Hybrid journal (It can contain Open Access articles) ISSN (Print) 0006-3444 - ISSN (Online) 1464-3510 Published by Oxford University Press[406 journals]

Authors:Sykulski A; Olhede S, Guillaumin A, et al. Pages: 251 - 266 Abstract: SummaryThe Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it is known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose a method for debiasing Whittle estimates for second-order stationary stochastic processes. The debiased Whittle likelihood can be computed in the same ${O}(n\log n)$ operations as the standard Whittle approach. We demonstrate the superior performance of our method in simulation studies and in application to a large-scale oceanographic dataset, where in both cases the debiased approach reduces bias by up to two orders of magnitude, achieving estimates that are close to those of the exact maximum likelihood, at a fraction of the computational cost. We prove that the method yields estimates that are consistent at an optimal convergence rate of $n^{-1/2}$ for Gaussian processes and for certain classes of non-Gaussian or nonlinear processes. This is established under weaker assumptions than in the standard theory, and in particular the power spectral density is not required to be continuous in frequency. We describe how the method can be readily combined with standard methods of bias reduction, such as tapering and differencing, to further reduce bias in parameter estimates. PubDate: Wed, 13 Feb 2019 00:00:00 GMT DOI: 10.1093/biomet/asy071 Issue No:Vol. 106, No. 2 (2019)

Authors:Guinness J. Pages: 267 - 286 Abstract: SummaryWe introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in $O(n\log n)$ time and $O(n)$ memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates. In addition, we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias. The paper contains theoretical results on properties of the imputed-data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios. We present an application to a gridded satellite surface temperature dataset with missing values. PubDate: Wed, 03 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz004 Issue No:Vol. 106, No. 2 (2019)

Authors:Heng J; Jacob P. Pages: 287 - 302 Abstract: SummaryWe propose a method for parallelization of Hamiltonian Monte Carlo estimators. Our approach involves constructing a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that the resulting estimators are unbiased. This allows us to produce independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the number of replicates, rather than in the usual limit of the number of Markov chain iterations. We investigate the scalability of our coupling in high dimensions on a toy example. The choice of algorithmic parameters and the efficiency of our proposed approach are then illustrated on a logistic regression with 300 covariates and a log-Gaussian Cox point processes model with low- to fine-grained discretizations. PubDate: Thu, 28 Feb 2019 00:00:00 GMT DOI: 10.1093/biomet/asy074 Issue No:Vol. 106, No. 2 (2019)

Authors:Livingstone S; Faulkner M, Roberts G. Pages: 303 - 319 Abstract: SummaryWe consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are established on integrator stability and geometric convergence, and we show that choices of kinetic energy that result in heavy-tailed momentum distributions can exhibit an undesirable negligible moves property, which we define. A general efficiency-robustness trade-off is outlined, and implementations which rely on approximate gradients are also discussed. Two numerical studies illustrate our theoretical findings, showing that the standard choice which results in a Gaussian momentum distribution is not always optimal in terms of either robustness or efficiency. PubDate: Mon, 22 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz013 Issue No:Vol. 106, No. 2 (2019)

Authors:Vats D; Flegal J, Jones G. Pages: 321 - 337 Abstract: SUMMARYMarkov chain Monte Carlo produces a correlated sample which may be used for estimating expectations with respect to a target distribution. A fundamental question is: when should sampling stop so that we have good estimates of the desired quantities' The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. The multivariate nature of this Monte Carlo error has been largely ignored in the literature. We present a multivariate framework for terminating a simulation in Markov chain Monte Carlo. We define a multivariate effective sample size, the estimation of which requires strongly consistent estimators of the covariance matrix in the Markov chain central limit theorem, a property we show for the multivariate batch means estimator. We then provide a lower bound on the number of minimum effective samples required for a desired level of precision. This lower bound does not depend on the underlying stochastic process and can be calculated a priori. This result is obtained by drawing a connection between terminating simulation via effective sample size and terminating simulation using a relative standard deviation fixed-volume sequential stopping rule, which we demonstrate is an asymptotically valid procedure. The finite-sample properties of the proposed method are demonstrated in a variety of examples. PubDate: Wed, 03 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz002 Issue No:Vol. 106, No. 2 (2019)

