arXiv subjects

Axel Gandy

Publications and source records attributed to Axel Gandy.

40 records · Page 3Linked to original sources

arXiv2012

Non-Restarting CUSUM charts and Control of the False Discovery Rate

Cumulative sum (CUSUM) charts are typically used to detect changes in a stream 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 detecting a change back into control. We present a novel algorithm to control the false discovery rate (FDR) pointwise in time when considering CUSUM charts based on multiple streams of data. We prove that the FDR is controlled under two definitions of a false discovery simultaneously. Simulations reveal the difference in FDR control when using these two definitions and other desirable definitions of a false discovery.

stat.ME↗

arXiv2011

Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the average run length. We suggest an adjustment of the monitoring schemes to overcome these problems. It guarantees, with a certain probability, a conditional performance given the estimated in-control state. The suggested method is based on bootstrapping the data used to estimate the in-control state. The method applies to different types of control charts, and also works with charts based on regression models, survival models, etc. If a nonparametric bootstrap is used, the method is robust to model errors. We show large sample properties of the adjustment. The usefulness of our approach is demonstrated through simulation studies.

stat.ME↗

arXiv2010

A Bayesian approach to star-galaxy classification

Star-galaxy classification is one of the most fundamental data-processing tasks in survey astronomy, and a critical starting point for the scientific exploitation of survey data. For bright sources this classification can be done with almost complete reliability, but for the numerous sources close to a survey's detection limit each image encodes only limited morphological information. In this regime, from which many of the new scientific discoveries are likely to come, it is vital to utilise all the available information about a source, both from multiple measurements and also prior knowledge about the star and galaxy populations. It is also more useful and realistic to provide classification probabilities than decisive classifications. All these desiderata can be met by adopting a Bayesian approach to star-galaxy classification, and we develop a very general formalism for doing so. An immediate implication of applying Bayes's theorem to this problem is that it is formally impossible to combine morphological measurements in different bands without using colour information as well; however we develop several approximations that disregard colour information as much as possible. The resultant scheme is applied to data from the UKIRT Infrared Deep Sky Survey (UKIDSS), and tested by comparing the results to deep Sloan Digital Sky Survey (SDSS) Stripe 82 measurements of the same sources. The Bayesian classification probabilities obtained from the UKIDSS data agree well with the deep SDSS classifications both overall (a mismatch rate of 0.022, compared to 0.044 for the UKIDSS pipeline classifier) and close to the UKIDSS detection limit (a mismatch rate of 0.068 compared to 0.075 for the UKIDSS pipeline classifier). The Bayesian formalism developed here can be applied to improve the reliability of any star-galaxy classification schemes based on the measured values of morphology statistics alone.

astro-ph.IM↗

arXiv2008

Sequential Implementation of Monte Carlo Tests with Uniformly Bounded Resampling Risk

This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical p-value, is uniformly bounded by an arbitrarily small constant. Previously suggested sequential or non-sequential algorithms, using a bounded sample size, do not have this property. Although the algorithm is open-ended, the expected number of steps is finite, except when the p-value is on the threshold between rejecting and not rejecting. The algorithm is suitable as standard for implementing tests that require (re-)sampling. It can also be used in other situations: to check whether a test is conservative, iteratively to implement double bootstrap tests, and to determine the sample size required for a certain power.

math.ST↗