arXiv subjects

Julie Bessac

Publications and source records attributed to Julie Bessac.

27 records · Page 2Linked to original sources

arXiv2021

Nonstationary seasonal model for daily mean temperature distribution bridging bulk and tails

In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct blocks of time, and subsequent estimation procedures are motivated by asymptotic theory for extremes of random processes. For environmental data, nonstationary behavior in the bulk of the distribution, such as seasonality or climate change, will also be observed in the tails. To accurately model such nonstationarity, it seems natural to use the entire dataset rather than just the most extreme values. It is also common to observe different types of nonstationarity in each tail of a distribution. Most work on extremes only focuses on one tail of a distribution, but for temperature, both tails are of interest. This paper builds on a recently proposed parametric model for the entire probability distribution that has flexible behavior in both tails. We apply an extension of this model to historical records of daily mean temperature at several locations across the United States with different climates and local conditions. We highlight the ability of the method to quantify changes in the bulk and tails across the year over the past decades and under different geographic and climatic conditions. The proposed model shows good performance when compared to several benchmark models that are typically used in extreme value analysis of temperature.

stat.AP↗

arXiv2021

Forecast score distributions with imperfect observations

The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In practice, however, observations are almost always tainted by errors and uncertainties. If the yardstick used to compare forecasts is imprecise, one can wonder whether such types of errors may or may not have a strong influence on decisions based on classical scoring rules. We propose a new scoring rule scheme in the context of models that incorporate errors of the verification data. We rely on existing scoring rules and incorporate uncertainty and error of the verification data through a hidden variable and the conditional expectation of scores when they are viewed as a random variable. The proposed scoring framework is compared to scores used in practice, and is expressed in various setups, mainly an additive Gaussian noise model and a multiplicative Gamma noise model. By considering scores as random variables one can access the entire range of their distribution. In particular we illustrate that the commonly used mean score can be a misleading representative of the distribution when this latter is highly skewed or have heavy tails. In a simulation study, through the power of a statistical test and the computation of Wasserstein distances between scores distributions, we demonstrate the ability of the newly proposed score to better discriminate between forecasts when verification data are subject to uncertainty compared with the scores used in practice. Finally, we illustrate the benefit of accounting for the uncertainty of the verification data into the scoring procedure on a dataset of surface wind speed from measurements and numerical model outputs.

stat.ME↗

arXiv2021

Neural Networks for Parameter Estimation in Intractable Models

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging even with small datasets but simulation is straightforward. We use data from model simulations as input and train deep neural networks to learn statistical parameters. Our neural-network-based method provides a competitive alternative to current approaches, as demonstrated by considerable accuracy and computational time improvements. It serves as a proof of concept for deep learning in statistical parameter estimation and can be extended to other estimation problems.

stat.ME↗

arXiv2021

Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE

Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional layers to solve an inverse problem, where we seek to estimate parameters of a FitzHugh-Nagumo model, which consists of a nonlinear system of ordinary differential equations (ODEs). We employ the neural networks to approximate reconstruction maps for model parameter estimation from observational data, where the data comes from the solution of the ODE and takes the form of a time series representing dynamically spiking membrane potential of a biological neuron. We target this dynamical model because of the computational challenges it poses in an inference setting, namely, having a highly nonlinear and nonconvex data misfit term and permitting only weakly informative priors on parameters. These challenges cause traditional optimization to fail and alternative algorithms to exhibit large computational costs. We quantify the prediction errors of model parameters obtained from the neural networks and investigate the effects of network architectures with and without the presence of noise in observational data. We generalize our framework for neural network-based reconstruction maps to simultaneously estimate ODE parameters and parameters of autocorrelated observational noise. Our results demonstrate that deep neural networks have the potential to estimate parameters in dynamical models and stochastic processes, and they are capable of predicting parameters accurately for the FitzHugh-Nagumo model.

stat.ML↗

arXiv2021

SDRBench: Scientific Data Reduction Benchmark for Lossy Compressors

Efficient error-controlled lossy compressors are becoming critical to the success of today's large-scale scientific applications because of the ever-increasing volume of data produced by the applications. In the past decade, many lossless and lossy compressors have been developed with distinct design principles for different scientific datasets in largely diverse scientific domains. In order to support researchers and users assessing and comparing compressors in a fair and convenient way, we establish a standard compression assessment benchmark -- Scientific Data Reduction Benchmark (SDRBench). SDRBench contains a vast variety of real-world scientific datasets across different domains, summarizes several critical compression quality evaluation metrics, and integrates many state-of-the-art lossy and lossless compressors. We demonstrate evaluation results using SDRBench and summarize six valuable takeaways that are helpful to the in-depth understanding of lossy compressors.

cs.DC↗

arXiv2019

Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation (PDE) with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations (DAEs). In both cases we show that the variogram and the hybrid scores show better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

math.OC↗

arXiv2018

Global sensitivity analysis for statistical model parameters

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. However, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and illustrated on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Non-influential parameters are discovered through GSA and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.

stat.CO↗

arXiv2016

Stochastic simulation of predictive space-time scenarios of wind speed using observations and physical models

We propose a statistical space-time model for predicting atmospheric wind speed based on deterministic numerical weather predictions and historical measurements. We consider a Gaussian multivariate space-time framework that combines multiple sources of past physical model outputs and measurements along with model predictions in order to produce a probabilistic wind speed forecast within the prediction window. We illustrate this strategy on a ground wind speed forecast for several months in 2012 for a region near the Great Lakes in the United States. The results show that the prediction is improved in the mean-squared sense relative to the numerical forecasts as well as in probabilistic scores. Moreover, the samples are shown to produce realistic wind scenarios based on the sample spectrum.

stat.AP↗

arXiv2013

Gaussian linear state-space model for wind fields in the North-East Atlantic

A space-time model for wind fields is proposed. It aims at simulating realistic wind conditions with a focus on reproducing the space-time motions of the meteorological systems. A Gaussian linear state-space model is used where the latent state may be interpreted as regional wind condition and the observation equation links regional and local scales. Parameter estimation is performed by combining a method of moment and the EM algorithm whose performances are discussed using simulation studies. The model is fitted to 6-hourly reanalysis data in the North-East Atlantic. It is shown that the fitted model is interpretable and provide a good description of important properties of the space-time covariance function of the data, such as the non full-symmetry induced by prevailing flows in this area.

stat.ME↗