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Offline state estimation for hybrid systems via nonsmooth variable projectionMay 22 2019A hybrid dynamical system switches between dynamic regimes at time- or state-triggered events. We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system's state. We formulate state estimation as ... More

Maximum Likelihood Estimation of Toric Fano VarietiesMay 17 2019We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all 2-dimensional Gorenstein toric Fano varieties. We show that the ML degree is equal to the degree of ... More

Non-Asymptotic Inference in a Class of Optimization ProblemsMay 16 2019This paper describes a method for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation ... More

Measuring Bayesian Robustness Using Rényi's Divergence and Relationship with Prior-Data ConflictMay 15 2019This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighbourhood of the elicited prior are considered. The first one is the well-known $\epsilon$-contaminated class, while ... More

Modeling failures times with dependent renewal type models via exchangeabilityMay 13 2019Failure times of a machinery cannot always be assumed independent and identically distributed, e.g. if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a generalization that considers ... More

Moment Identifiability of Homoscedastic Gaussian MixturesMay 13 2019We consider the problem of identifying a mixture of Gaussian distributions with same unknown covariance matrix by their sequence of moments up to certain order. Our approach rests on studying the moment varieties obtained by taking special secants to ... More

Avoiding Backtesting Overfitting by Covariance-Penalties: an empirical investigation of the ordinary and total least squares casesMay 01 2019Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt ... More

Ranking top-k trees in tree-based phylogenetic networksApr 29 2019'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support trees', about ... More

Multilevel adaptive sparse Leja approximations for Bayesian inverse problemsApr 27 2019Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic ... More

Multilevel adaptive sparse Leja approximations for Bayesian inverse problemsApr 27 2019May 07 2019Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic ... More

New visualizations for Monte Carlo simulationsApr 26 2019In Monte Carlo simulations, samples are obtained from a target distribution in order to estimate various features. We present a flexible class of visualizations for assessing the quality of estimation, which are principled, practical, and easy to implement. ... More

ssMousetrack: Analysing computerized tracking data via Bayesian state-space models in {R}Apr 23 2019Recent technological advances have provided new settings to enhance individual-based data collection and computerized-tracking data have became common in many behavioral and social research. By adopting instantaneous tracking devices such as computer-mouse, ... More

Sylvester equations and polynomial separation of spectraApr 16 2019Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ ... More

On a class of distributions generated by stochastic mixture of the extreme order statistics of a sample of size twoApr 08 2019This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and symmetric Laplace ... More

On shrinkage estimation for balanced loss functionsApr 05 2019The estimation of a multivariate mean $\theta$ is considered under natural modifications of balanced loss function of the form: (i) $\omega \, \rho(\|\delta-\delta_0\|^2) + (1-\omega) \, \rho(\|\delta-\theta\|^2) $, and (ii) $\ell \left( \omega \, \|\delta-\delta_0\|^2 ... More

A deterministic and computable Bernstein-von Mises theoremApr 04 2019Apr 30 2019Bernstein-von Mises results (BvM) establish that the Laplace approximation is asymptotically correct in the large-data limit. However, these results are inappropriate for computational purposes since they only hold over most, and not all, datasets and ... More

A deterministic and computable Bernstein-von Mises theoremApr 04 2019Bernstein-von Mises results (BvM) establish that the Laplace approximation is asymptotically correct in the large-data limit. However, these results are inappropriate for computational purposes since they only hold over most, and not all, datasets and ... More

A Bayesian Nonparametric Test for Assessing Multivariate NormalityApr 04 2019Apr 19 2019In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian counterparts. ... More

A Bayesian Nonparametric Test for Assessing Multivariate NormalityApr 04 2019In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian counterparts. ... More

A Bayesian Nonparametric Test for Assessing Multivariate NormalityApr 04 2019Apr 10 2019In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian counterparts. ... More

Statistical Analysis of Some Evolution Equations Driven by Space-only NoiseApr 03 2019We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been studied, ... More

Approximate spectral gaps for Markov chains mixing times in high-dimensionMar 28 2019This paper introduces a concept of approximate spectral gap to analyze the mixing time of Markov Chain Monte Carlo (MCMC) algorithms for which the usual spectral gap is degenerate or almost degenerate. We use the idea to analyze a class of MCMC algorithms ... More

Bayesian Experimental Design for Oral Glucose Tolerance Tests (OGTT)Mar 27 2019OGTT is a common test, frequently used to diagnose insulin resistance or diabetes, in which a patient's blood sugar is measured at various times over the course of a few hours. Recent developments in the study of OGTT results have framed it as an inverse ... More

Strong Convergence of Multivariate MaximaMar 25 2019It is well known and readily seen that the maximum of $n$ independent and uniformly on $[0,1]$ distributed random variables, suitably standardized, converges in total variation distance, as $n$ increases, to the standard negative exponential distribution. ... More

Approximate Information Tests on Statistical SubmanifoldsMar 20 2019Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a subset of the ... More

Autocovariance Varieties of Moving Average Random FieldsMar 20 2019We study the autocovariance functions of moving average random fields over the integer lattice $\mathbb{Z}^d$ from an algebraic perspective. These autocovariances are parametrized polynomially by the moving average coefficients, hence tracing out algebraic ... More

Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Mar 20 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More

Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More

Estimating a pressure dependent thermal conductivity coefficient with applications in food technologyMar 07 2019In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. To address the known smoothing effect of the direct problem, we model the uncertainty ... More

Spectral Analysis of Saddle-point Matrices from Optimization problems with Elliptic PDE ConstraintsMar 05 2019The main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential equations. We ... More

On one-sample Bayesian tests for the meanMar 03 2019This paper deals with a new Bayesian approach to the standard one-sample $z$- and $t$- tests. More specifically, let $x_1,\ldots,x_n$ be an independent random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. The goal is to test ... More

On one-sample Bayesian tests for the meanMar 03 2019Apr 04 2019This paper deals with a new Bayesian approach to the standard one-sample $z$- and $t$- tests. More specifically, let $x_1,\ldots,x_n$ be an independent random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. The goal is to test ... More

Discrete gradients for computational Bayesian inferenceMar 01 2019Mar 25 2019In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman filter and a particle ... More

Discrete gradients for computational Bayesian inferenceMar 01 2019In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman filter and a particle ... More

Discrete gradients for computational Bayesian inferenceMar 01 2019Apr 10 2019In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy filter and a particle ... More

Optimal Stopping of a Brownian Bridge with an Uncertain Pinning TimeFeb 26 2019We consider the problem of optimally stopping a Brownian bridge with an uncertain pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we consider a general prior distribution of the pinning time and allow ... More

On the well-posedness of Bayesian inverse problemsFeb 26 2019The subject of this article is the introduction of a weaker concept of well-posedness of Bayesian inverse problems. The conventional concept of (`Lipschitz') well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice, ... More

Acceleration of expensive computations in Bayesian statistics using vector operationsFeb 25 2019Many applications in Bayesian statistics are extremely computationally intensive. However, they are also often inherently parallel, making them prime targets for modern massively parallel central processing unit (CPU) architectures. While the use of multi-core ... More

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

A note on the geometry of the MAP partition in some Normal Bayesian Mixture ModelsFeb 04 2019We investigate the geometry of the maximal a posteriori (MAP) partition in the Bayesian Mixture Model where the component distribution is multivariate Normal with Normal-inverse-Wishart prior on the component mean and covariance. We prove that in this ... 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

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

Bayesian Graph Selection Consistency Under Model MisspecificationJan 14 2019Apr 01 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 2019Mar 05 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

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

Bayesian Inference for Persistent HomologyJan 07 2019Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains absent. This ... More

Almost sure convergence for weighted sums of pairwise PQD random variablesDec 24 2018We obtain Marcinkiewicz-Zygmund strong laws of large numbers for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable $X \in \mathscr{L}_{p}$, $1 \leqslant p < 2$. We use our results to ... 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

Bayesian semiparametric modelling of phase-varying point processesDec 22 2018We propose a Bayesian semiparametric approach for modelling registration of multiple point processes. Our approach entails modelling the mean measures of the phase-varying point processes with a Bernstein--Dirichlet prior, which induces a prior on the ... 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

High dimensional inference for the structural health monitoring of lock gatesDec 13 2018Locks and dams are critical pieces of inland waterways. However, many components of existing locks have been in operation past their designed lifetime. To ensure safe and cost effective operations, it is therefore important to monitor the structural health ... 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

A panorama of positivityDec 13 2018May 13 2019This 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

Arena Model: Inference About CompetitionsNov 25 2018The authors propose a parametric model called the arena model for prediction in paired competitions, i.e. paired comparisons with eliminations and bifurcations. The arena model has a number of appealing advantages. First, it predicts the results of competitions ... 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

Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factorsOct 19 2018Feb 14 2019A polynomial indicator function of designs is first introduced by Fontana, Pistone and Rogantin (2000) for two-level designs. They give the structure of the indicator function of two-level designs, especially from the viewpoints of the orthogonality of ... More

Bayesian wavelet de-noising with the caravan priorOct 17 2018According to both domain expertise knowledge and empirical evidence, wavelet coefficients of real signals typically exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising ... 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

Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic TermsOct 15 2018Apr 16 2019This 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

Categorical Aspects of Parameter LearningOct 13 2018Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known. There are ... 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

Nonparametric statistical inference for drift vector fields of multi-dimensional diffusionsOct 03 2018Mar 07 2019The 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

Nonparametric statistical inference for drift vector fields of multi-dimensional diffusionsOct 03 2018Apr 13 2019The 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

Adaptive Gaussian process surrogates for Bayesian inferenceSep 27 2018We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the ... 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

An alternative quality of life ranking on the basis of remittancesSep 11 2018Mar 04 2019Remittances 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

Parameter estimation for Gaussian processes with application to the model with two independent fractional Brownian motionsAug 25 2018The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function, and $\theta$ ... More

A Bayesian Approach to Restricted Latent Class Models for Scientifically-Structured Clustering of Multivariate Binary OutcomesAug 24 2018In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms cluster the multivariate ... 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

Optimal proposals for Approximate Bayesian ComputationAug 18 2018We derive the optimal proposal density for Approximate Bayesian Computation (ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective number of samples ... 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

A Bayesian Approach to Estimating Background Flows from a Passive ScalarAug 03 2018Sep 18 2018We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a pollutant). Here the unknown is a vector field that is specified ... 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