Serge Guillas

Bivariate splines for spatial functional regression models

We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, in various situations where both the explanatory variable and the noise can be unbounded and dependent. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with a penalisation term. Under the assumptions that the regressors in the sample span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the USA that illustrates the predictive skills of the method.

Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes

We show consistency in the mean integrated quadratic sense of an estimator of the autocorrelation operator [rho] in the autoregressive Hilbertian of order one model. Two main cases are considered, and we obtain upper bounds for the corresponding rates.

Sequential design with mutual information for computer experiments (MICE): Emulation of a tsunami model

Computer simulators can be computationally intensive to run over a large number of input values, as required for optimization and various uncertainty quantification tasks. The standard paradigm for the design and analysis of computer experiments is to employ Gaussian random fields to model computer simulators. Gaussian process models are trained on input-output data obtained from simulation runs at various input values. Following this approach, we propose a sequential design algorithm, MICE (Mutual Information for Computer Experiments), that adaptively selects the input values at which to run the computer simulator, in order to maximize the expected information gain (mutual information) over the input space. The superior computational efficiency of the MICE algorithm compared to other algorithms is demonstrated by test functions, and a tsunami simulator with overall gains of up to 20% in that case.

Quantile Curve Estimation and Visualization for Nonstationary Time Series

There is an increasing interest in studying time-varying quantiles, particularly for environmental processes. For instance, high pollution levels may cause severe respiratory problems, and large precipitation amounts can damage the environment, and have negative impacts on the society. In this article we address the problem of quantile curve estimation for a wide class of nonstationary and/or non-Gaussian processes. We discuss several nonparametric quantile curve estimates, give asymptotic results, and propose a data-driven procedure for the selection of smoothing parameters. This methodology provides a statistically reliable and computationally efficient graphical tool that can be used for the exploration and visualization of the behavior of time-varying quantiles for nonstationary time series. A Monte Carlo simulation study and two applications to ozone time series illustrate our method. R codes with the algorithm for selection of smoothing parameters (described in Section 3) are available in the online supplements.

Functional semiparametric partially linear model with autoregressive errors

In this paper, we introduce a functional semiparametric model, where a real-valued random variable is explained by the sum of a unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable. The errors can be autocorrelated. We focus here on the parametric estimation of the coefficients in the linear combination. First, we use a nonparametric kernel method to remove the effect of the functional explanatory variable. Then, we use generalized least squares approach to obtain an estimator of these coefficients. Under some technical assumptions, we prove consistency and asymptotic normality of our estimator. Finally, we present Monte Carlo simulations that illustrate these characteristics.

Surrogate based Optimisation for Design of Pressure Swing Adsorption Systems

Abstract Pressure swing adsorption (PSA) is a cyclic adsorption process for gas separation and purification. PSA offers a broad range of design possibilities influencing the device behaviour. In the last decade much attention has been devoted towards simulation and optimisation of various PSA cycles. The PSA beds are modelled with hyperbolic/parabolic partial differential algebraic equations and the separation performance should be assessed at cyclic steady state (CSS). Detailed mathematical models together with the CSS constraint makes design difficult. We propose a surrogate based optimisation procedure based on kriging for the design of PSA systems. The numerical implementation is tested with a genetic algorithm, with a multi-start sequential quadratic programming method and with an efficient global optimisation algorithm. The case study is the design of a dual piston PSA system for the separation of a binary gas mixture of N 2 and CO 2 .

Statistical analysis of the El Niño–Southern Oscillation and sea-floor seismicity in the eastern tropical Pacific

