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Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codesFeb 13 2019Uncertainty Quantification of closure relationships integrated into thermal-hydraulic system codes is a critical prerequisite so that the Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and licensing processes can be implemented. ... More
Truth and Feasible ReducibilityFeb 01 2019Let $\mathcal{T}$ be any of the three canonical truth theories $\textsf{CT}^-$ (Compositional truth without extra induction), $\textsf{FS}^-$ (Friedman--Sheard truth without extra induction), and $\textsf{KF}^-$ (Kripke--Feferman truth without extra induction), ... More
Some new Stein operators for product distributionsJan 31 2019We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of \cite{gms18}. This framework applies to non-centered normal and ... More
Data recovery in computational fluid dynamics through deep image priorsJan 30 2019One of the challenges encountered by computational simulations at exascale is the reliability of simulations in the face of hardware and software faults. These faults, expected to increase with the complexity of the computational systems, will lead to ... More
Data recovery in computational fluid dynamics through deep image priorsJan 30 2019Feb 17 2019One of the challenges encountered by computational simulations at exascale is the reliability of simulations in the face of hardware and software faults. These faults, expected to increase with the complexity of the computational systems, will lead to ... More
Neutron drip line in the Ca region from Bayesian model averagingJan 22 2019The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around ... More
Admissibility of solution estimators for stochastic optimizationJan 21 2019Jan 23 2019We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem ... More
A weighted Discrepancy Bound of quasi-Monte Carlo Importance SamplingJan 21 2019Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte Carlo. We obtain ... More
Algorithms for high-dimensional non-linear filtering and smoothing problemsJan 18 2019Several numerical tools designed to overcome the challenges of smoothing in a high dimensional nonlinear setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of Linear Ensemble Transform ... More
Bayesian Prediction of Nitrate Concentration Using a Gaussian Log-Gaussian Spatial Model with Measurement Error in Explanatory VariablesJan 18 2019The occurrence of high nitrate levels in groundwater has to be recognized as a threat to humans and animals. An accurate prediction of pollutant concentrations is a basal component for a correct detection of areas with excess of contamination. The groundwater ... More
Preservers of partial orders on the set of all variance-covariance matricesJan 15 2019Let $H_{n}^{+}(\mathbb{R})$ be the cone of all positive semidefinite $n\times n$ real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L\"owner and the minus partial orders. Motivated ... More
Bayesian Graph Selection Consistency For Decomposable GraphsJan 14 2019Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously learn the covariance ... More
On the Convergence of the Laplace Approximation and Noise-Level-Robustness of Laplace-based Monte Carlo Methods for Bayesian Inverse ProblemsJan 13 2019The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust w.r.t. the size ... More
Inference in Graded Bayesian NetworksDec 23 2018Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional dependencies by ... More
On strong stationary times and approximation of Markov chain hitting times by geometric sumsDec 19 2018Consider a discrete time, ergodic Markov chain with finite state space which is started from stationarity. Fill and Lyzinski (2014) showed that, in some cases, the hitting time for a given state may be represented as a sum of a geometric number of IID ... More
Efficient treatment of model discrepancy by Gaussian Processes - Importance for imbalanced multiple constraint inversionsDec 19 2018Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of detailed processes ... More
A panorama of positivityDec 13 2018This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). ... More
Modelling trait dependent speciation with Approximate Bayesian ComputationDec 10 2018Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the ... More
Statistics with improper posteriorsDec 04 2018In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a general concept ... More
Two-sample Test of Community Memberships of Weighted Stochastic Block ModelsNov 30 2018Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the ... More
Naive Dictionary On Musical Corpora: From Knowledge Representation To Pattern RecognitionNov 29 2018In this paper, we propose and develop the novel idea of treating musical sheets as literary documents in the traditional text analytics parlance, to fully benefit from the vast amount of research already existing in statistical text mining and topic modelling. ... More
A QR Decomposition Approach to Factor Modelling: A Thesis ReportNov 27 2018An observed $K$-dimensional series $\left\{ y_{n}\right\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\varepsilon_{n}$ is taken to relate ... More
Interacting reinforced stochastic processes: statistical inference based on the weighted empirical meansNov 26 2018This work deals with a system of interacting reinforced stochastic processes, where each process $X^j=(X_{n,j})_n$ is located at a vertex $j$ of a finite weighted direct graph, and it can be interpreted as the sequence of "actions" adopted by an agent ... More
Recovery guarantees for polynomial approximation from dependent data with outliersNov 25 2018Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is ill-posed; ... More
Tanaka's Theorem RevisitedNov 20 2018Tanaka (1997) proved a powerful generalization of Friedman's self-embedding theorem that states that given a countable nonstandard model $(\mathcal{M},\mathcal{A})$ of the subsystem $\mathrm{WKL}_{0}$ of second order arithmetic, and any element $m$ of ... More
