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Nitrogen (N) loss through ammonia $$({\mathrm{NH}}_{3})$$ volatilization in agricultural soils is a significant source of atmospheric $${\mathrm{NH}}_{3}$$ , contributing to low N use efficiency in crops, risk to human health, environmental pollution, and is an indirect source of nitrous oxide $$({\mathrm{N}}_{2}\mathrm{O})$$ emissions. Our objective was to develop an ammonia volatilization method within the DayCent ecosystem model that incorporates key 4R N management practices (right type, right rate, right placement, and right timing) that influence $${\mathrm{NH}}_{3}$$ volatilization associated with application of urea-based nitrogen fertilizers to agricultural soils. The $${\mathrm{NH}}_{3}$$ volatilization method was developed with Bayesian calibration using sampling importance resampling methods and Bayes factors to select the level of complexity in the model that best represents $${\mathrm{NH}}_{3}$$ volatilization given the observed data. The final model included urea hydrolysis and the influence of urease inhibitors; short-term soil pH changes following fertilization; fertilizer incorporation into the soil (mechanically and through irrigation/precipitation); and specification of the fertilizer placement method (i.e. broadcast vs. banding and surface vs incorporated). DayCent predicts $${\mathrm{NH}}_{3}$$ volatilization with a root-mean-squared error of 158 (95% interval ranging from 133 to 192), bias of 7 (95% interval ranging from − 106 to 102) g NH3-N ha−1 day−1, and with a Bayesian R2 value of 0.39 (95% interval ranging from 0.17 to 0.62). Furthermore, the model incorporates key management options influencing $${\mathrm{NH}}_{3}$$ volatilization related to placement method and fertilizer type with and without urease inhibitors that can be used to evaluate management and policy options for reducing losses of NH3 from urea fertilization.

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.

Marine recreational fishing from shore and from private boats in Hawaiʻi is monitored via the Hawaiʻi Marine Recreational Fishing Survey (HMRFS), using an access point intercept survey to collect catch rate information, and the Coastal Household Telephone Survey (CHTS) to collect fishing effort data. In response to a recent HMRFS review, roving surveys of shoreline fishing effort and catch rate, an aerial fishing effort survey, and a mail survey of fishing effort were tested simultaneously on one of the main Hawaiian Islands (Oʻahu) and compared with the current HMRFS approach for producing shoreline fishing estimates. The pilot roving surveys were stratified by region (rural vs urban), shift (three 4-h periods during the day), and day type (weekday vs weekend). A pilot access point survey of private boat fishing was also conducted on Oʻahu, using an alternate sampling design created by NOAA Fisheries’ Marine Recreational Information Program (MRIP). Three overlapping 6-h time blocks and site clusters with unequal inclusion probabilities were used to cover daytime fishing. Group catch was recorded for an entire vessel rather than individual catch, which is the current standard for MRIP intercept surveys. Although catch estimates from the pilot private boat survey were comparable to the current HMRFS catch estimates, the catch estimates from the pilot roving survey were lower than the HMRFS estimates. HMRFS uses effort data from the CHTS, which includes both day and night fishing in all areas, to estimate total catch, whereas effort data from the roving shoreline survey covered only daytime fishing from publicly accessible areas. We therefore suggest that a roving survey conducted during the day should have complementary surveys to include night fishing and fishing in remote and private/restricted areas. Results from these pilot studies will be used to improve the current surveys of marine recreational fishing activities in Hawaiʻi.

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...