Authors:Petersen A; Müller H. Pages: 339 - 351 Abstract: SummaryA common feature of methods for analysing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fréchet mean is typically used to quantify and visualize the average density of the sample. For one-dimensional densities, the Wasserstein metric is popular due to its theoretical appeal and interpretive value as an optimal transport metric, leading to the Wasserstein–Fréchet mean or barycentre as the mean density. We extend the existing methodology for samples of densities in two key directions. First, motivated by applications in neuroimaging, we consider dependent density data, where a $p$-vector of univariate random densities is observed for each sampling unit. Second, we introduce a Wasserstein covariance measure and propose intuitively appealing estimators for both fixed and diverging $p$, where the latter corresponds to continuously indexed densities. We also give theory demonstrating consistency and asymptotic normality, while accounting for errors introduced in the unavoidable preparatory density estimation step. The utility of the Wasserstein covariance matrix is demonstrated through applications to functional connectivity in the brain using functional magnetic resonance imaging data and to the secular evolution of mortality for various countries. PubDate: Wed, 03 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz005 Issue No:Vol. 106, No. 2 (2019)

Authors:Karmakar B; French B, Small D. Pages: 353 - 367 Abstract: SummaryA sensitivity analysis for an observational study assesses how much bias, due to nonrandom assignment of treatment, would be necessary to change the conclusions of an analysis that assumes treatment assignment was effectively random. The evidence for a treatment effect can be strengthened if two different analyses, which could be affected by different types of biases, are both somewhat insensitive to bias. The finding from the observational study is then said to be replicated. Evidence factors allow for two independent analyses to be constructed from the same dataset. When combining the evidence factors, the Type I error rate must be controlled to obtain valid inference. A powerful method is developed for controlling the familywise error rate for sensitivity analyses with evidence factors. It is shown that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for either evidence factor alone. The proposed methods are illustrated through a study of the effect of radiation exposure on the risk of cancer. An R package, evidenceFactors, is available from CRAN to implement the methods of the paper. PubDate: Wed, 03 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz003 Issue No:Vol. 106, No. 2 (2019)

Authors:Chen S; Haziza D, Léger C, et al. Pages: 369 - 384 Abstract: SummaryThe most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables. Treating the imputed values as if they were observed may lead to invalid inferences. Bootstrap variance estimators for various finite population parameters are obtained using two pseudo-population bootstrap schemes. We establish the asymptotic properties of the resulting bootstrap variance estimators for population totals and population quantiles. A simulation study suggests that the methods perform well in terms of relative bias and coverage probability. PubDate: Wed, 03 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz001 Issue No:Vol. 106, No. 2 (2019)

Authors:Neumeyer N; Van Keilegom I. Pages: 385 - 400 Abstract: SummaryIn this paper we consider regression models with centred errors, independent of the covariates. Given independent and identically distributed data and given an estimator of the regression function, which can be parametric or nonparametric in nature, we estimate the distribution of the error term by the empirical distribution of estimated residuals. To approximate the distribution of this estimator, Koul & Lahiri (1994) and Neumeyer (2009) proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples. So far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context. Here we solve this open problem and show that the nonsmooth residual bootstrap is consistent. We illustrate the theoretical result by means of simulations, which demonstrate the accuracy of this bootstrap procedure for various models, testing procedures and sample sizes. PubDate: Mon, 08 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz009 Issue No:Vol. 106, No. 2 (2019)

Authors:Cai T; Li H, Ma J, et al. Pages: 401 - 416 Abstract: SummaryMicro-organisms such as bacteria form complex ecological community networks that can be greatly influenced by diet and other environmental factors. Differential analysis of microbial community structures aims to elucidate systematic changes during an adaptive response to changes in environment. In this paper, we propose a flexible Markov random field model for microbial network structure and introduce a hypothesis testing framework for detecting differences between networks, also known as differential network analysis. Our global test for differential networks is particularly powerful against sparse alternatives. In addition, we develop a multiple testing procedure with false discovery rate control to identify the structure of the differential network. The proposed method is applied to data from a gut microbiome study on U.K. twins to evaluate how age affects the microbial community network. PubDate: Mon, 22 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz012 Issue No:Vol. 106, No. 2 (2019)

Authors:Jiang F; Ma Y, Wei Y. Pages: 417 - 432 Abstract: SummaryRapid improvement in technology has made it relatively cheap to collect genetic data, however statistical analysis of existing data is still much cheaper. Thus, secondary analysis of single-nucleotide polymorphism, SNP, data, i.e., reanalysing existing data in an effort to extract more information, is an attractive and cost-effective alternative to collecting new data. We study the relationship between gene expression and SNPs through a combination of factor analysis and dimension reduction estimation. To take advantage of the flexibility in traditional factor models where the latent factors are not required to be normal, we recommend using semiparametric sufficient dimension reduction methods in the joint estimation of the combined model. The resulting estimator is flexible and has superior performance relative to the existing estimator, which relies on additional assumptions on the latent factors. We quantify the asymptotic performance of the proposed parameter estimator and perform inference by assessing the estimation variability and by constructing confidence intervals. The new results enable us to identify, for the first time, statistically significant SNPs concerning gene-SNP relations in lung tissue from genotype-tissue expression data. PubDate: Mon, 22 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz010 Issue No:Vol. 106, No. 2 (2019)

