Beyond Brownian Motion and the Ornstein-Uhlenbeck Process: Stochastic Diffusion Models for the Evolution of Quantitative Characters.

Gaussian processes, such as Brownian motion and the Ornstein-Uhlenbeck process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that limit their utility. Here we describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. We present general methods for deriving new diffusion models and develop new software for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution.

On the classification of microarray gene-expression data.

We consider the classification of microarray gene-expression data. First, attention is given to the supervised case, where the tissue samples are classified with respect to a number of predefined classes and the intent is to assign a new unclassified tissue to one of these classes. The problems of forming a classifier and estimating its error rate are addressed in the context of there being a relatively small number of observations (tissue samples) compared to the number of variables (that is, the genes, which can number in the tens of thousands). We then proceed to the unsupervised case and consider the clustering of the tissue samples and also the clustering of the gene profiles. Both problems can be viewed as being non-standard ones in statistics and we address some of the key issues involved. The focus is on the use of mixture models to effect the clustering for both problems.

Testing for group structure in high-dimensional data.

With the use of finite mixture models for the clustering of a data set, the crucial question of how many clusters there are in the data can be addressed by testing for the smallest number of components in the mixture model compatible with the data. We investigate the performance of a resampling approach to this latter problem in the context of high-dimensional data, where the number of variables p is extremely large relative to the number of observations n. In order to be able to fit normal mixture models to such data, some form of dimension reduction has to be performed. This raises the question of whether a practically significant bias results if the bootstrapping is undertaken solely on the basis of the reduced dimensional form of the data, rather than using the full data from which to draw the bootstrap sample replications.

Nonlinear features for single-channel diagnosis of sleep-disordered breathing diseases.

Studies have shown that algorithms based on single-channel airflow records are effective in screening for sleep-disordered breathing diseases (SDB). In this study, we investigate the diagnostic effectiveness of a classifier trained on a set of features derived from single-channel airflow measurements. The features considered are based on recurrence quantification analysis (RQA) of the measurement time series and are optionally augmented with single measurements of neck circumference and body mass index. The airflow measurement utilized is the nasal pressure (NP). The study used an overnight recording from each of 77 patients undergoing PSG testing. Mixture discriminant analysis was used to obtain a classifier, which predicts whether or not a measurement segment contains an SDB event. Patients were diagnosed as having SDB disease if the recording contained measurement segments predicted to include an SDB event at a rate exceeding a threshold value. A patient can be diagnosed as having SDB disease if the rate of SDB events per hour of sleep, the respiratory disturbance index (RDI), is > or = 15 or sometimes > or = 5. Here we trained and evaluated the classifier under each assumption, obtaining areas under receiver operating curves using fivefold cross-validation of 0.96 and 0.93, respectively. We used a two-layer structure to select the optimal operating point and assess the resulting classifier to avoid unbiased estimates. The resulting estimates for diagnostic sensitivity/specificity were 71.5%/89.5% for disease classification when RDI > or = 15 and 63.3%/100% for RDI > or = 5. These results were found assuming that the costs of misclassifying healthy and diseased subjects are equal, but we provide a framework to vary these costs. The results suggest that a classifier based on RQA features derived from NP measurements could be used in an automated SDB screening device.

Prediction of respiratory measurements based on cross embedding techniques.

Measurements of multiple physiological signals are required for diagnostic procedures such as for sleep disordered breathing. Accuracy of automated diagnostic procedures and home based screening methods can be affected when phisiological measurements contains artifacts or signal losses. We investigate on predicting one physiological signal measurement from others, using dependencies exists in physiological signals, in order to obtain a measure of reliability to the measurements. Modeling such relationships are done with the use of artificial neural networks. We conclude that via such cross prediction tasks, it is possible to identify and correct both artifacts and signal losses in these measurements.

Sleep-stage and event dependency of brain asynchrony as manifested through surface EEG.

Electroencephalography (EEG) is a core measurement in overnight sleep studies. In this paper we study functional asymmetries of the brain as manifested through spectral correlation coefficient. Our target group is patients symptomatic of sleep apnea and referred for routine Polysomnography (PSG) testing at the hospital. We measured EEG data (using electrodes C4/A1 and C3/A2 of the International 10/20 System) as a part of the routine PSG test. Spectral correlation coefficients were computed between EEG data from the two hemispheres, for each frequency band of interest: delta, theta, alpha, and beta. Our results indicated that hemispheric correlation distinctly changes with the gross sleep type (REM/NREM) as well as with different sleep stages (stages 1-4) within NREM. It also varies in the presence of arousal events and apnea. These results may provide a basis for novel insights into the functional asymmetries of brain in sleep and sleep associated events such as arousals and apnea.

Dynamic data analysis in obstructive sleep apnea.

Obstructive Sleep Apnea (OSA) is a serious disease caused by the collapse of upper airways during sleep. The present method of measuring the severity of OSA is the Apnea Hypopnea Index (AHI). The AHI is defined as the average number of Obstructive events (Apnea and Hypopnea, OAH-events) during the total sleep period. The number of occurrence of OAH events during each hour of sleep is a random variable with an unknown probability density function. Thus the measure AHI alone is insufficient to describe its true nature. We propose a new measure Dynamic Apnea Hypopnea Index Time Series (DAHI), which captures the temporal density of Apnea event over shorter time intervals, and use its higher moments to obtain a dynamic characterization of OSA.