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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
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
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
Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building wallsNov 26 2017In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary ... More
Sign controlled solvers for the absolute value equation with an application to support vector machinesJul 28 2017Let $A$ be a real $n\times n$ matrix and $z,b\in \mathbb R^n$. The piecewise linear equation system $z-A\vert z\vert = b$ is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP hard in general. ... More
Informed Sub-Sampling MCMC: Approximate Bayesian Inference for Large DatasetsJun 26 2017Dec 11 2017This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an {unknown} fraction of {fixed size} of the available data that is randomly refreshed ... More
A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, with an Application to HDR ImagingJun 10 2017Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly ... More
A novel algorithmic approach to Bayesian Logic RegressionMay 22 2017Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the ... More
Maximum likelihood drift estimation for Gaussian process with stationary incrementsDec 01 2016The paper deals with the regression model $X_t = \theta t + B_t$, $t\in[0, T ]$, where $B=\{B_t, t\geq 0\}$ is a centered Gaussian process with stationary increments. We study the estimation of the unknown parameter $\theta$ and establish the formula ... More
Convergence of depths and depth-trimmed regionsNov 26 2016Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with increasing sample ... More
Gaussian Approximations for Probability Measures on $\mathbf{R}^d$Nov 26 2016This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this divergence, from ... More
Robust regression for mixed Poisson-Gaussian modelNov 23 2016This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson-Gaussian noise, and when there are outliers in the measured data. The Poisson-Gaussian noise ... More
Maximum a Posteriori Estimators as a Limit of Bayes EstimatorsNov 17 2016Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. A number of references claim that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper, we provide ... More
Contributed Discussion to Bayesian Solution Uncertainty Quantification for Differential EquationsNov 17 2016We begin by introducing the main ideas of the paper under discussion, and we give a brief description of the method proposed. Next, we discuss an alternative approach based on B-spline expansion, and lastly we make some comments on the method's convergence ... More
Extracting information from random data. Applications of laws of large numbers in technical sciences and statisticsNov 10 2016We formulate conditions for convergence of Laws of Large Numbers and show its links with of parts mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of Law of Large Numbers such as Stochastic ... More
Strong approximations for the $p$-fold integrated empirical process with applications to statistical testsNov 10 2016The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian ... More
Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA)Nov 04 2016The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities of interest. ... More
Posterior Graph Selection and Estimation Consistency for High-dimensional Bayesian DAG ModelsNov 03 2016Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce ... More
A Pareto scale-inflated outlier model and its Bayesian analysisNov 02 2016This paper develops a Pareto scale-inflated outlier model. This model is intended for use when data from some standard Pareto distribution of interest is suspected to have been contaminated with a relatively small number of outliers from a Pareto distribution ... More
Asymptotic behaviors of bivariate Gaussian powered extremesOct 21 2016In this paper, joint asymptotics of powered maxima for a triangular array of bivariate powered Gaussian random vectors are considered. Under the H\"usler-Reiss condition, limiting distributions of powered maxima are derived. Furthermore, the second-order ... More
Sampling hyperparameters in hierarchical models: improving on Gibbs for high-dimensional latent fields and large data setsOct 21 2016We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the latent variables ... More
Non-stationary POT modelling of air pollution concentrations: Statistical analysis of traffic and meteorological impactOct 18 2016Predicting occurrence, level and duration of high air pollution concentrations exceeding a given critical level enables researchers to study the health impact of road traffic on local air quality and information public policy action. Precise estimates ... More
Mitigating the Influence of the Boundary on PDE-based Covariance OperatorsOct 17 2016Oct 24 2016Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators. The use of elliptic PDE operators to construct covariance operators allows to build on fast PDE solvers for manipulations with ... More
Mitigating the Influence of the Boundary on PDE-based Covariance OperatorsOct 17 2016Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators. The use of elliptic PDE operators to construct covariance operators allows to build on fast PDE solvers for manipulations with ... More
Monotone Empirical Bayes Estimators for the Reproduction Number in Borel-Tanner DistributionOct 11 2016A monotone version of an empirical Bayes estimator for the parameter of the Borel-Tanner distribution is constructed. Some properties of the estimator's regret risk are illustrated through simulations.