We present statistical evidence for a temporal link between variations in the El Niño–Southern Oscillation (ENSO) and the occurrence of earthquakes on the East Pacific Rise (EPR). We adopt a zero-inflated Poisson regression model to represent the relationship between the number of earthquakes in the Easter microplate on the EPR and ENSO (expressed using the southern oscillation index (SOI) for east Pacific sea-level pressure anomalies) from February 1973 to February 2009. We also examine the relationship between the numbers of earthquakes and sea levels, as retrieved by Topex/Poseidon from October 1992 to July 2002. We observe a significant (95% confidence level) positive influence of SOI on seismicity: positive SOI values trigger more earthquakes over the following 2 to 6 months than negative SOI values. There is a significant negative influence of absolute sea levels on seismicity (at 6 months lag). We propose that increased seismicity is associated with ENSO-driven sea-surface gradients (rising from east to west) in the equatorial Pacific, leading to a reduction in ocean-bottom pressure over the EPR by a few kilopascal. This relationship is opposite to reservoir-triggered seismicity and suggests that EPR fault activity may be triggered by plate flexure associated with the reduced pressure.

Efficient Spatial Modeling Using the SPDE Approach With Bivariate Splines

Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be gained by doing the computations using Gaussian Markov random fields (GMRFs) as the GFs can be seen as weak solutions to corresponding stochastic partial differential equations (SPDEs) using piecewise linear finite elements. We introduce a new class of representations of GFs with bivariate splines instead of finite elements. This allows an easier implementation of piecewise polynomial representations of various degrees. It leads to GMRFs that can be inferred efficiently and can be easily extended to nonstationary fields. The solutions approximated with higher order bivariate splines converge faster, hence the computational cost can be alleviated. Numerical simulations using both real and simulated data also demonstrate that our framework increases the flexibility and efficiency. Supplementary materials are available online.

Healthcare Environments and Spatial Variability of Healthcare Associated Infection Risk: Cross-Sectional Surveys

Prevalence of healthcare associated infections remains high in patients in intensive care units (ICU), estimated at 23.4% in 2011. It is important to reduce the overall risk while minimizing the cost and disruption to service provision by targeted infection control interventions. The aim of this study was to develop a monitoring tool to analyze the spatial variability of bacteriological contamination within the healthcare environment to assist in the planning of interventions. Within three cross-sectional surveys, in two ICU wards, air and surface samples from different heights and locations were analyzed. Surface sampling was carried out with tryptic Soy Agar contact plates and Total Viable Counts (TVC) were calculated at 48hrs (incubation at 37°C). TVCs were analyzed using Poisson Generalized Additive Mixed Model for surface type analysis, and for spatial analysis. Through three cross-sectional survey, 370 samples were collected. Contamination varied from place-to-place, height-to-height, and by surface type. Hard-to-reach surfaces, such as bed wheels and floor area under beds, were generally more contaminated, but the height level at which maximal TVCs were found changed between cross-sectional surveys. Bedside locations and bed occupation were risk factors for contamination. Air sampling identified clusters of contamination around the nursing station and surface sampling identified contamination clusters at numerous bed locations. By investigating dynamic hospital wards, the methodology employed in this study will be useful to monitor contamination variability within the healthcare environment and should help to assist in the planning of interventions.

Statistical emulation of landslide-induced tsunamis at the Rockall Bank, NE Atlantic

Statistical methods constitute a useful approach to understand and quantify the uncertainty that governs complex tsunami mechanisms. Numerical experiments may often have a high computational cost. This forms a limiting factor for performing uncertainty and sensitivity analyses, where numerous simulations are required. Statistical emulators, as surrogates of these simulators, can provide predictions of the physical process in a much faster and computationally inexpensive way. They can form a prominent solution to explore thousands of scenarios that would be otherwise numerically expensive and difficult to achieve. In this work, we build a statistical emulator of the deterministic codes used to simulate submarine sliding and tsunami generation at the Rockall Bank, NE Atlantic Ocean, in two stages. First we calibrate, against observations of the landslide deposits, the parameters used in the landslide simulations. This calibration is performed under a Bayesian framework using Gaussian Process (GP) emulators to approximate the landslide model, and the discrepancy function between model and observations. Distributions of the calibrated input parameters are obtained as a result of the calibration. In a second step, a GP emulator is built to mimic the coupled landslide-tsunami numerical process. The emulator propagates the uncertainties in the distributions of the calibrated input parameters inferred from the first step to the outputs. As a result, a quantification of the uncertainty of the maximum free surface elevation at specified locations is obtained.