Bernstein-von Mises theorems and uncertainty quantification for linear inverse problemsNov 09 2018We consider the statistical inverse problem of approximating an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the posterior-based ... More
Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic TermsOct 15 2018This 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 ... More
Deep calibration of rough stochastic volatility modelsOct 08 2018Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution ... More
Transmission of harmonic functions through quasicircles on compact Riemann surfacesOct 04 2018Oct 07 2018Let $R$ be a compact surface and let $\Gamma$ be a Jordan curve which separates $R$ into two connected components $\Sigma_1$ and $\Sigma_2$. A harmonic function $h_1$ on $\Sigma_1$ of bounded Dirichlet norm has boundary values $H$ in a certain conformally ... More
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusionsOct 03 2018The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential equation \begin{equation*} dX_t = b(X_t)dt + dW_t, \quad ... More
Approximation and sampling of multivariate probability distributions in the tensor train decompositionOct 02 2018Nov 21 2018General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate distributions ... More
Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical ModelsSep 27 2018We consider the problem of identifying intermediate variables (or mediators) that regulate the effect of a treatment on a response variable. While there has been significant research on this topic, little work has been done when the set of potential mediators ... More
Bayesian shrinkage in mixture of experts models: Identifying robust determinants of class membershipSep 13 2018Jan 12 2019A method for implicit variable selection in mixture of experts frameworks is proposed. We introduce a prior structure where information is taken from a set of independent covariates. Robust class membership predictors are identified using a normal gamma ... More
An alternative quality of life ranking on the basis of remittancesSep 11 2018Oct 14 2018Remittances mean an important connection between people working abroad and their home countries. This paper considers them as a measure of preferences revealed by workers, underlying a ranking of countries around the world. We use the World Bank bilateral ... More
Shape-Enforcing Operators for Point and Interval EstimatorsSep 04 2018A common problem in statistics is to estimate and make inference on functions that satisfy shape restrictions. For example, distribution functions are nondecreasing and range between zero and one, height growth charts are nondecreasing in age, and production ... More
From Bayesian Inference to Logical Bayesian Inference: A New Mathematical Frame for Semantic Communication and Machine LearningSep 03 2018Bayesian Inference (BI) uses the Bayes' posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI was proposed because BI was not compatible with the classical Bayes' prediction and didn't ... More
Bayesian Multi--Dipole Modeling in the Frequency DomainAug 24 2018Dec 13 2018Background: Magneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and in the frequency ... More
Trimmed Ensemble Kalman Filter for Nonlinear and Non-Gaussian Data Assimilation ProblemsAug 15 2018We study the ensemble Kalman filter (EnKF) algorithm for sequential data assimilation in a general situation, that is, for nonlinear forecast and measurement models with non-additive and non-Gaussian noises. Such applications traditionally force us to ... More
Probabilistic forecasting of heterogeneous consumer transaction-sales time seriesAug 14 2018Aug 20 2018We present new Bayesian methodology for consumer sales forecasting. With a focus on multi-step ahead forecasting of daily sales of many supermarket items, we adapt dynamic count mixture models to forecast individual customer transactions, and introduce ... More
NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networksAug 14 2018Dec 12 2018The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, ... More
Machine Learning of Space-Fractional Differential EquationsAug 02 2018Aug 14 2018Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial data, treating ... More
Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption modelAug 01 2018Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and ... More
The Grassmannian of affine subspacesJul 28 2018The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show that, like the ... More
A computational geometry method for the inverse scattering problemJul 23 2018In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the support of ... More
Wasserstein metric-driven Bayesian inversion with applications to signal processingJul 21 2018Dec 26 2018We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm ($L_2$ norm), the ... More
A Unified Framework for Sparse Relaxed Regularized Regression: SR3Jul 14 2018Nov 08 2018Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, ... More
Data Likelihood of Active Fires Satellite Detection and Applications to Ignition Estimation and Data AssimilationJul 09 2018Data likelihood of fire detection is the probability of the observed detection outcome given the state of the fire spread model. We derive fire detection likelihood of satellite data as a function of the fire arrival time on the model grid. The data likelihood ... More
Power Maxwell distribution: Statistical Properties, Estimation and ApplicationJul 03 2018In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure rate. Different ... More
Discussion on Using Stacking to Average Bayesian Predictive Distributions by Yao et alJun 27 2018I begin by summarizing key ideas of the paper under discussion. Then I will talk about a graphical modeling perspective, posterior contraction rates and alternative methods of aggregation. Moreover, I will also discuss possible applications of the stacking ... More
Expanding the Active Inference Landscape: More Intrinsic Motivations in the Perception-Action LoopJun 21 2018Active inference is an ambitious theory that treats perception, inference and action selection of autonomous agents under the heading of a single principle. It suggests biologically plausible explanations for many cognitive phenomena, including consciousness. ... More