Local M-estimation with Discontinuous Criterion for Dependent and Limited ObservationsOct 10 2016This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a panel data discrete ... More
New testing procedures for Structural Equation ModelingOct 07 2016We introduce and evaluate a new class of hypothesis testing procedures for moment structures. The methods are valid under weak assumptions and includes the well-known Satorra-Bentler adjustment as a special case. The proposed procedures applies also to ... More
A probabilistic network for the diagnosis of acute cardiopulmonary diseasesSep 22 2016We describe our experience in the development of a probabilistic network for the diagnosis of acute cardiopulmonary diseases. A panel of expert physicians collaborated to specify the qualitative part, that is a directed acyclic graph defining a factorization ... More
Multiple testing via relative belief ratiosSep 21 2016Some large scale inference problems are considered based on using the relative belief ratio as a measure of statistical evidence. This approach is applied to the multiple testing problem. A particular application of this is concerned with assessing sparsity. ... More
Generalized Kalman Smoothing: Modeling and AlgorithmsSep 20 2016Sep 25 2016State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes ... More
Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite meanSep 16 2016We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds. In case that ... More
Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite meanSep 16 2016Nov 07 2016We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds. In case that ... More
The Inverse Gamma Distribution and Benford's LawSep 14 2016According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive ... More
Non-asymptotic upper bounds for the reconstruction error of PCASep 13 2016Principal component analysis (PCA) is a standard tool for dimension reduction. In this paper, we analyse the reconstruction error of PCA and prove non-asymptotic upper bounds for the corresponding excess risk. These bounds unify and improve several upper ... More
Naturality properties and comparison results for topological and infinitesimal embedded jump lociSep 09 2016We use augmented commutative differential graded algebra (ACDGA) models to study $G$-representation varieties of fundamental groups $\pi=\pi_1(M)$ and their embedded cohomology jump loci, around the trivial representation 1. When the space $M$ admits ... More
On Concentration Properties of Partially Observed Chaotic SystemsAug 30 2016This article presents results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz equations, as well ... More
Second-order accurate ensemble transform particle filtersAug 29 2016Sep 22 2016Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) (S. Reich, {\it ... More
Empirical Null Estimation using Discrete Mixture Distributions and its Application to Protein Domain DataAug 25 2016In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents ... More
Nonuniform Berry-Esseen bounds for martingales with applications to statistical estimationAug 18 2016We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when $x\rightarrow ... More
Approximate Bayesian Computation via Sufficient Dimension ReductionAug 18 2016Approximate Bayesian computation (ABC) has gained popularity in recent years owing to its easy implementation, nice interpretation and good performance. Its advantages are more visible when one encounters complex models where maximum likelihood estimation ... More
Generic Inference on Quantile and Quantile Effect Functions for Discrete OutcomesAug 18 2016This paper provides a method to construct simultaneous confidence bands for quantile and quantile effect functions for possibly discrete or mixed discrete-continuous random variables. The construction is generic and does not depend on the nature of the ... More
Estimation of the parameters of the Ornstein-Uhlenbeck's stochastic processAug 16 2016Aug 28 2016It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k \in N}$ of corresponding ... More
Quantifying minimal non-collinearity among random pointsAug 16 2016Aug 26 2016Let $\varphi_{n,K}$ denote the largest angle in all the triangles with vertices among the $n$ points selected at random in a compact convex subset $K$ of $\mathbb{R}^d$ with nonempty interior, where $d\ge2$. It is shown that the distribution of the random ... More
Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurementsAug 12 2016Sep 12 2017The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of temperature and ... More
Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EMAug 07 2016Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid initialization is ... More
Second-order asymptotics on distributions of maxima of bivariate elliptical arraysAug 06 2016Let $\{ (\xi_{ni}, \eta_{ni}), 1\leq i \leq n, n\geq 1 \}$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $(S_{1}, \rho_{n}S_{1}+\sqrt{1-\rho_{n}^2}S_{2})$, $\rho_{n}\in (0,1)$, where $(S_{1},S_{2})$ ... More
Synchronization of Reinforced Stochastic Processes with a Network-based InteractionJul 28 2016Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different ... More
Inference for Multivariate Regression Model based on synthetic data generated under Fixed-Posterior Predictive Sampling: comparison with Plug-in SamplingJul 21 2016The authors derive likelihood-based exact inference methods for the multivariate regression model, for singly imputed synthetic data generated via Posterior Predictive Sampling (PPS) and for multiply imputed synthetic data generated via a newly proposed ... More
