A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series.

Understanding the regulatory mechanisms that are responsible for an organism's response to environmental change is an important issue in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question whether a gene is differentially expressed, they do not explicitly address the question when a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates, and is robust with respect to outliers. We apply our algorithm to study the response of Arabidopsis thaliana genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 observed time points. In classification experiments, our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.

Sediment flux at selected coastal sites: proposed time series measurment by particle traps

Particle flux in the ocean reflects ongoing biological and geological processes operating under the influence of the local environment. Estimation of this particle flux through sediment trap deployment is constrained by sampler accuracy, particle preservation, and swimmer distortion. Interpretation of specific particle flux is further constrained by indeterminate particle dispersion and the absence of a clear understanding of the sedimentary consequences of ecosystem activity. Nevertheless, the continuous and integrative properties of the particle trap measure, along with the logistic advantage of a long-term moored sampler, provide a set of strategic advantages that appear analogous to those underlying conventional oceanographic survey programs. Emboldened by this perception, several stations along the coast of Southern California and Mexico have been targeted as coastal ocean flux sites (COFS).

Snow accumulation time series and their climatic interpretation

EXTRACT (SEE PDF FOR FULL ABSTRACT): Several snow accumulation time series derived from ice cores and extending over 3 to 5 centuries are examined for spatial and temporal climatic information. ... A significant observation is the widespread depression of net snow accumulation during the latter part of the "Little Ice Age". This initially suggests sea surface temperatures were significantly depressed during the same period. However, prior to this, the available core records indicate generally higher than average precipitation rates. This also implies that influences such as shifted storm tracks or a dustier atmosphere may have been involved. Without additional spatial data coverage, these observations should properly be studied using a coupled (global) ocean/atmosphere GCM.

Effects of observation time on interpretation of climatic time series - a need for consistency

Much of what we know about the climate of the United States is derived from data gathered under the auspices of the cooperative climate network. Particular aspects of the way observations are taken can have significant influences on the values of climate statistics derived from the data. These influences are briefly reviewed. The purpose of this paper is to examine their effects on climatic time series. Two other items discussed are: (1) a comparison of true (24-hour) means with means derived from maximums and minimums only, and (2) preliminary work on the times of day at which maximums and minimums are set.

A 10-year time series of zooplankton anomalies off the British Columbia coast [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Zooplankton biomass and species composition have been sampled since 1985 at a set of standard locations off Vancouver Island. From these data, I have estimated multi-year average seasonal cycles and time series of anomalies from these averages.

Variability in a radiolarian time series and its relationship to climate

EXTRACT (SEE PDF FOR FULL ABSTRACT): Recently, paleoceanographers have been challenged to produce reliable proxies of climate variables that can be incorporated into climate models. In developing proxies using time series of annual radiolarian species fluxes from Santa Barbara Basin, we identify groups of species associated with years of extreme sea surface temperatures and sea level heights.

Integrating varve and tree-ring time series for southern California climate reconstruction: a 20th century outlook [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Our objective is to combine terrestrial and oceanic records for reconstructing West Coast climate. Tree rings and marine laminated sediments provide high-resolution, accurately dated proxy data on the variability of climate and on the productivity of the ocean and have been used to reconstruct precipitation, temperature, sea level pressure, primary productivity, and other large-scale parameters. We present here the latest Santa Barbara basin varve chronology for the twentieth century as well as a newly developed tree-ring chronology for Torrey pine.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Two problems with variational expectation maximisation for time-series models

Variational methods are a key component of the approximate inference and learning toolbox. These methods fill an important middle ground, retaining distributional information about uncertainty in latent variables, unlike maximum a posteriori methods (MAP), and yet generally requiring less computational time than Monte Carlo Markov Chain methods. In particular the variational Expectation Maximisation (vEM) and variational Bayes algorithms, both involving variational optimisation of a free-energy, are widely used in time-series modelling. Here, we investigate the success of vEM in simple probabilistic time-series models. First we consider the inference step of vEM, and show that a consequence of the well-known compactness property of variational inference is a failure to propagate uncertainty in time, thus limiting the usefulness of the retained distributional information. In particular, the uncertainty may appear to be smallest precisely when the approximation is poorest. Second, we consider parameter learning and analytically reveal systematic biases in the parameters found by vEM. Surprisingly, simpler variational approximations (such a mean-field) can lead to less bias than more complicated structured approximations.