Bruce Worton

Statistical estimation of gene expression using multiple laser scans of microarrays

UNLABELLED We propose a statistical model for estimating gene expression using data from multiple laser scans at different settings of hybridized microarrays. A functional regression model is used, based on a non-linear relationship with both additive and multiplicative error terms. The function is derived as the expected value of a pixel, given that values are censored at 65 535, the maximum detectable intensity for double precision scanning software. Maximum likelihood estimation based on a Cauchy distribution is used to fit the model, which is able to estimate gene expressions taking account of outliers and the systematic bias caused by signal censoring of highly expressed genes. We have applied the method to experimental data. Simulation studies suggest that the model can estimate the true gene expression with negligible bias. AVAILABILITY FORTRAN 90 code for implementing the method can be obtained from the authors.

Raced profiles: efficient selection of competing compiler optimizations

Many problems in embedded compilation require one set of optimizations to be selected over another based on run time performance. Self-tuned libraries, iterative compilation and machine learning techniques all compare multiple compiled program versions. In each, program versions are timed to determine which has the best performance. The program needs to be run multiple times for each version because there is noise inherent in most performance measurements. The number of runs must be enough to compare different versions, despite the noise, but executing more than this will waste time and energy. The compiler writer must either risk taking too few runs, potentially getting incorrect results, or taking too many runs increasing the time for their experiments or reducing the number of program versions evaluated. Prior works choose constant size sampling plans where each compiled version is executed a fixed number of times without regard to the level of noise. In this paper we develop a sequential sampling plan which can automatically adapt to the experiment so that the compiler writer can have both confidence in the results and also be sure that no more runs were taken than were needed. We show that our system is able to correctly determine the best optimization settings with between 76% and 87% fewer runs than needed by a brute force, constant sampling size approach. We also compare our approach to JavaSTATS(10); we needed 77% to 89% fewer runs than it needed.

Modelling radio-tracking data

This paper considers the analysis of locational data collected by sampling the path of an animal as it moves about its home range. In particular, the use of the bivariate Omstein-Uhlenbeck diffusion process as a model of path movement for a single animal, proposed by Dunn and Gipson (1977, Biometrics33, 85–101), is studied when the tracking data are generated from more complex processes. Three distinct cases are investigated. These represent movement patterns that frequently occur in real tracking data. Although Dunns model is often considered to be inappropriate in such situations, it is shown that the parameter estimates may still be used in a descriptive way to summarize complex animal movement patterns as they contain information on three important aspects of movement: the average location, the dispersion and the correlation between successive radio-locations. Radio-tracking data on a male coyote are used to illustrate a quasi-Newton method for calculating maximum likelihood estimates, and a method for assessing model adequacy. There is found to be a systematic departure from the assumed process, but estimates are interpreted as a summary of the coyotes movement pattern, and non-parameric standard errors are obtained.

Modelling larval movement data from individual bioassays

We consider modelling the movements of larvae using individual bioassays in which data are collected at a high-frequency rate of five observations per second. The aim is to characterize the behaviour of the larvae when exposed to attractant and repellent compounds. Mixtures of diffusion processes, as well as Hidden Markov models, are proposed as models of larval movement. These models account for directed and localized movements, and successfully distinguish between the behaviour of larvae exposed to attractant and repellent compounds. A simulation study illustrates the advantage of using a Hidden Markov model rather than a simpler mixture model. Practical aspects of model estimation and inference are considered on extensive data collected in a study of novel approaches for the management of cabbage root fly.

Efficient and accurate approximate Bayesian inference with an application to insurance data

Efficient and accurate Bayesian Markov chain Monte Carlo methodology is proposed for the estimation of event rates under an overdispersed Poisson distribution. An approximate Gibbs sampling method and an exact independence-type Metropolis-Hastings algorithm are derived, based on a log-normal/gamma mixture density that closely approximates the conditional distribution of the Poisson parameters. This involves a moment matching process, with the exact conditional moments obtained employing an entropy distance minimisation (Kullback-Liebler divergence) criterion. A simulation study is conducted and demonstrates good Bayes risk properties and robust performance for the proposed estimators, as compared with other estimating approaches under various loss functions. Actuarial data on insurance claims are used to illustrate the methodology. The approximate analysis displays superior Markov chain Monte Carlo mixing efficiency, whilst providing almost identical inferences to those obtained with exact methods.