Search

Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution structural information of biological macromolecules by exposing a large ensemble of molecules in solution to a powerful...

In the U.S. Forest Service’s Forest Inventory and Analysis (FIA) program, as in other natural resource surveys, many auxiliary variables are available for use in model-assisted inference about finite population parameters. Some of this auxiliary information may be extraneous, and therefore model selection is appropriate to improve the efficiency of the survey regression estimators of finite population totals. A model-assisted survey regression estimator using the lasso is presented and extended to the adaptive lasso. For a sequence of finite populations and probability sampling designs, asymptotic properties of the lasso survey regression estimator are derived, including design consistency and central limit theory for the estimator and design consistency of a variance estimator. To estimate multiple finite population quantities with the method, lasso survey regression weights are developed, using both a model calibration approach and a ridge regression approximation. The gains in efficiency of the lasso estimator over the full regression estimator are demonstrated through a simulation study estimating tree canopy cover for a region in Utah.

Nonlinear dynamical systems are encountered in many areas of social science, natural science, and engineering, and are of particular interest for complex biological processes like the spiking activity of neural ensembles in the brain. To describe such spiking activity, we adapt the Volterra series expansion of an analytic function to account for the point-process nature of multiple inputs and a single output (MISO) in a neural ensemble. Our model describes the transformed spiking probability for the output as the sum of kernel-weighted integrals of the inputs. The kernel functions need to be identified and estimated, and both local sparsity (kernel functions may be zero on part of their support) and global sparsity (some kernel functions may be identically zero) are of interest. The kernel functions are approximated by B-splines and a penalized likelihood-based approach is proposed for estimation. Even for moderately complex brain functionality, the identification and estimation of this sparse fun...

We consider small area estimation for the departure times of recreational anglers along the Atlantic and Gulf coasts of the United States. A Bayesian area-level Fay–Herriot model is considered to obtain estimates of the departure time distribution functions. The departure distribution functions are modelled as circular distributions plus area-specific errors. The circular distributions are modelled as projected normal, and a regression model is specified to borrow information across domains. Estimation is conducted through the use of a Hamiltonian Monte Carlo sampler and a projective approach onto the probability simplex. The Canadian Journal of Statistics 44: 416–430; 2016 © 2016 Statistical Society of Canada

Fine stratification is commonly used to control the distribution of a sample from a finite population and to improve the precision of resulting estimators. One-per-stratum designs represent the finest possible stratification and occur in practice, but designs with very low numbers of elements per stratum (say, two or three) are also common. The classical variance estimator in this context is the collapsed stratum estimator, which relies on creating larger “pseudo-strata” and computing the sum of the squared differences between estimated stratum totals across the pseudo-strata. We propose here a nonparametric alternative that replaces the pseudo-strata by kernel-weighted stratum neighborhoods and uses deviations from a fitted mean function to estimate the variance. We establish the asymptotic behavior of the kernel-based estimator and show its superior practical performance relative to the collapsed stratum variance estimator in a simulation study. An application to data from the U.S. Consumer Expe...

Variational approximations provide fast, deterministic alternatives to Markov Chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroskedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the non-conjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov Chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroskedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.

This paper reviews the design-based, model-assisted approach to using data from a complex survey together with auxiliary information to estimate finite population parameters. A general recipe for deriving model-assisted estimators is presented and design-based asymptotic analysis for such estimators is reviewed. The recipe allows for a very broad class of prediction methods, with examples from the literature including linear models, linear mixed models, nonparametric regression and machine learning techniques.

Terrestrial CO2 flux estimates are obtained from two fundamentally different methods generally termed bottom-up and top-down approaches. Inventory methods are one type of bottom-up approach which uses various sources of information such as crop production surveys and forest monitoring data to estimate the annual CO2 flux at locations covering a study region. Top-down approaches are various types of atmospheric inversion methods which use CO2 concentration measurements from monitoring towers and atmospheric transport models to estimate CO2 flux over a study region. Both methods can also quantify the uncertainty associated with their estimates. Historically, these two approaches have produced estimates that differ considerably. The goal of this work is to construct a statistical model which sensibly combines estimates from the two approaches to produce a new estimate of CO2 flux for our study region. The two approaches have complementary strengths and weaknesses, and our results show that certain aspects of the uncertainty associated with each of the approaches are greatly reduced by combining the methods. Our model is purposefully simple and designed to take the two approaches’ estimates and measures of uncertainty at ‘face value’. Specifically, we use a constrained least-squares approach to appropriately weigh the estimates by the inverse of their variance, and the constraint imposes agreement between the two sources. Our application involves nearly 18,000 flux estimates for the upper midwest United States. The constrained dependencies result in a non-sparse covariance matrix, but computation requires only minutes due to the structure of the model.

Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging; that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This paper reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.

Many environmental data sets have a continuous domain, in time and/or space, and complex features that may be poorly modelled with a stationary (in space and time) Gaussian process (GP). We adapt stochastic volatility modelling to this context, resulting in a stochastic heteroscedastic process (SHP), which is unconditionally stationary and non-Gaussian. Conditional on a latent GP, the SHP is a heteroscedastic GP with non-stationary (in space and time) covariance structure. The realizations from SHP are versatile and can represent spatial inhomogeneities. The unconditional correlation functions of SHP form a rich isotropic class that can allow for a smoothed nugget effect. We apply an importance sampling strategy to implement pseudo maximum likelihood parameter estimation for the SHP. To predict the process at unobserved locations, we develop a plug-in best predictor. We extend the single-realization SHP model to handle replicates across time of SHP realizations in space. Empirical results with simulated data show that SHP is nearly as efficient as a stationary GP in out-of-sample prediction when the true process is a stationary GP, and outperforms a stationary GP substantially when the true process is SHP. The SHP methodology is applied to enhanced vegetation index data and US NO3 deposition data for illustration.

The cube method proposed by Deville and Tille (2004) enables the selection of balanced samples: that is, samples such that the Horvitz–Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is maintained, and a “landing phase” in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tille (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulation-based method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. We formalize this problem as a linear model and propose the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. Spatially dependent errors are accounted for using generalized least squares and spatial smoothness in selected coefficients is incorporated through use of a priori spatial covariance structure. This leads to a modification of the Lasso procedure, called spatial Lasso. The spatial Lasso can be implemented by a fast algorithm and it performs well in numerical examples, including an applicat...

We consider hierarchical regression models for circular data using the projected normal distribution, applied in the development of weights for the Access Point Angler Intercept Survey, a recreational angling survey conducted by the US National Marine Fisheries Service. Weighted estimates of recreational fish catch are used in stock assessments and fisheries regulation. The construction of the survey weights requires the distribution of daily departure times of anglers from fishing sites, within spatio-temporal domains subdivided by the mode of fishing. Because many of these domains have small sample sizes, small area estimation methods are developed. Bayesian inference for the circular distributions on the 24-hour clock is conducted, based on a large set of observed daily departure times from another National Marine Fisheries Service study, the Coastal Household Telephone Survey. A novel variational/Laplace approximation to the posterior distribution allows fast comparison of a large number of models in this context, by dramatically speeding up computations relative to the fast Markov Chain Monte Carlo method while giving virtually identical results.

Motivated by the problem of detecting spatial autocorrelation in increment- averaged data from soil core samples, we use the Cholesky decomposition of the inverse of an autocovariance matrix to derive a parametric linear regression model for autocovariances. In the absence of autocorrelation, the off-diagonal terms in the lower triangular matrix from the Cholesky decomposition should be identically zero, and so the regression coefficients should be identically zero. The standard F-test of this hypothesis and two bootstrapped versions of the test are evaluated as autocorrelation diagnostics via simulation. Size is assessed for a variety of heteroskedastic null hypotheses. Power is evaluated against autocorrelated alternatives, including increment-averaged Ornstein-Uhlenbeck and Matern processes. The bootstrapped tests maintain approximately the correct size and have good power against moderately autocorrelated alternatives. The methods are applied to data from a study of carbon sequestration in agricultural soils.

Adoption of conservation tillage practice in agriculture offers the potential to mitigate greenhouse gas emissions. Studies comparing conservation tillage methods to traditional tillage pair fields under the two management systems and obtain soil core samples from each treatment. Cores are divided into multiple increments, and matching increments from one or more cores are aggregated and analyzed for carbon stock. These data represent not the actual value at a specific depth, but rather the total or average over a depth increment. A semiparametric mixed model is developed for such increment-averaged data. The model uses parametric fixed effects to represent covariate effects, random effects to capture correlation within studies, and an integrated smooth function to describe effects of depth. The depth function is specified as an additive model, estimated with penalized splines using standard mixed model software. Smoothing parameters are automatically selected using restricted maximum likelihood. The meth...

It is common in practice to estimate the quantiles of a complicated distribution by using the order statistics of a simulated sample. If the distribution of interest has known population mean, then it is often possible to improve the mean square error of the standard quantile estimator substantially through the simple device of mean-correction: subtract off the sample mean and add on the known population mean. Asymptotic results for the meancorrected quantile estimator are derived and compared to the standard sample quantile. Simulation results for a variety of distributions and processes illustrate the asymptotic theory. Application to Markov chain Monte Carlo and to simulation-based uncertainty analysis is described.

