Credal Networks under Epistemic Irrelevance

A credal network under epistemic irrelevance is a generalised type of Bayesian network that relaxes its two main building blocks. On the one hand, the local probabilities are allowed to be partially specified. On the other hand, the assessments of independence do not have to hold exactly. Conceptually, these two features turn credal networks under epistemic irrelevance into a powerful alternative to Bayesian networks, offering a more flexible approach to graph-based multivariate uncertainty modelling. However, in practice, they have long been perceived as very hard to work with, both theoretically and computationally. The aim of this paper is to demonstrate that this perception is no longer justified. We provide a general introduction to credal networks under epistemic irrelevance, give an overview of the state of the art, and present several new theoretical results. Most importantly, we explain how these results can be combined to allow for the design of recursive inference methods. We provide numerous concrete examples of how this can be achieved, and use these to demonstrate that computing with credal networks under epistemic irrelevance is most definitely feasible, and in some cases even highly efficient. We also discuss several philosophical aspects, including the lack of symmetry, how to deal with probability zero, the interpretation of lower expectations, the axiomatic status of graphoid properties, and the difference between updating and conditioning

Credal networks under epistemic irrelevance using sets of desirable gambles

We present a new approach to credal networks, which are graphical models that generalise Bayesian nets to deal with imprecise probabilities. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of epistemic irrelevance. We show how assessments of epistemic irrelevance allow us to construct a global model out of given local uncertainty models, leading to an intuitive expression for the so-called irrelevant natural extension of a network. In contrast with Cozman (2000), who introduced this notion in terms of credal sets, our main results are presented using the language of sets of desirable gambles. This has allowed us to derive a number of useful properties of the irrelevant natural extension. It has powerful marginalisation properties and satisfies all graphoid properties but symmetry, both in their direct and reverse forms

Investment-Specific Technology Shocks and Labor Market Frictions

This paper studies the implications of technical progress through investment-specific technical change in a business cycle model with search and matching frictions and endogenous job destruction. The interaction between the capital formation needed to reap the benefits of an investment-specific technology shock and gradual labor-market matching, generates hump-shaped, persistent responses in output, vacancies, and unemployment. The endogenous job destruction decision also leads to small but persistent endogenous fluctuations in total factor productivity. Simulations suggest a limited role for investment-specific technology shocks as a source of business cycle fluctuations compared to a standard real business cycle model.LaborMarket Frictions, Investment-specific Technology Shocks, Business Cycles

Bounding inferences for large-scale continuous-time Markov chains : a new approach based on lumping and imprecise Markov chains

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed—smaller—state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality