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  • High-dimensional changepoint detection via a geometrically inspired mapping
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-28
    Thomas Grundy, Rebecca Killick, Gueorgui Mihaylov

    Abstract High-dimensional changepoint analysis is a growing area of research and has applications in a wide range of fields. The aim is to accurately and efficiently detect changepoints in time series data when both the number of time points and dimensions grow large. Existing methods typically aggregate or project the data to a smaller number of dimensions, usually one. We present a high-dimensional

  • Optimal allocation of Monte Carlo simulations to multiple hypothesis tests
    Stat. Comput. (IF 2.383) Pub Date : 2019-10-05
    Georg Hahn

    Abstract Multiple hypothesis tests are often carried out in practice using p-value estimates obtained with bootstrap or permutation tests since the analytical p-values underlying all hypotheses are usually unknown. This article considers the allocation of a pre-specified total number of Monte Carlo simulations \(K \in \mathbb {N}\) (i.e., permutations or draws from a bootstrap distribution) to a given

  • Robust Bayesian synthetic likelihood via a semi-parametric approach
    Stat. Comput. (IF 2.383) Pub Date : 2019-10-04
    Ziwen An, David J. Nott, Christopher Drovandi

    Abstract Bayesian synthetic likelihood (BSL) is now a well-established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable likelihood function of a carefully chosen summary statistic at a parameter value with a multivariate normal distribution. The mean and covariance matrix

  • Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs
    Stat. Comput. (IF 2.383) Pub Date : 2019-11-05
    Evelyn Buckwar, Massimiliano Tamborrino, Irene Tubikanec

    Abstract Approximate Bayesian computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool for modelling time-dependent, real-world phenomena with underlying random effects. When applying ABC to stochastic models, two major difficulties arise:

  • Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations
    Stat. Comput. (IF 2.383) Pub Date : 2019-09-10
    Michael B. Giles, Mateusz B. Majka, Lukasz Szpruch, Sebastian J. Vollmer, Konstantinos C. Zygalakis

    Abstract We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles in Acta Numer. 24:259–328, 2015. https://doi.org/10.1017/S096249291500001X) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin equations with a strongly concave potential. We show that when appropriate contracting

  • Regularized estimation for highly multivariate log Gaussian Cox processes
    Stat. Comput. (IF 2.383) Pub Date : 2019-11-15
    Achmad Choiruddin, Francisco Cuevas-Pacheco, Jean-François Coeurjolly, Rasmus Waagepetersen

    Abstract Statistical inference for highly multivariate point pattern data is challenging due to complex models with large numbers of parameters. In this paper, we develop numerically stable and efficient parameter estimation and model selection algorithms for a class of multivariate log Gaussian Cox processes. The methodology is applied to a highly multivariate point pattern data set from tropical

  • Data-driven stochastic inversion via functional quantization
    Stat. Comput. (IF 2.383) Pub Date : 2019-09-13
    Mohamed Reda El Amri, Céline Helbert, Olivier Lepreux, Miguel Munoz Zuniga, Clémentine Prieur, Delphine Sinoquet

    Abstract In this paper, we propose a new methodology for solving stochastic inversion problems through computer experiments, the stochasticity being driven by a functional random variables. This study is motivated by an automotive application. In this context, the simulator code takes a double set of simulation inputs: deterministic control variables and functional uncertain variables. This framework

  • Sampling from manifold-restricted distributions using tangent bundle projections
    Stat. Comput. (IF 2.383) Pub Date : 2019-10-14
    Alvin J. K. Chua

    Abstract A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density and to compute credible regions. Often by construction, many target distributions can be expressed as some higher-dimensional closed-form distribution with parametrically constrained variables, i.e., one that is restricted to a

  • High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking
    Stat. Comput. (IF 2.383) Pub Date : 2019-12-19
    Fan Wang, Sach Mukherjee, Sylvia Richardson, Steven M. Hill

    Abstract Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well developed, the relative efficacy of different approaches in finite-sample settings, as encountered in practice, remains incompletely understood. There is therefore a need for empirical investigations in this area that can offer practical

  • Local dimension reduction of summary statistics for likelihood-free inference
    Stat. Comput. (IF 2.383) Pub Date : 2019-10-04
    Jukka Sirén, Samuel Kaski