Authors:Tank A; Fox E, Shojaie A. Pages: 433 - 452 Abstract: SummaryCausal inference in multivariate time series is challenging because the sampling rate may not be as fast as the time scale of the causal interactions, so the observed series is a subsampled version of the desired series. Furthermore, series may be observed at different sampling rates, yielding mixed-frequency series. To determine instantaneous and lagged effects between series at the causal scale, we take a model-based approach that relies on structural vector autoregressive models. We present a unifying framework for parameter identifiability and estimation under subsampling and mixed frequencies when the noise, or shocks, is non-Gaussian. By studying the structural case, we develop identifiability and estimation methods for the causal structure of lagged and instantaneous effects at the desired time scale. We further derive an exact expectation-maximization algorithm for inference in both subsampled and mixed-frequency settings. We validate our approach in simulated scenarios and on a climate and an econometric dataset. PubDate: Mon, 08 Apr 2019 00:00:00 GMT DOI: 10.1093/biomet/asz007 Issue No:Vol. 106, No. 2 (2019)

Authors:He X. Pages: 453 - 464 Abstract: SummaryWe propose a new method to construct maximin distance designs with arbitrary numbers of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more dimensions. Applicable to distance measures with equal or unequal weights, our method is useful for emulating computer experiments when a relatively accurate a priori guess on variable importance is available. PubDate: Wed, 16 Jan 2019 00:00:00 GMT DOI: 10.1093/biomet/asy069 Issue No:Vol. 106, No. 2 (2019)

Authors:Lyddon S; Holmes C, Walker S. Pages: 465 - 478 Abstract: SummaryIn this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined through minimizing an expected negative loglikelihood under an unknown sampling distribution. This interpretation enables us to extend the weighted likelihood bootstrap to posterior sampling for parameters minimizing an expected loss. We call this method the loss-likelihood bootstrap, and we make a connection between it and general Bayesian updating, which is a way of updating prior belief distributions that does not need the construction of a global probability model, yet requires the calibration of two forms of loss function. The loss-likelihood bootstrap is used to calibrate the general Bayesian posterior by matching asymptotic Fisher information. We demonstrate the proposed method on a number of examples. PubDate: Mon, 18 Mar 2019 00:00:00 GMT DOI: 10.1093/biomet/asz006 Issue No:Vol. 106, No. 2 (2019)

Authors:Basse G; Feller A, Toulis P. Pages: 487 - 494 Abstract: SummaryMany causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized evaluation of an intervention targeting student absenteeism in the school district of Philadelphia. We show improvements over existing methods in terms of computational and statistical power. PubDate: Mon, 04 Feb 2019 00:00:00 GMT DOI: 10.1093/biomet/asy072 Issue No:Vol. 106, No. 2 (2019)

Authors:Syring N; Martin R. Pages: 479 - 486 Abstract: SummaryCalibration of credible regions derived from under- or misspecified models is an important and challenging problem. In this paper, we introduce a scalar tuning parameter that controls the posterior distribution spread, and develop a Monte Carlo algorithm that sets this parameter so that the corresponding credible region achieves the nominal frequentist coverage probability. PubDate: Mon, 10 Dec 2018 00:00:00 GMT DOI: 10.1093/biomet/asy054 Issue No:Vol. 106, No. 2 (2018)

Authors:Ghosh M; Kubokawa T. Pages: 495 - 500 Abstract: SummaryConsider the problem of finding a predictive density of a new observation drawn independently of observations sampled from a multivariate normal distribution with the same unknown mean vector and the same known variance under general divergence loss. In this paper, we consider two kinds of prior distribution for the mean vector: one is a multivariate normal distribution with mean based on unknown regression coefficients, and the other further assumes that the regression coefficients have uniform prior distributions. The two kinds of prior distribution provide, respectively, the empirical Bayes and hierarchical Bayes predictive distributions. Both predictive distributions have the same mean, but they have different covariance matrices, with the hierarchical Bayes predictive distribution having a larger covariance matrix. We compare the two Bayesian predictive densities in terms of their frequentist risks under the general divergence loss and show that the hierarchical Bayes predictive density has a uniformly smaller risk than the empirical Bayes predictive density. As an offshoot of our result, we show that best linear unbiased predictors in mixed linear models, optimal under normality and squared error loss, maintain their optimality under the general divergence loss. PubDate: Tue, 25 Dec 2018 00:00:00 GMT DOI: 10.1093/biomet/asy073 Issue No:Vol. 106, No. 2 (2018)