One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance function as a factorization, i.e., product of conditional probability tables (CPTs). Given diagnostic evidence, we do not have explicit forms for the CPTs in the ...

Using a multivariable Faa di Bruno formula we give conditions on transformations τ : [0, 1] → X where X is a closed and bounded subset of R such that f ◦ τ is of bounded variation in the sense of Hardy and Krause for all f ∈ C(X ). We give similar conditions for f◦τ to be smooth enough for scrambled net sampling to attain O(n−3/2+ ) accuracy. Some popular symmetric transformations to the simple...

This brief paper is an exploratory investigation of how we can apply sensitivity analysis over importance sampling weights in order to obtain sampling estimates of lower previsions described by a parametric family of distributions. We demonstrate our results on the imprecise Dirichlet model, where we can compare with the analytically exact solution. We discuss the computational limitations of t...

Most aircraft fleets nowadays are operating under the concept of damage tolerance, which requires an aircraft to have sufficient residual strength in the presence of damage in one of its principal structural elements (PSE) during the interval of service inspections. The residual strength however is significantly reduced due to multi site damage (MSD). In the present paper, a probabilistic frame...

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in the literature to date, particularly considering that it includes many standard inference problems as special cases. In this paper, we propose two algorithms ...

In this paper we consider a stylized multidimensional rare-event simulation problem for a heavy-tailed process. More precisely, the problem of e¢ cient estimation via simulation of …rst passage time probabilities for a multidimensional random walk with t distributed increments. This problem is a natural generalization of ruin probabilities in insurance, in which the focus is a one dimensional r...

We present a new technique called Multiple Vertex Next Event Estimation, which outperforms current direct lighting techniques in forward scattering, optically dense media with the Henyey-Greenstein phase function. Instead of a one-segment connection from a vertex within the medium to the light source, an entire sub path of arbitrary length can be created and we show experimentally that 4-10 seg...

We provide a comparative study of several widely used off-policy estimators (Empirical Average, Basic Importance Sampling and Normalized Importance Sampling), detailing the different regimes where they are individually suboptimal. We then exhibit properties optimal estimators should possess. In the case where examples have been gathered using multiple policies, we show that fused estimators dom...

Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying black-box importance sampling methods that calculate importance weights for samples generated from any unknown proposal or black-box mechanism. Our method all...

We present algorithms for Bayesian learning of decomposable models from data. Priors of a certain form admit exact averaging in O(3nn3) time and sampling T graphs from the posterior in O(4n + nT) time. To target a broader class of priors we associate each sample with an importance weight. Empirically, we compare averaging to optimization and demonstrate the accuracy of our importance sampling e...