Jacqueline Christmas

Robust Autoregression: Student-t Innovations Using Variational Bayes

Autoregression (AR) is a tool commonly used to understand and predict time series data. Traditionally the excitation noise is modelled as a Gaussian. However, real-world data may not be Gaussian in nature, and it is known that Gaussian models are adversely affected by the presence of outliers. We introduce a Bayesian AR model in which the excitation noise is assumed to be Student-t distributed. Variational Bayesian approximations to the posterior distributions of the model parameters are used to overcome the intractable integrations inherent in the Bayesian model. Independent automatic relevance determination (ARD) priors over each of the AR coefficients are used to estimate the model order. Using synthetic data, we show that the Student-t model performs well against both Gaussian and leptokurtic data, in terms of parameter estimation (including the model order) and is much more robust to outliers than either Gaussian or finite mixtures of Gaussian models. We apply the model to strongly leptokurtic EEG signals and show that the Student-t model makes more accurate one-step-ahead predictions than the Gaussian model and provides more consistent estimates of the AR coefficients over simultaneously recorded EEG channels.

An update: improvements in imaging perfluorocarbon-mounted plant leaves with implications for studies of plant pathology, physiology, development and cell biology

Plant leaves are optically complex, which makes them difficult to image by light microscopy. Careful sample preparation is therefore required to enable researchers to maximize the information gained from advances in fluorescent protein labeling, cell dyes and innovations in microscope technologies and techniques. We have previously shown that mounting leaves in the non-toxic, non-fluorescent perfluorocarbon (PFC), perfluorodecalin (PFD) enhances the optical properties of the leaf with minimal impact on physiology. Here, we assess the use of the PFCs, PFD, and perfluoroperhydrophenanthrene (PP11) for in vivo plant leaf imaging using four advanced modes of microscopy: laser scanning confocal microscopy (LSCM), two-photon fluorescence microscopy, second harmonic generation microscopy, and stimulated Raman scattering (SRS) microscopy. For every mode of imaging tested, we observed an improved signal when leaves were mounted in PFD or in PP11, compared to mounting the samples in water. Using an image analysis technique based on autocorrelation to quantitatively assess LSCM image deterioration with depth, we show that PP11 outperformed PFD as a mounting medium by enabling the acquisition of clearer images deeper into the tissue. In addition, we show that SRS microscopy can be used to image PFCs directly in the mesophyll and thereby easily delimit the “negative space” within a leaf, which may have important implications for studies of leaf development. Direct comparison of on and off resonance SRS micrographs show that PFCs do not to form intracellular aggregates in live plants. We conclude that the application of PFCs as mounting media substantially increases advanced microscopy image quality of living mesophyll and leaf vascular bundle cells.

Ant colony optimisation to identify genetic variant association with type 2 diabetes

Around 1.8 million people in the UK have type 2 diabetes, representing about 90% of all diabetes cases in the UK. Genome wide association studies have recently implicated several new genes that are likely to be associated with this disease. However, common genetic variants so far identified only explain a small proportion of the heritability of type 2 diabetes. The interaction of two or more gene variants, may explain a further element of this heritability but full interaction analyses are currently highly computationally burdensome or infeasible. For this reason this study investigates an ant colony optimisation (ACO) approach for its ability to identify common gene variants associated with type 2 diabetes, including putative epistatic interactions. This study uses a dataset comprising 15,309 common (>5% minor allele frequency) SNPs from chromosome 16, genotyped in 1924 type 2 diabetes cases and 2938 controls. This chromosome contains two previously determined associations, one of which is replicated in additional samples. Although no epistatic interactions have been previously reported on this dataset, we demonstrate that ACO can be used to discover single SNP and plausible epistatic associations from this dataset and is shown to be both accurate and computationally tractable on large, real datasets of SNPs with no expert knowledge included in the algorithm.

Micromechanical response of articular cartilage to tensile load measured using nonlinear microscopy

Articular cartilage (AC) is a highly anisotropic biomaterial, and its complex mechanical properties have been a topic of intense investigation for over 60 years. Recent advances in the field of nonlinear optics allow the individual constituents of AC to be imaged in living tissue without the need for exogenous contrast agents. Combining mechanical testing with nonlinear microscopy provides a wealth of information about microscopic responses to load. This work investigates the inhomogeneous distribution of strain in loaded AC by tracking the movement and morphological changes of individual chondrocytes using point pattern matching and Bayesian modeling. This information can be used to inform models of mechanotransduction and pathogenesis, and is readily extendable to various other connective tissues.