An Empirical Study of Customer Spillover Learning about Service QualityJul 20 2016"Spillover" learning is defined as customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. In this paper, we propose a novel, parsimonious and general Bayesian hierarchical ... More
The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big DataJul 11 2016Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with ... More
Bayesian emulation for optimization in multi-step portfolio decisionsJul 06 2016We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to that of Bayesian ... More
Parameter estimation based on cumulative Kullback-Leibler divergenceJun 29 2016In this paper, we propose some estimators for the parameters of a statistical model based on Kullback-Leibler divergence of the survival function in continuous setting. We prove that the proposed estimators are subclass of "generalized estimating equations" ... More
Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy imageJun 27 2016Dec 06 2016Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation, with numerous applications in medical imaging and engineering. From a statistical point of view, the challenge is that likelihood-based ... More
Posterior inference on the boundary of a noisy image via a Gibbs modelJun 27 2016Detection of an image boundary when the pixel intensities are noisy is an important problem in epidemiology, geography, and ecology. A practical challenge to implementing a Bayesian approach in such problems is modeling the pixel intensity distributions ... More
Dynamic dependence networks: Financial time series forecasting and portfolio decisions (with discussion)Jun 27 2016We discuss Bayesian forecasting of increasingly high-dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state-space models characterizing sparse patterns of dependence ... More
Dynamics and sparsity in latent threshold factor models: A study in multivariate EEG signal processingJun 27 2016We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated ... More
Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic modelsJun 27 2016The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and ... More
Fractional Brownian motion and asymptotic Bayesian estimationJun 24 2016In this paper, we study the recovery of the Hurst parameter from a given discrete sample of fractional Brownian motion with statistical inverse theory. In particular, we show that in the limit the posteriori distribution of the parameter given the sample ... More
Bahadur--Kiefer Representations for Time Dependent Quantile ProcessesJun 20 2016We define a time dependent empirical process based on $n$ independent fractional Brownian motions and describe strong approximations to it by Gaussian processes. They lead to strong approximations and functional laws of the iterated logarithm for the ... More
Reducing MSE in estimation of heavy tails: a Bayesian approachJun 17 2016Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying classical methods such ... More
Applications of Distance Correlation to Time SeriesJun 17 2016The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and Mureika (1977), ... More
Bayesian estimation of incompletely observed diffusionsJun 13 2016We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete, in the sense that at each observation time a fixed linear combination ... More
Consistency and convergence rate of phylogenetic inference via regularizationJun 09 2016It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the ... More
A gamma approximation to the Bayesian posterior distribution of a discrete parameter of the Generalized Poisson modelJun 06 2016Let $X$ have a Generalized Poisson distribution with mean $kb$, where $b$ is a known constant in the unit interval and $k$ is a discrete, non-negative parameter. We show that if an uninformative uniform prior for $k$ is assumed, then the posterior distribution ... More
Second Order Concentration via Logarithmic Sobolev InequalitiesMay 27 2016We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the discrete cube and ... More
Nonparametric estimation of a regression function using the gamma kernel method in ergodic processesMay 24 2016In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen(2000). Strong uniform consistency and asymptotic normality of the corresponding estimators ... More
Nonparametric estimation of a regression function using the gamma kernel method in ergodic processesMay 24 2016Oct 16 2016In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen (2000). Strong uniform consistency and asymptotic normality of the corresponding estimators ... More
Well-posed Bayesian inverse problems and heavy-tailed stable Banach space priorsMay 19 2016May 31 2016This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, ... More
Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priorsMay 19 2016Nov 18 2016This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, ... More
Orthogonal symmetric non-negative matrix factorization under the stochastic block modelMay 17 2016We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to ... More
Randomized Matrix-free Trace and Log-Determinant EstimatorsMay 16 2016We present randomized algorithms for estimating the trace and deter- minant of Hermitian positive semi-definite matrices. The algorithms are based on subspace iteration, and access the matrix only through matrix vector products. We analyse the error due ... More
Wavelet Scattering Regression of Quantum Chemical EnergiesMay 16 2016Nov 08 2016We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. ... More
Wavelet Scattering Regression of Quantum Chemical EnergiesMay 16 2016We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. ... More