Poisson Source Localization on the Plane. Change-Point CaseJun 17 2018We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based ... More
Simultaneous model calibration and source inversion in atmospheric dispersion modelsJun 14 2018We present a cost-effective method for model calibration and solution of source inversion problems in atmospheric dispersion modelling. We use Gaussian process emulations of atmospheric dispersion models within a Bayesian framework for solution of inverse ... More
Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covarianceJun 13 2018Aug 16 2018This paper develops mixed-normal approximations for probabilities that vectors of multiple Skorohod integrals belong to random convex polytopes when the dimensions of the vectors possibly diverge to infinity. We apply the developed theory to establish ... More
Bounds for the asymptotic distribution of the likelihood ratioJun 10 2018In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit bound which ... More
Accurate computation of conditional expectation for highly non-linear problemsJun 08 2018Jan 31 2019This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a unique solution ... More
q-Space Novelty Detection with Variational AutoencodersJun 08 2018Oct 25 2018In machine learning, novelty detection is the task of identifying novel unseen data. During training, only samples from the normal class are available. Test samples are classified as normal or abnormal by assignment of a novelty score. Here we propose ... More
Deep Bayesian regression modelsJun 06 2018Jun 07 2018Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number ... More
Bayesian identification of sound sources with the Helmholtz equationMay 29 2018Jan 15 2019In this work we discuss the problem of identifying sound sources from pressure measurements with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about the number, strength and position of the ... More
Bayesian Learning with Wasserstein BarycentersMay 28 2018Dec 27 2018We introduce a novel paradigm for Bayesian learning based on optimal transport theory. Namely, we propose to use the Wasserstein barycenter of the posterior law on models as a predictive posterior, thus introducing an alternative to classical choices ... More
Learning Nonlinear Brain Dynamics: van der Pol Meets LSTMMay 24 2018Many real-world data sets, especially in biology, are produced by highly multivariate and nonlinear complex dynamical systems. In this paper, we focus on brain imaging data, including both calcium imaging and functional MRI data. Standard vector-autoregressive ... More
Bayesian predictive densities as an interpretation of a class of Skew--Student $t$ distributions with application to medical dataMay 24 2018This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter space, corresponding ... More
Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning AlgorithmsMay 23 2018Dec 28 2018Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting, of the probit ... More
Maximum-entropy and representative samples of neuronal activity: a dilemmaMay 23 2018The present work shows that the maximum-entropy method can be applied to a sample of neuronal recordings along two different routes: (1) apply to the sample; or (2) apply to a larger, unsampled neuronal population from which the sample is drawn, and then ... More
Trans-Gaussian Kriging in a Bayesian framework : a case studyMay 23 2018In the context of Gaussian Process Regression or Kriging, we propose a full-Bayesian solution to deal with hyperparameters of the covariance function. This solution can be extended to the Trans-Gaussian Kriging framework, which makes it possible to deal ... More
Propriety of the reference posterior distribution in Gaussian Process regressionMay 23 2018In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several objective prior distributions for the parameters of Gaussian Process regression models with isotropic correlation kernel. The reference prior distribution stands out among them ... More
Bayesian forecasting of many count-valued time seriesMay 14 2018This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson time series, ... More
Moderate deviations for the $L_1$-norm of kernel density estimatorsMay 02 2018The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are estimated. By assumption, ... More
Semantic Channel and Shannon's Channel Mutually Match for Multi-Label ClassificationMay 02 2018A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's channels match ... More
Intrinsic Complexity And Scaling Laws: From Random Fields to Random VectorsMay 01 2018May 04 2018Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g., the covariance ... More
Fast sampling of parameterised Gaussian random fieldsApr 30 2018Dec 12 2018Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and covariance operator. ... More
Tight MMSE Bounds for the AGN Channel Under KL Divergence Constraints on the Input DistributionApr 26 2018Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler divergence. The distributions ... More
Bayesian Updating and Uncertainty Quantification using Sequential Tempered MCMC with the Rank-One Modified Metropolis AlgorithmApr 23 2018Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic predictions ... More
The Dirichlet problem for semi-linear equationsApr 16 2018Jan 03 2019We study the Dirichlet problem for the semi--linear partial differential equations in the simple connected domains $D$ in $\mathbb C$, the linear part of which is written in a divergence (anisotropic !) form. Thanking to a factorization theorem established ... More
Monodromy, liftings of holomorphic maps, and extensions of holomorphic motionsApr 11 2018We study monodromy of holomorphic motions and show the equivalence of triviality of monodromy of holomorphic motions and extensions of holomorphic motions to continuous motions of the Riemann sphere. We also study liftings of holomorphic maps into certain ... More
Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear RegressionApr 08 2018Jun 29 2018Concentration inequalities form an essential toolkit in the study of high-dimensional statistical methods. Most of the relevant statistics literature is based on the assumptions of sub-Gaussian/sub-exponential random vectors. In this paper, we bring together ... More
From Shannon's Channel to Semantic Channel via New Bayes' Formulas for Machine LearningMar 22 2018A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. By the third kind of Bayes' theorem, we can directly convert a Shannon's channel into an optimized semantic channel. When ... More
Inferring health conditions from fMRI-graph dataMar 07 2018May 04 2018Automated classification methods for disease diagnosis are currently in the limelight, especially for imaging data. Classification does not fully meet a clinician's needs, however: in order to combine the results of multiple tests and decide on a course ... More
Fast Robust Methods for Singular State-Space ModelsMar 07 2018Jun 28 2018State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a ... More
Limit distribution of the quartet balance index for Aldous's b>=0-modelMar 06 2018Nov 21 2018This paper builds up on T. Martinez-Coronado, A. Mir, F. Rossello and G. Valiente's work "A balance index for phylogenetic trees based on quartets", introducing a new balance index for trees. We show here that this balance index, in the case of Aldous's ... More
Mutation and selection in bacteria: modelling and calibrationMar 05 2018Oct 28 2018Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. ... More
Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimizationMar 02 2018Nov 06 2018We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem. The method ... More
Markov Switch Smooth Transition HYGARCH Model: Stability and EstimationMar 02 2018HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides ... More
On the Statistical Challenges of Echo State Networks and Some Potential RemediesFeb 20 2018Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network is a challenging ... More
Bayesian inference for bivariate ranksFeb 09 2018A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are assumed to be induced ... More
Relative perturbation bounds with applications to empirical covariance operatorsFeb 08 2018The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and limit theorems. ... More
Unlearning and Seyab's theorem: a dialogue about updating probabilityFeb 03 2018This dialogue explores the possibility of updating a probability as a consequence of unlearning, reversing the role of prior and posterior probabilities.
Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic ProcessesFeb 02 2018Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical ... More
Biot's parameters estimation in ultrasound propagation through cancellous boneFeb 02 2018Of interest is the characterization of a cancellous bone immersed in an acoustic fluid. The bone is placed between an ultrasonic point source and a receiver. Cancellous bone is regarded as a porous medium saturated with fluid according to Biot's theory. ... More
Weil-Petersson Teichmüller space IIJan 31 2018Given a continuous vector field $\lambda(t, \cdot)$ of Sobolev class $H^{\frac 32}$ on the unit circle $S^1$ with the normalized condition $\Re\bar{\eta}\lambda(t, \eta)=0$, $\eta\in S^1$, the flow maps $\eta=g(t, \cdot)$ of the differential equation ... More
Identification of multiple hard X-ray sources in solar flares: A Bayesian analysis of the February 20 2002 eventJan 27 2018Hard X-ray emission in solar flares is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship amongst these sources is critical to determine the role of each ... More
Identification of multiple hard X-ray sources in solar flares: A Bayesian analysis of the February 20 2002 eventJan 27 2018Jun 12 2018The hard X-ray emission in a solar flare is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship amongst these sources is critical to determine the role of ... More
Factor graph fragmentization of expectation propagationJan 16 2018Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes at the cost ... More
A Comprehensive Bayesian Treatment of the Universal Kriging model with Matérn correlation kernelsJan 03 2018Jan 15 2018The Gibbs reference posterior distribution provides an objective full-Bayesian solution to the problem of prediction of a stationary Gaussian process with Mat\'ern anisotropic kernel. A full-Bayesian approach is possible, because the posterior distribution ... More
New robust confidence intervals for the mean under dependenceDec 30 2017The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not known or even the ... More
Are Extreme Value Estimation Methods Useful for Network Data?Dec 19 2017Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However, there are often ... More
Random forward models and log-likelihoods in Bayesian inverse problemsDec 15 2017Sep 28 2018We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated ... More
Continuous-discrete smoothing of diffusionsDec 11 2017Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a linear transformation of the state of the process is observed with additive noise. The smoothing problem consists of recovering the path of ... More
High-dimensional robust regression and outliers detection with SLOPEDec 07 2017The problems of outliers detection and robust regression in a high-dimensional setting are fundamental in statistics, and have numerous applications. Following a recent set of works providing methods for simultaneous robust regression and outliers detection, ... More
Randomized incomplete $U$-statistics in high dimensionsDec 03 2017Jan 27 2019This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of the $U$-statistic ... More
Bayesian inference for spectral projectors of covariance matrixNov 30 2017Dec 10 2017Let $X_1, \ldots, X_n$ be i.i.d. sample in $\mathbb{R}^p$ with zero mean and the covariance matrix $\mathbf{\Sigma^*}$. The classic principal component analysis estimates the projector $\mathbf{P^*_{\mathcal{J}}}$ onto the direct sum of some eigenspaces ... More