F. Din-Houn Lau

Non-restarting cumulative sum charts and control of the false discovery rate

Cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations, e.g., shifts in the mean. Usually, after signalling, the chart is restarted by setting it to some value below the signalling threshold. We propose a non-restarting cusum chart which is able to detect periods during which the stream is out of control. Further, we advocate an upper boundary to prevent the cusum chart rising too high, which helps to detect a change back into control. We present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data. We consider two definitions of a false discovery: signalling out-of-control when the observations have been in control since the start and signalling out-of-control when the observations have been in control since the last time the chart was at zero. We prove that the false discovery rate is controlled under both these definitions simultaneously. Simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery. Copyright 2013, Oxford University Press.

The Chopthin Algorithm for Resampling

Resampling is a standard step in particle filters and more generally sequential Monte Carlo methods. We present an algorithm, called chopthin, for resampling weighted particles. In contrast to standard resampling methods the algorithm does not produce a set of equally weighted particles; instead it merely enforces an upper bound on the ratio between the weights. Simulation studies show that the chopthin algorithm consistently outperforms standard resampling methods. The algorithms chops up particles with large weight and thins out particles with low weight, hence its name. It implicitly guarantees a lower bound on the effective sample size. The algorithm can be implemented efficiently, making it practically useful. We show that the expected computational effort is linear in the number of particles. Implementations for C++, R (on CRAN), Python and Matlab are available.

RMCMC: A system for updating Bayesian models

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted samples stored in a database. The stored samples are maintained such that the accuracy of the estimates and quality of the samples are satisfactory. This maintenance involves varying the number of samples in the database and updating their weights. New samples are generated, when required, by a Markov chain Monte Carlo algorithm. The system is demonstrated using a football league model that is used to predict the end of season table. The correctness of the estimates and their accuracy are shown in a simulation using a linear Gaussian model.

Real-time statistical modelling of data generated from self-sensing bridges

Instrumentation of infrastructure is changing the way engineers design, construct, monitor and maintain structures such as roads, bridges and underground structures. Data gathered from these instru...

Optimality of Non-Restarting CUSUM Charts

Abstract Cumulative sum (CUSUM) charts are typically used to detect a change in the distribution of a sequence of observations. These charts were originally developed for use in industry, where the deterioration of the quality of a product is monitored. If the chart signals a deterioration, the production may be suspended or a machine reset. The CUSUM chart is then restarted by setting it to some value below the signaling threshold. For processes that cannot be reset, Gandy and Lau (2013) suggest using non-restarting CUSUM charts that give continuous signals. In this article, we explore the signaling properties of these non-restarting CUSUM charts. First, we show that non-restarting CUSUM charts are optimal, in a well-defined sense. Second, we investigate the performance of these charts when its upper boundary is varied. The results show a trade-off between the height of the upper boundary of the chart and the false signal rate.