Quasiconformal Teichmuller theory as an analytical foundation for two dimensional conformal field theoryMay 02 2016The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. ... More
Sequential Bayesian optimal experimental design via approximate dynamic programmingApr 28 2016The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the ... More
Global-Local MixturesApr 26 2016Sep 21 2016Global-local mixtures are derived from the Cauchy-Schlomilch and Liouville integral transformation identities. We characterize well-known normal-scale mixture distributions including the Laplace or lasso, logit and quantile as well as new global-local ... More
Bayesian modelling and quantification of Raman spectroscopyApr 25 2016Raman spectroscopy is a technique for detecting and identifying molecules such as DNA. It is sensitive at very low concentrations and can accurately quantify the amount of a given molecule in a sample. The presence of a large, nonuniform background presents ... More
Efficient mode jumping MCMC for Bayesian variable selection in GLMMApr 21 2016May 20 2016Generalized linear mixed models (GLMM) are addressed for inference and prediction in a wide range of different applications providing a powerful scientific tool for the researchers and analysts coming from different fields. In most of these fields more ... More
Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arraysApr 20 2016Apr 27 2016In this paper, joint limit distributions of maxima and minima on independent and non-identically distributed bivariate Gaussian triangular arrays is derived as the correlation coefficient of $i$th vector of given $n$th row is the function of $i/n$. Furthermore, ... More
Quenched Asymptotics for the Discrete Fourier Transforms of a Stationary ProcessApr 01 2016May 24 2016In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization introduced to extend ... More
Risk contagion under regular variation and asymptotic tail independenceMar 30 2016Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of high values of ... More
PAC-Bayesian bounds for the Gram matrix and least squares regression with a random designMar 16 2016The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares regression with ... More
Convex spaces, affine spaces, and commutants for algebraic theoriesMar 10 2016Certain axiomatic notions of $\textit{affine space}$ over a ring and $\textit{convex space}$ over a preordered ring are examples of the notion of $\mathcal{T}$-algebra for an algebraic theory $\mathcal{T}$ in the sense of Lawvere. Herein we study the ... More
An Introduction to Mechanized ReasoningMar 08 2016Aug 10 2016Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We ... More
Insurance Applications of Some New Dependence Models derived from Multivariate Collective ModelsMar 06 2016Oct 06 2016Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes $(X_i,Y_i), i\ge 1$ and a claim counting random variable $N$. In ... More
Markov Switching Smooth Transition GARCH ModelMar 06 2016A Markov switching asymmetric GARCH model which imposes more leverage effect of the negative shocks is considered. The asymptotic behavior of the second moment is investigated and an upper bound for it is calculated. A bayesian strategy through Gibbs ... More
Fast calculation of correlations in recognition systemsMar 06 2016Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition system architectures ... More
Reversible Markov chain estimation using convex-concave programmingMar 04 2016We present a convex-concave reformulation of the reversible Markov chain estimation problem and outline an efficient numerical scheme for the solution of the resulting problem based on a primal-dual interior point method for monotone variational inequalities. ... More
Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian NoiseMar 01 2016We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry--Esseen bound of the so-called alternative estimator of the mean reversion parameter. The conditions and results ... More
Post-selection inference for L1-penalized likelihood modelsFeb 24 2016Feb 25 2016We present a new method for post-selection inference for L1 (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al (2014). The method provides p-values ... More
Post-selection inference for L1-penalized likelihood modelsFeb 24 2016Oct 13 2016We present a new method for post-selection inference for L1 (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al (2014). The method provides p-values ... More
Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimationFeb 18 2016We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein-Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with probability 1 for ... More
Central limit theorems for functionals of large dimensional sample covariance matrix and mean vector in matrix-variate skewed modelFeb 17 2016In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix variate general skew normal distribution. The central ... More
A Bayes interpretation of stacking for M-complete and M-open settingsFeb 16 2016In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model averaging procedure ... More
Bayesian generalized fused lasso modeling via NEG distributionFeb 16 2016The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma ... More
Option Pricing in Markets with Unknown Stochastic DynamicsFeb 15 2016We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty of a market ... More
Schur polynomials and matrix positivity preserversFeb 15 2016Apr 28 2016A classical result by Schoenberg (1942) identifies all real-valued functions that preserve positive semidefiniteness (psd) when applied entrywise to matrices of arbitrary dimension. Schoenberg's work has continued to attract significant interest, including ... More