We propose a prior robustness approach for the Bayesian implementation of the fault tree analysis (FTA). FTA is often used to evaluate risk in large, safety critical systems but has limitations due to its static structure. Bayesian approaches have been proposed as a superior alternative to it, however, this involves prior elicitation, which is not straightforward. We show that minor misspecification of priors for elementary events can result in a significant prior misspecification for the top event. A large amount of data is required to correctly update a misspecified prior and such data may not be available for many complex, safety critical systems. In such cases, prior misspecification equals posterior misspecification. Therefore, there is a need to develop a robustness approach for FTA, which can quantify the effects of prior misspecification on the posterior analysis. Here, we propose the first prior robustness approach specifically developed for FTA. We not only prove a few important mathematical properties of this approach, but also develop easy to use Monte Carlo sampling algorithms to implement this approach on any given fault tree with and and/or or gates. We then implement this Bayesian robustness approach on two real-life examples: a spacecraft re-entry example and a feeding control system example. We also provide a step-by-step illustration of how this approach can be applied to a real-life problem.

The conventional mean shift algorithm has been known to be sensitive to selecting a bandwidth. We present a robust mean shift algorithm with heterogeneous node weights that come from a geometric structure of a given data set. Before running MS procedure, we reconstruct un-normalized weights (a rough surface of data points) from the Delaunay Triangulation. The un-normalized weights help MS to avoid the problem of failing of misled mean shift vectors. As a result, we can obtain a more robust clustering result compared to the conventional mean shift algorithm. We also propose an alternative way to assign weights for large size datasets and noisy datasets.

This paper considers the use of a recently developed Bayesian statistical approximation technique that leads to very fast determination of highly accurate estimates for latent radio signal power. Following suitable data analysis, a first order non-stationary auto-regressive process is considered for latent radio signal and the fast approximation technique is then used to provide accurate estimates of the hidden model parameters. These estimates are based on having received several noisy, but spatially correlated, observations of the true latent signal. The implication of this technique for real time decision analysis and the problem of finding, and making use of, so-called radio spectrum holes is also discussed.

We describe estimation of the parameters of a manufacturing test and repair model using data available from that test. The model allows imperfect testing and imperfect repair. The principal problem that we address is of parameter identification, given insufficient data, that we address by making conservative assumptions on the property being measured and the associated parameter values. Several cases of commonly occurring test types, in the manufacture of electronic products, are considered.

In the literature on statistical inference in software reliability, the assumptions of parametric models and random sampling of bugs have been pervasive. We argue that both assumptions are problematic, the first because of robustness concerns and the second due to logical and practical difficulties. These considerations motivate the approach taken in this paper. We propose a nonparametric software reliability model based on the order-statistic paradigm. The objective of the work is to estimate, from data on discovery times observed within a type I censoring framework, both the underlying distribution F from which discovery times are generated and N, the unknown number of bugs in the software. The estimates are used to predict the next time to failure. The approach makes use of Bayesian nonparametric inference methods, in particular, the beta-Stacy process. The proposed methodology is illustrated on both real and simulated data

We describe the double Markov random field, a natural hierarchical model for a Bayesian approach to model-based textured image segmentation. The model is difficult to implement, even using Markov chain Monte Carlo (MCMC) methods, so we describe an approximation that is computationally feasible. This is applied to a satellite image. We emphasise the valuable additional information about uncertainties in the segmentation that can be gained from the use of MCMC.