A new sampling-based Bayesian approach for fractionally integrated autoregressive moving average (ARFIMA) processes is presented. A particular type of ARMA process is used as an approximation for the ARFIMA in a Metropolis–Hastings algorithm, and then importance sampling is used to adjust for the approximation error. This algorithm is relatively time-efficient because of fast convergence in the sampling procedures and fewer computations than competitors. Its frequentist properties are investigated through a simulation study. The performance of the posterior means is quite comparable to that of the maximum likelihood estimators for small samples, but the algorithm can be extended easily to a variety of related processes, including ARFIMA plus short-memory noise. The methodology is illustrated using the Nile River data. Copyright © 2003 John Wiley & Sons, Ltd.

Post-straticatio n is used to improve the precision of survey estimators when categorical auxiliary information is available from external sources. In natu- ral resource surveys, such information may be obtained from remote sensing data classied into categories and displayed as maps. These maps may be based on clas- sication models tted to the sample data. Such \endogenous post-straticatio n" violates the standard assumptions that observations are classied without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-straticatio n estimator (EPSE) are derived for the case of sample-tted nonparametric models, with particular emphasis on monotone regres- sion models. Asymptotic properties of the nonparametric EPSE are investigated under a superpopulation model framework. Simulation experiments illustrate the practical eects of rst tting a nonparametric model to survey data before post- stratifying.

We consider bootstrap construction and calibration of prediction intervals for nonGaussian autoregressions. In particular, we address the question of prediction conditioned on the last p observations of the process, for which we offer an exact simulation technique and an approximate bootstrap approach. In simulations for a variety of first-order autoregressions, we compare various nonparametric prediction intervals and find that calibration gives reasonably narrow prediction intervals with the lowest coverage probability mean squared error among the methods used.

Post-stratification is frequently used to improve the precision of survey estimators when categorical auxiliary information is available from sources outside the survey. In natural resource surveys, such information is often obtained from remote sensing data, classified into categories and displayed as pixel-based maps. These maps may be constructed based on classification models fitted to the sample data. Post-stratification of the sample data based on categories derived from the sample data (``endogenous post-stratification'') violates the standard post-stratification assumptions that observations are classified without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-stratification estimator are derived for the case of a sample-fitted generalized linear model, from which the post-strata are constructed by dividing the range of the model predictions into predetermined intervals. Design consistency of the endogenous post-stratification estimator is established under mild conditions. Under a superpopulation model, consistency and asymptotic normality of the endogenous post-stratification estimator are established, showing that it has the same asymptotic variance as the traditional post-stratified estimator with fixed strata. Simulation experiments demonstrate that the practical effect of first fitting a model to the survey data before post-stratifying is small, even for relatively small sample sizes., Comment: Published in at http://dx.doi.org/10.1214/009053607000000703 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram., Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005], Comment: Published in at http://dx.doi.org/10.1214/088342307000000195 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Multiphase surveys are often conducted in forest inventories, with the goal of estimating forested area and tree characteristics over large regions. This article describes how design-based estimation of such quantities, based on information gathered during ground visits of sampled plots, can be made more precise by incorporating auxiliary information available from remote sensing. The relationship between the ground visit measurements and the remote sensing variables is modeled using generalized additive models. Nonparametric estimators for these models are discussed and applied to forest data collected in the mountains of northern Utah. Model-assisted estimators that use the nonparametric regression fits are proposed for these data. The design context of this study is two-phase systematic sampling from a spatial continuum, under which properties of model-assisted estimators are derived. Difficulties with the standard variance estimation approach, which assumes simple random sampling in each phase, are de...

An autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the case of Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, which can be used even if the underlying noise is not Laplacian. Asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions. Behavior of the estimators in finite samples is studied via simulation. The methodology is applied to exchange rate returns to show that linear all-pass models can mimic “nonlinear” behavior, and is applied to stock market volume data to illustrate a two-step procedure for fitting noncausal autoregressions.

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are considerably weaker. The estimators are shown to be asymptotically design-unbiased and consistent under mild assumptions. A variance approximation based on Taylor linearization is suggested and shown to be consistent for the design mean squared error of the estimators. The estimators are robust in the sense of asymptotically attaining the Godambe–Joshi lower bound to the anticipated variance. Simulation experiments indicate that the estimators are more efficient than regression estimators when the model regression function is incorrectly specified, while being approximately as efficient when the parametric specification is correct.

We discuss a maximum likelihood procedure for estimating parameters in possibly noncausal autoregressive processes driven by i.i.d. non-Gaussian noise. Under appropriate conditions, estimates of the parameters that are solutions to the likelihood equations exist and are asymptotically normal. The estimation procedure is illustrated with a simulation study for AR(2) processes.