Bayesian Spectral Analysis With Student-t Noise

We introduce a Bayesian spectral analysis model for one-dimensional signals where the observation noise is assumed to be Student-t distributed, for robustness to outliers, and we estimate the posterior distributions of the Student-t hyperparameters, as well as the amplitudes and phases of the component sinusoids. The integrals required for exact Bayesian inference are intractable, so we use variational approximation. We show that the approximate phase posteriors are Generalised von Mises distributions of order 2 and that their spread increases as the signal to noise ratio decreases. The model is demonstrated against synthetic data, and real GPS and Wolfs sunspot data.

The effect of missing data on robust Bayesian spectral analysis

We investigate the effects of missing observations on the robust Bayesian model for spectral analysis introduced by Christmas [2013]. The model assumes Student-t distributed noise and uses an automatic relevance determination prior on the precisions of the amplitudes of the component sinusoids and it is not obvious what their effect will be when some of the otherwise temporally uniformly sampled data is missing.

Temporally coupled Principal Component Analysis: A Probabilistic autoregression method

Despite the apparent spatio-temporal decomposition given by (Probabilistic) Principal Component Analysis ((P)PCA), there is in fact no temporal coupling built into these models. Here we augment PPCA with a temporal model in the latent space by coupling the latent variables in time with an autoregressive model and show that the new model may be viewed as a generalisation of PPCA. We present an algorithm which utilises both expectation maximisation and a forward-backward algorithm to infer the values of the model parameters and demonstrate that it is able to make good estimates of the parameter values for synthetic data. We show that the additional temporal information is advantageous when imputing values for missing observations when compared with two non-temporal PPCA methods, both against synthetic data and real UK industrial production output data.

Variational Bayesian tracking: Whole track convergence for large-scale ecological video monitoring

Variational Bayesian approximations offer a computationally fast alternative to numerical approximations for Bayesian inference. We examine variational Bayesian methods for filtering and smoothing continuous hidden Markov models, in particular those with sharply-peaked, nonlinear observations densities. We show that, by making variational updates in the correct order, robust convergence to the tracked state may be achieved. We apply the whole track convergence algorithm to tracking wild crickets in video streams and describe how animals may be identified from the characteristics of their tracks. We also show how identifying alphanumeric tags may be read under poor lighting conditions.

Theoretical Motion Functions for Video Analysis, with a Passive Navigation Example

We introduce a method for estimating the motion of an image field between two images, in which the displacement of pixels between the images is specified by some theoretical motion function of the spatial coordinates based on a small number of parameters. The form of the function is selected to represent the expected features of the class of problem and the values of the parameters are estimated by considering the images as a whole. The probability distributions of the parameters are estimated through a Bayesian model that makes use of variational approximation and importance sampling. The method is demonstrated on a passive navigation problem, with the theoretical motion based on the Focus of Expansion model. The example video is taken from a car driving down a country lane, so there are few, if any, distinctive features that can be tracked. We show that even theoretical motion functions that are gross simplifications of the true underlying motion are able to give useful results.

Predicting sea waves in the presence of pink noise

It has been shown that the power output of some wave energy converters can be greatly increased if they respond to very short-term predictions of the shapes of the waves. Observations of sea waves are traditionally made using buoys carrying GPS and accelerometers. The recent development of low-cost MEMS devices has led to cheaper devices, but also to a renewed interest in the effects of pink (1/f) noise and signal processing methods for mitigating its effects. Bandpass filtering reduces the effects of this noise, but its remaining influence disrupts, in particular, the phase of the signal, which has significant consequences for prediction. We introduce a Bayesian model that promotes the smooth theoretical spectral shapes of the signal and the pink noise and estimates the true signal from one or more sets of observations recorded in parallel. The signal we are aiming to discover is the profile of sea waves at a fixed location; the spectral shape is determined by the Pierson-Moskowitz model. We demonstrate the model on synthetic data and give some preliminary results for the prediction of real sea waves.