Benefits of carbon sequestration in agricultural soils are well recognized, and process-based models have been developed to better understand sequestration potential. However, most studies ignore the uncertainty arising during model prediction—a critical requirement for scientific understanding, policy implementation and carbon emission trading. Furthermore, the dependencies created in process-based models due to many parameters and a relatively small set of empirical data hinder parameterization. We have implemented a Bayesian approach using the sampling importance resampling (SIR) method to calibrate the DayCent ecosystem model for estimating soil organic carbon (SOC) stocks, and to quantify uncertainty in model predictions. A SOC dataset compiled from 19 long-term field experiments, representing 117 combinations of management treatments, with 491 measurements of SOC, was split into independent datasets for model calibration and evaluation. The most important DayCent model parameters were identified through a global sensitivity analysis (GSA) for parameterization and SIR was used to calibrate the model and produce posterior distributions for the most sensitive parameters. On average, the Bayesian calibration reduced the model uncertainty by a factor of 6.6 relative to the uncertainty associated with the prior. The Bayesian model analysis framework will allow for ongoing updates to the model as new datasets and model structural improvements are made in future research, and overall provide a stronger basis for models to support policy and management decisions associated with GHG mitigation through C sequestration in agricultural soils.

International audience; Inference for the parametric distribution of a response given covariates is considered under informative selection of a sample from a finite population. Under this selection, the conditional distribution of a response in the sample, given the covariates and given that it was selected for observation, is not the same as the conditional distribution of the response in the finite population, given only the covariates. It is instead a weighted version of the conditional distribution of interest. Inference must be modified to account for this informative selection. An established approach in this context is maximum “sample likelihood”, developing a weight function that reflects the informative sampling design, then treating the observations as if they were independently distributed according to the weighted distribution. While the sample likelihood methodology has been widely applied, its theoretical foundation has been less developed. A precise asymptotic description of a wide range of informative selection mechanisms is proposed. Under this framework, consistency and asymptotic normality of the maximum sample likelihood estimators are established. The theory allows for the possibility of nuisance parameters that describe the selection mechanism. The proposed regularity conditions are verifiable for various sample schemes, motivated by real problems in surveys. Simulation results for these examples illustrate the quality of the asymptotic approximations, and demonstrate a practical approach to variance estimation that combines aspects of model-based information theory and design-based variance estimation.

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.

The general projected normal distribution is a simple and intuitive model for directional data in any dimension: a multivariate normal random vector divided by its length is the projection of that vector onto the surface of the unit hypersphere. Observed data consist of the projections, but not the lengths. Inference for this model has been restricted to the two-dimensional (circular) case, using Bayesian methods with data augmentation to generate the latent lengths and a Metropolis-within-Gibbs algorithm to sample from the posterior. We describe a new parameterization of the general projected normal distribution that makes inference in any dimension tractable, including the important three-dimensional (spherical) case, which has not previously been considered. Under this new parameterization, the full conditionals of the unknown parameters have closed forms, and we propose a new slice sampler to draw the latent lengths without the need for rejection. Gibbs sampling with this new scheme is fast and easy, leading to improved Bayesian inference; for example, it is now feasible to conduct model selection among complex mixture and regression models for large data sets. Our parameterization also allows straightforward incorporation of covariates into the covariance matrix of the multivariate normal, increasing the ability of the model to explain directional data as a function of independent regressors. Circular and spherical cases are considered in detail and illustrated with scientific applications. For the circular case, seasonal variation in time-of-day departures of anglers from recreational fishing sites is modeled using covariates in both the mean vector and covariance matrix. For the spherical case, we consider paired angles that describe the relative positions of carbon atoms along the backbone chain of a protein. We fit mixtures of general projected normals to these data, with the best-fitting mixture accurately describing biologically meaningful structures including helices, $\beta$ -sheets, and coils and turns. Finally, we show via simulation that our methodology has satisfactory performance in some 10-dimensional and 50-dimensional problems.

Kernel density estimation of the probability density function (pdf) of a response variable is considered under informative selection from a finite population. The informative selection implies that the conditional pdf of a response, given that it was selected for observation, is not the same as the inferential target, which is the unconditional pdf of the response in the superpopulation. Instead, the pdf of the observations (sample pdf) is a weighted version of the superpopulation pdf of interest. Properties of the standard kernel density estimator are described under an asymptotic framework that covers a wide range of informative selection mechanisms. The theory allows for the possibility that the selection mechanism has a parametric structure. A variety of adjustments (parametric or nonparametric) to account for the informative selection are proposed, and investigated via simulation.

