We describe computational procedures to solve a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets’ progressive hedging algorithm. Experiments demonstrate ...

Structural product form and decomposition results for stochastic Petri nets are surveyed, unified and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of T -invariants. Second, based on the underlying concept of group-local-balance, the product form results ...

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...

Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We study in these models a decomposition of predictive uncertainty into its epistemic and aleatoric components. We show how such a decomposition arises naturally in a Bayesian active learning scenario and develop a new objective for reliable re...

Two generalizations of Bacon's theory of loop-free decomposition of probabilistic finite-state systems are proposed. The first of these consists of a modification of the structure of the decomposition which then allows for the decomposition of a larger class of systems. The second generalization subsumes the first: sufficient conditions for a stochastic finite-state system to be decomposable fo...

We study orthogonal decomposition of symmetric statistics based on samples drawn without replacement from finite populations. Under very mild smoothness conditions the first k terms of the decomposition provide stochastic expansion with remainder O(N−k/2). Assuming that the linear part of the decomposition is nondegenerate we establish one term Edgeworth expansion of the distribution function o...