain

We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of priors, we reconsider the problem in discrete time, where we can use the well-known Imprecise Dirichlet Model. In particular, we show how the limit of the resulting discrete-time estimators is a continuous-time estimator. It corresponds to a specific choice of hyperparameters and has an exceptionally simple closed-form expression.