    Abstract Approximate Bayesian computation (ABC) and other likelihood-free inference methods have gained popularity in the last decade, as they allow rigorous statistical inference for complex models without analytically tractable likelihood functions. A key component for accurate inference with ABC is the choice of summary statistics, which summarize the information in the data, but at the same time

  • Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components
    Stat. Comput. (IF 2.383) Pub Date : 2019-08-27
    Panagiotis Papastamoulis

    Abstract Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting mixture models yields a simple and efficient way in order to estimate the unknown number of clusters and model parameters by Markov chain Monte Carlo sampling

  • Sequential Monte Carlo with transformations.
    Stat. Comput. (IF 2.383) Pub Date : 2019-11-17
    Richard G Everitt,Richard Culliford,Felipe Medina-Aguayo,Daniel J Wilson

    This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an

  • Approximation and sampling of multivariate probability distributions in the tensor train decomposition
    Stat. Comput. (IF 2.383) Pub Date : 2019-11-02
    Sergey Dolgov, Karim Anaya-Izquierdo, Colin Fox, Robert Scheichl

    Abstract General 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 that is based on low-rank surrogates in the tensor train format, a methodology that has been exploited for many years for scalable, high-dimensional

  • Central quantile subspace
    Stat. Comput. (IF 2.383) Pub Date : 2019-12-18
    Eliana Christou

    Abstract Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the conditional quantiles received particular attention, due to its model flexibility. However, nonparametric QR techniques are limited in the number of covariates. Dimension

  • Coordinate sampler: a non-reversible Gibbs-like MCMC sampler
    Stat. Comput. (IF 2.383) Pub Date : 2019-12-26
    Changye Wu, Christian P. Robert

    Abstract We derive a novel non-reversible, continuous-time Markov chain Monte Carlo sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process, which is a variant of the Zigzag sampler of Bierkens et al. (Ann Stat 47(3):1288–1320, 2019). In addition to providing a theoretical validation for this new simulation algorithm, we show that the Markov chain it induces exhibits geometrical

  • High-dimensional VAR with low-rank transition
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-16
    Pierre Alquier, Karine Bertin, Paul Doukhan, Rémy Garnier

    Abstract We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. While our model has formal similarities with factor models, its structure is more a way to reduce the dimension in order to improve the predictions, rather

  • Matrix completion with nonconvex regularization: spectral operators and scalable algorithms
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-14
    Rahul Mazumder, Diego Saldana, Haolei Weng

    Abstract In this paper, we study the popularly dubbed matrix completion problem, where the task is to “fill in” the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of low rank. Our contributions herein enhance our prior work on nuclear norm regularized problems for matrix completion (Mazumder et al. in J Mach Learn Res 1532(11):2287–2322

  • Optimal classification of Gaussian processes in homo- and heteroscedastic settings
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-12
    José L. Torrecilla, Carlos Ramos-Carreño, Manuel Sánchez-Montañés, Alberto Suárez

    Abstract A procedure to derive optimal discrimination rules is formulated for binary functional classification problems in which the instances available for induction are characterized by random trajectories sampled from different Gaussian processes, depending on the class label. Specifically, these optimal rules are derived as the asymptotic form of the quadratic discriminant for the discretely monitored

  • Likelihood-free approximate Gibbs sampling
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-11
    G. S. Rodrigues, David J. Nott, S. A. Sisson

    Abstract Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional problems, but suffer a curse of dimensionality in the number of model parameters. We introduce a likelihood-free approximate Gibbs sampler that naturally

  • Adaptive iterative Hessian sketch via A -optimal subsampling
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-11
    Aijun Zhang, Hengtao Zhang, Guosheng Yin

    Abstract Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (J Mach Learn Res 17(1):1842–1879, 2016) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorithm under the unconstrained least squares problem

  • Accelerating Metropolis-within-Gibbs sampler with localized computations of differential equations
    Stat. Comput. (IF 2.383) Pub Date : 2020-03-06
    Qiang Liu, Xin T. Tong

    Abstract Inverse problem is ubiquitous in science and engineering, and Bayesian methodologies are often used to infer the underlying parameters. For high-dimensional temporal-spatial models, classical Markov chain Monte Carlo methods are often slow to converge, and it is necessary to apply Metropolis-within-Gibbs (MwG) sampling on parameter blocks. However, the computation cost of each MwG iteration

  • Bayesian Additive Regression Trees using Bayesian Model Averaging.
    Stat. Comput. (IF 2.383) Pub Date : 2018-11-20
    Belinda Hernández,Adrian E Raftery,Stephen R Pennington,Andrew C Parnell

    Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However for datasets where the number of variables p is large the algorithm can become inefficient and computationally expensive. Another method which is popular for high dimensional data is

  • Optimal Bayesian estimators for latent variable cluster models.
    Stat. Comput. (IF 2.383) Pub Date : 2018-09-18
    Riccardo Rastelli,Nial Friel

    In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden

  • Trajectory inference and parameter estimation in stochastic models with temporally aggregated data.
    Stat. Comput. (IF 2.383) Pub Date : 2018-08-28
    Maria Myrto Folia,Magnus Rattray

    Stochastic models are of fundamental importance in many scientific and engineering applications. For example, stochastic models provide valuable insights into the causes and consequences of intra-cellular fluctuations and inter-cellular heterogeneity in molecular biology. The chemical master equation can be used to model intra-cellular stochasticity in living cells, but analytical solutions are rare

  • Fast covariance estimation for sparse functional data.
    Stat. Comput. (IF 2.383) Pub Date : 2018-02-17
    Luo Xiao,Cai Li,William Checkley,Ciprian Crainiceanu

    Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing using

  • Double-Parallel Monte Carlo for Bayesian Analysis of Big Data.
    Stat. Comput. (IF 2.383) Pub Date : 2017-11-27
    Jingnan Xue,Faming Liang

    This paper proposes a simple, practical and efficient MCMC algorithm for Bayesian analysis of big data. The proposed algorithm suggests to divide the big dataset into some smaller subsets and provides a simple method to aggregate the subset posteriors to approximate the full data posterior. To further speed up computation, the proposed algorithm employs the population stochastic approximation Monte

  • Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.
    Stat. Comput. (IF 2.383) Pub Date : 2017-10-07
    Cheng Zhang,Babak Shahbaba,Hongkai Zhao

    For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore

  • A second-order iterated smoothing algorithm.
    Stat. Comput. (IF 2.383) Pub Date : 2017-09-02
    Dao Nguyen,Edward L Ionides

    Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation

  • Unbiased Bayesian inference for population Markov jump processes via random truncations.
    Stat. Comput. (IF 2.383) Pub Date : 2017-07-12
    Anastasis Georgoulas,Jane Hillston,Guido Sanguinetti

    We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose

  • Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems.
    Stat. Comput. (IF 2.383) Pub Date : 2016-07-16
    Anindya Bhadra,Raymond J Carroll

    In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a Metropolis-Hastings

  • Model-based clustering based on sparse finite Gaussian mixtures.
    Stat. Comput. (IF 2.383) Pub Date : 2016-02-24
    Gertraud Malsiner-Walli,Sylvia Frühwirth-Schnatter,Bettina Grün

    In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting

  • Fast Covariance Estimation for High-dimensional Functional Data.
    Stat. Comput. (IF 2.383) Pub Date : 2016-02-24
    Luo Xiao,Vadim Zipunnikov,David Ruppert,Ciprian Crainiceanu

    We propose two fast covariance smoothing methods and associated software that scale up linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension J > 500; a recently introduced sandwich smoother is an exception but is not adapted to smooth covariance matrices of large dimensions, such as J = 10, 000. We introduce two new

  • de Finetti Priors using Markov chain Monte Carlo computations.
    Stat. Comput. (IF 2.383) Pub Date : 2015-09-29
    Sergio Bacallado,Persi Diaconis,Susan Holmes

    Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three

  • Sampling from Dirichlet process mixture models with unknown concentration parameter: mixing issues in large data implementations.
    Stat. Comput. (IF 2.383) Pub Date : 2015-09-01
    David I Hastie,Silvia Liverani,Sylvia Richardson

    We consider the question of Markov chain Monte Carlo sampling from a general stick-breaking Dirichlet process mixture model, with concentration parameter [Formula: see text]. This paper introduces a Gibbs sampling algorithm that combines the slice sampling approach of Walker (Communications in Statistics - Simulation and Computation 36:45-54, 2007) and the retrospective sampling approach of Papaspiliopoulos

