which can be shown to be equivalent to MMDH(q, p) 2 = Ex,x′∼p[k(x, x′)]− 2Ex∼p;y∼q[k(x, y)] + Ey,y′∼q[k(y, y′)]. We show that kernelized discrepancy is equivalent to MMDHp(q, p), equipped with the p-Steinalized kernel kp(x, x ′). Proposition 1.1. Assume (3) is true, we have S(q, p) = MMDHp(q, p). Proof. Simply note that Ex′∼p[kp(x, x′)] = 0 for any x, we have MMDHp(q, p) 2 = Ex,x′∼q[kp(x, x′)] ...

In this paper, we first provide a new theoretical understanding of the Evidence Pre-propagated Importance Sampling algorithm (EPIS-BN) (Yuan & Druzdzel 2003; 2006b) and show that its importance function minimizes the KL-divergence between the function itself and the exact posterior probability distribution in Polytrees. We then generalize the method to deal with inference in general hybrid Baye...

The paper presents a model that extends the stochastic finite element method to the modelling of transitional energetic–statistical size effect in unnotched quasibrittle structures of positive geometry (i.e. failing at the start of macro-crack growth), and to the low probability tail of structural strength distribution, important for safe design. For small structures, the model captures the ene...

Factorisation of probability trees is a useful tool for inference in Bayesian networks. Probabilistic potentials some of whose parts are proportional can be decomposed as a product of smaller trees. Some algorithms, like lazy propagation, can take advantage of this fact. Also, the factorisation can be used as a tool for approximating inference, if the decomposition is carried out even if the pr...

In this paper, a method is presented for the efficient estimation of rare-event (overflow) probabilities in Jackson queueing networks using importance sampling. The method differs in two ways from methods discussed in most earlier literature: the change of measure is state-dependent, i.e., it is a function of the content of the buffers, and the change of measure is determined using a cross-entr...

A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous. In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating qu...

We present a method to obtain stateand time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a stateand time-dependent estimator for the one-tailed probability of ...

This paper considers importance sampling as a tool for rareevent simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson twonode tandem queue. It is known that in this setting ‘traditional’ state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure that is provably...

Abstract: The basic idea of importance sampling is to use independent samples from one measure in order to approximate expectations with respect to another measure. Understanding how many samples are needed is key to understanding the computational complexity of the method, and hence to understanding when it will be effective and when it will not. It is intuitive that the size of the difference...

Causal inference in cue combination is to decide whether the cues have a single cause or multiple causes. Although the Bayesian causal inference model explains the problem of causal inference in cue combination successfully, how causal inference in cue combination could be implemented by neural circuits, is unclear. The existing method based on calculating log posterior ratio with variable elim...