Bayesian inference for reliability of systems and networks using the survival signature

The concept of survival signature has recently been introduced as an alternative to the signature for reliability quantification of systems. While these two concepts are closely related for systems consisting of a single type of component, the survival signature is also suitable for systems with multiple types of component, which is not the case for the signature. This also enables the use of the survival signature for reliability of networks. In this article, we present the use of the survival signature for reliability quantification of systems and networks from a Bayesian perspective. We assume that data are available on tested components that are exchangeable with those in the actual system or network of interest. These data consist of failure times and possibly right-censoring times. We present both a nonparametric and parametric approach

Bayesian nonparametric system reliability using sets of priors

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test data these bounds are propagated to bounds on the posterior predictive distribution for the functioning probability of a new system containing components exchangeable with those used in testing. The method further enables identification of prior–data conflict at the system level based on component level test data. New results on first-order stochastic dominance for the Beta-Binomial distribution make the technique computationally tractable. Our methodological contributions can be immediately used in applications by reliability practitioners as we provide easy to use software tools

Encrypted accelerated least squares regression.

Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradient descent is shown to dominate in terms of encrypted computational speed, and theoretical results are proven to give parameter bounds which ensure correctness of decryption. The characteristics of encrypted computation are empirically shown to favour a non-standard acceleration technique. This demonstrates the possibility of approximating conventional statistical regression methods using encrypted data without compromising privacy

Multilevel Monte Carlo for Reliability Theory

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the number of cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) — a simulation approach which is typically used for stochastic differential equation models — can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime for non-repairable and repairable components, demonstrating the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures, or where the desired precision is lower

Statistical machine learning of sleep and physical activity phenotypes from sensor data in 96,220 UK Biobank participants

Current public health guidelines on physical activity and sleep duration are limited by a reliance on subjective self-reported evidence. Using data from simple wrist-worn activity monitors, we developed a tailored machine learning model, using balanced random forests with Hidden Markov Models, to reliably detect a number of activity modes. We show that physical activity and sleep behaviours can be classified with 87% accuracy in 159,504 minutes of recorded free-living behaviours from 132 adults. These trained models can be used to infer fine resolution activity patterns at the population scale in 96,220 participants. For example, we find that men spend more time in both low- and high- intensity behaviours, while women spend more time in mixed behaviours. Walking time is highest in spring and sleep time lowest during the summer. This work opens the possibility of future public health guidelines informed by the health consequences associated with specific, objectively measured, physical activity and sleep behaviours

Encrypted accelerated least squares regression

Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradient descent is shown to dominate in terms of encrypted computational speed, and theoretical results are proven to give parameter bounds which ensure correctness of decryption. The characteristics of encrypted computation are empirically shown to favour a non-standard acceleration technique. This demonstrates the possibility of approximating conventional statistical regression methods using encrypted data without compromising privacy

Using Storm for scaleable sequential statistical inference.

This article describes Storm, an environment for doing streaming data analysis. Two examples of sequential data analysis — computation of a running summary statistic and sequential updating of a posterior distribution — are implemented and their performance is investigated