Understanding sensitive behaviors-those that are socially unacceptable or non-compliant with rules or regulations-is essential for creating effective interventions. Sensitive behaviors are challenging to study, because participants are unlikely to disclose sensitive behaviors for fear of retribution or due to social undesirability. Methods for studying sensitive behavior include randomized response techniques, which provide anonymity to interviewees who answer sensitive questions. A variation on this approach, the quantitative randomized response technique (QRRT), allows researchers to estimate the frequency or quantity of sensitive behaviors. However, to date no studies have used QRRT to identify potential drivers of non-compliant behavior because regression methodology has not been developed for the nonnegative count data produced by QRRT. We develop a Poisson regression methodology for QRRT data, based on maximum likelihood estimation computed via the expectation-maximization (EM) algorithm. The methodology can be implemented with relatively minor modification of existing software for generalized linear models. We derive the Fisher information matrix in this setting and use it to obtain the asymptotic variance-covariance matrix of the regression parameter estimates. Simulation results demonstrate the quality of the asymptotic approximations. The method is illustrated with a case study examining potential drivers of non-compliance with hunting regulations in Sierra Leone. The new methodology allows assessment of the importance of potential drivers of different quantities of non-compliant behavior, using a likelihood-based, information-theoretic approach. Free, open-source software is provided to support QRRT regression.

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.

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.

Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the superpopulation model. The selection is informative in the sense that the sample responses, given that they were selected, are not i.i.d. f. In general, the informative selection mechanism may induce dependence among the selected observations. The impact of such dependence on the empirical cumulative distribution function (c.d.f.) is studied. An asymptotic framework and weak conditions on the informative selection mechanism are developed under which the (unweighted) empirical c.d.f. converges uniformly, in $L_2$ and almost surely, to a weighted version of the superpopulation c.d.f. This yields an analogue of the Glivenko-Cantelli theorem. A series of examples, motivated by real problems in surveys and other observational studies, shows that the conditions are verifiable for specified designs., Published in at http://dx.doi.org/10.3150/11-BEJ369 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

The first-order moving average model or MA(1) is given by $X_t=Z_t-\theta_0Z_{t-1}$, with independent and identically distributed $\{Z_t\}$. This is arguably the simplest time series model that one can write down. The MA(1) with unit root ($\theta_0=1$) arises naturally in a variety of time series applications. For example, if an underlying time series consists of a linear trend plus white noise errors, then the differenced series is an MA(1) with unit root. In such cases, testing for a unit root of the differenced series is equivalent to testing the adequacy of the trend plus noise model. The unit root problem also arises naturally in a signal plus noise model in which the signal is modeled as a random walk. The differenced series follows a MA(1) model and has a unit root if and only if the random walk signal is in fact a constant. The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root case and nearly unit root case ($\theta=1+\beta/n,\beta\le0$). Unlike standard $1/\sqrt{n}$-asymptotics, these estimation procedures have $1/n$-asymptotics and a so-called pile-up effect, in which P$(\hat{\theta}=1)$ converges to a positive value. One explanation for this pile-up phenomenon is the lack of identifiability of $\theta$ in the Gaussian case. That is, the Gaussian likelihood has the same value for the two sets of parameter values $(\theta,\sigma^2)$ and $(1/\theta,\theta^2\sigma^2$). It follows that $\theta=1$ is always a critical point of the likelihood function. In contrast, for non-Gaussian noise, $\theta$ is identifiable for all real values. Hence it is no longer clear whether or not the same pile-up phenomenon will persist in the non-Gaussian case. In this paper, we focus on limiting pile-up probabilities for estimates of $\theta_0$ based on a Laplace likelihood. In some cases, these estimates can be viewed as Least Absolute Deviation (LAD) estimates. Simulation results illustrate the limit theory., Comment: Published at http://dx.doi.org/10.1214/074921706000000923 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)