Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Directionality and Reversibility in Time Series

Abstract: Summary This paper gives a review and development of what is currently known about the directionality (irreversibility) of time series models, together with briefer coverage of the still limited statistical methodology. Reversibility is shown to imply stationarity; Weiss's result concerning the reversibility of linear Gaussian processes is stressed, and contrasted to the directional nature of much time series data. Reversed ARMA models are explored, and non-linear examples given; the stationarity and invertibility conditions of ARMA models are shown to be implicitly directional, and a consequence of the future-independent nature of such models. Invertibility is extended to the two-sided futuredependent generalised linear model, and applied to reversible moving average models. The directional and reversible implications of autoregressive roots are covered. Work applying directional-sensitive methods of statistical analysis to reversed data series is mentioned; possible dangers in transforming directional series to Gaussian marginal distributions are noted. The directional nature of most non-linear models is invoked to emphasise the current importance of the area.

Goodness of Fit Problem and Scanning Innovation Martingales

Abstract: This paper is mainly devoted to the following statistical problem: in the case of random variables of any finite dimension and both simple or parametric hypotheses, how to construct convenient "empirical" processes which could provide the basis for goodness of fit tests-more or less in the same way as the uniform empirical process does in the case of simple hypothesis and scalar random variables. The solution of this problem is connected here with the theory of multiparameter martingales and the theory of function-parametric processes. Namely, for the limiting Gaussian processes some kind of filtration is introduced and so-called scanning innovation processes are constructed-the adapted standard Wiener processes in one-to-one correspondence with initial Gaussian processes. This is done for the function-parametric versions of the processes.

A Simple Approach to Ranking Differentially Expressed Gene Expression Time Courses through Gaussian Process Regression

Abstract: The analysis of gene expression from time series underpins many biological studies. Two basic forms of analysis recur for data of this type: removing inactive (quiet) genes from the study and determining which genes are differentially expressed. Often these analysis stages are applied disregarding the fact that the data is drawn from a time series. In this paper we propose a simple model for accounting for the underlying temporal nature of the data based on a Gaussian process. We review Gaussian process (GP) regression for estimating the continuous trajectories underlying in gene expression time-series. We present a simple approach which can be used to filter quiet genes, or for the case of time series in the form of expression ratios, quantify differential expression. We assess via ROC curves the rankings produced by our regression framework and compare them to a recently proposed hierarchical Bayesian model for the analysis of gene expression time-series (BATS). We compare on both simulated and experimental data showing that the proposed approach considerably outperforms the current state of the art. Gaussian processes offer an attractive trade-off between efficiency and usability for the analysis of microarray time series. The Gaussian process framework offers a natural way of handling biological replicates and missing values and provides confidence intervals along the estimated curves of gene expression. Therefore, we believe Gaussian processes should be a standard tool in the analysis of gene expression time series.

Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution

Abstract: Variable-stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution. We consider a fatigue failure model in which accumulated decay is governed by a continuous Gaussian process W(y) whose distribution changes at certain stress change points to < t l < < …