  • Scalable estimation strategies based on stochastic approximations: Classical results and new insights.
    Stat. Comput. (IF 2.383) Pub Date : 2015-07-04
    Edoardo M Airoldi,Panos Toulis

    Estimation with large amounts of data can be facilitated by stochastic gradient methods, in which model parameters are updated sequentially using small batches of data at each step. Here, we review early work and modern results that illustrate the statistical properties of these methods, including convergence rates, stability, and asymptotic bias and variance. We then overview modern applications where

  • Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution.
    Stat. Comput. (IF 2.383) Pub Date : 2015-06-23
    S R White,T Kypraios,S P Preston

    Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC

  • Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors.
    Stat. Comput. (IF 2.383) Pub Date : 2015-03-10
    Patrick Breheny,Jian Huang

    Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and shown

  • Shrinkage Estimation of Varying Covariate Effects Based On Quantile Regression.
    Stat. Comput. (IF 2.383) Pub Date : 2014-10-22
    Limin Peng,Jinfeng Xu,Nancy Kutner

    Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed

  • Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models.
    Stat. Comput. (IF 2.383) Pub Date : 2014-10-14
    Dingfeng Jiang,Jian Huang

    Recent studies have demonstrated theoretical attractiveness of a class of concave penalties in variable selection, including the smoothly clipped absolute deviation and minimax concave penalties. The computation of the concave penalized solutions in high-dimensional models, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm for computing the

  • A Tutorial on Rank-based Coefficient Estimation for Censored Data in Small- and Large-Scale Problems.
    Stat. Comput. (IF 2.383) Pub Date : 2013-08-21
    Matthias Chung,Qi Long,Brent A Johnson

    The analysis of survival endpoints subject to right-censoring is an important research area in statistics, particularly among econometricians and biostatisticians. The two most popular semiparametric models are the proportional hazards model and the accelerated failure time (AFT) model. Rank-based estimation in the AFT model is computationally challenging due to optimization of a non-smooth loss function

  • Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution.
    Stat. Comput. (IF 2.383) Pub Date : 2011-11-30
    Kenneth Lo,Raphael Gottardo

    Cluster analysis is the automated search for groups of homogeneous observations in a data set. A popular modeling approach for clustering is based on finite normal mixture models, which assume that each cluster is modeled as a multivariate normal distribution. However, the normality assumption that each component is symmetric is often unrealistic. Furthermore, normal mixture models are not robust against

  • A quasi-Newton acceleration for high-dimensional optimization algorithms.
    Stat. Comput. (IF 2.383) Pub Date : 2011-03-02
    Hua Zhou,David Alexander,Kenneth Lange

    In many statistical problems, maximum likelihood estimation by an EM or MM algorithm suffers from excruciatingly slow convergence. This tendency limits the application of these algorithms to modern high-dimensional problems in data mining, genomics, and imaging. Unfortunately, most existing acceleration techniques are ill-suited to complicated models involving large numbers of parameters. The squared

  • Rank-based variable selection with censored data.
    Stat. Comput. (IF 2.383) Pub Date : 2010-04-01
    Jinfeng Xu,Chenlei Leng,Zhiliang Ying

    A rank-based variable selection procedure is developed for the semiparametric accelerated failure time model with censored observations where the penalized likelihood (partial likelihood) method is not directly applicable. The new method penalizes the rank-based Gehan-type loss function with the ℓ1 penalty. To correctly choose the tuning parameters, a novel likelihood-based χ2-type criterion is proposed

  • Model fitting and inference under Latent Equilibrium Processes.
    Stat. Comput. (IF 2.383) Pub Date : 2008-10-07
    Sourabh Bhattacharya,Alan E Gelfand,Kent E Holsinger

    This paper presents a methodology for model fitting and inference in the context of Bayesian models of the type f(Y | X, theta)f(X | theta)f(theta), where Y is the (set of) observed data, theta is a set of model parameters and X is an unobserved (latent) stationary stochastic process induced by the first order transition model f(X((t+1)) | X((t)), theta), where X((t)) denotes the state of the process

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