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.

A comparison of parametric and nonparametric methods for normalising cDNA microarray data.

Normalisation is an essential first step in the analysis of most cDNA microarray data, to correct for effects arising from imperfections in the technology. Loess smoothing is commonly used to correct for trends in log-ratio data. However, parametric models, such as the additive plus multiplicative variance model, have been preferred for scale normalisation, though the variance structure of microarray data may be of a more complex nature than can be accommodated by a parametric model. We propose a new nonparametric approach that incorporates location and scale normalisation simultaneously using a Generalised Additive Model for Location, Scale and Shape (GAMLSS, Rigby and Stasinopoulos, 2005, Applied Statistics, 54, 507-554). We compare its performance in inferring differential expression with Huber et al.'s (2002, Bioinformatics, 18, 96-104) arsinh variance stabilising transformation (AVST) using real and simulated data. We show GAMLSS to be as powerful as AVST when the parametric model is correct, and more powerful when the model is wrong.

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.