Assessing isotropy for spatial point processes

A common assumption while analyzing spatial point processes is direction invariance, i.e., isotropy. In this article, we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive an L(2) consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a chi(2) limiting distribution. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.     

The genetical bandwidth mapping: a spatial and graphical representation of population genetic structure based on the Wombling method

Characterizing the spatial variation of allele frequencies in a population has a wide range of applications in population genetics. This article introduces a new nonparametric method, which provides a two-dimensional representation of a structural parameter called the genetical bandwidth, which describes genetic structure around arbitrary spatial locations in a study area. This parameter corresponds to the shortest distance to areas of significant allele variation, and its computation is based on the Womble's systemic function. A simulation study and application to data sets taken from the literature give evidence that the method is particularly demonstrative when the fine-scale structure is stronger than the large-scale structure, and that it is generally able to locate genetic boundaries or clines precisely.     

Kriging with nonparametric variance function estimation

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.     

Nonparametric estimation of a multivariate distribution in the presence of censoring

This paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right-censored. A distinction is made between what we term 'homogeneous' and 'heterogeneous' censoring. It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function. A closed-form solution, similar to the product-limit estimate of Kaplan and Meier, is possible with homogeneous censoring, but an iterative method, such as the EM algorithm, is required with heterogeneous censoring. An example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables; this anomaly is shown to disappear if the methods of this paper are used.     

Inference for clustered inhomogeneous spatial point processes

Summary .  We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K -function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures.     

Estimating the intensity of a spatial point process from locations coarsened by incomplete geocoding

Summary .   The estimation of spatial intensity is an important inference problem in spatial epidemiologic studies. A standard data assimilation component of these studies is the assignment of a geocode, that is, point-level spatial coordinates, to the address of each subject in the study population. Unfortunately, when geocoding is performed by the standard automated method of street-segment matching to a georeferenced road file and subsequent interpolation, it is rarely completely successful. Typically, 10–30% of the addresses in the study population, and even higher percentages in particular subgroups, fail to geocode, potentially leading to a selection bias, called geographic bias, and an inefficient analysis. Missing-data methods could be considered for analyzing such data; however, because there is almost always some geographic information coarser than a point (e.g., a Zip code) observed for the addresses that fail to geocode, a coarsened-data analysis is more appropriate. This article develops methodology for estimating spatial intensity from coarsened geocoded data. Both nonparametric (kernel smoothing) and likelihood-based estimation procedures are considered. Substantial improvements in the estimation quality of coarsened-data analyses relative to analyses of only the observations that geocode are demonstrated via simulation and an example from a rural health study in Iowa.     

Estimating incident population distribution from prevalent data

A prevalent sample consists of individuals who have experienced disease incidence but not failure event at the sampling time. We discuss methods for estimating the distribution function of a random vector defined at baseline for an incident disease population when data are collected by prevalent sampling. Prevalent sampling design is often more focused and economical than incident study design for studying the survival distribution of a diseased population, but prevalent samples are biased by design. Subjects with longer survival time are more likely to be included in a prevalent cohort, and other baseline variables of interests that are correlated with survival time are also subject to sampling bias induced by the prevalent sampling scheme. Without recognition of the bias, applying empirical distribution function to estimate the population distribution of baseline variables can lead to serious bias. In this article, nonparametric and semiparametric methods are developed for distribution estimation of baseline variables using prevalent data.     

A Computer Programme Package for the Statistical Analysis of Spatial Point Processes in a Square

A computer programme for the statistical analysis of point data in a square is described. Several tests for randomness of the distribution of points are possible. The most comprehensive of these are comparisons of the empirical distributions of the inter-point and closest neighbour distances with their respective expected distributions under complete randomness, and tests based on Ripley' L function; using these, significant aggregation or regularity can be identified. It is also possible to calculate statistics of properties (“attributes”) associated with each spatial point, as well as to compare statistics for sub-areas of the experimental square. Several measures of spatial autocorrelation are available, amongst them correlograms and variograms. The programme can also find the tesselation of the study area and correlate tile properties with the point attributes. The procedures are illustrated by references to the spatial distribution and mound heights of Trinevitermes trinervoides on a study area in South Africa. Although the programme was developed specifically for application in entomology, it could be used to analyse data from many other disciplines.     

Bayesian nonparametric analysis of restricted mean survival time

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.     

Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis

Summary .  In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose–response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose–response analysis.     

Ponasterone A: a new ecdysteroid from the embryos and serum of brachyuran crustaceans

The apolar ecdysteroid present in the developing embryo of the blue crab, Callinectes sapidus Rathbun, is tentatively identified as ponasterone A (2 beta, 14 alpha, 20,22-pentahydroxy-5, beta-cholest-7-en-6-one) on the basis of chromatographic, immunological, and mass spectral evidence. The apolar ecdysteroid present in the serum of land crabs, Gecarcinus lateralis, in the late premolt stages of the intermolt cycle is also tentatively identified as ponasterone A on the basis of chromatographic and immunological evidence.     

Targeted maximum likelihood estimation of the parameter of a marginal structural model

Targeted maximum likelihood estimation is a versatile tool for estimating parameters in semiparametric and nonparametric models. We work through an example applying targeted maximum likelihood methodology to estimate the parameter of a marginal structural model. In the case we consider, we show how this can be easily done by clever use of standard statistical software. We point out differences between targeted maximum likelihood estimation and other approaches (including estimating function based methods). The application we consider is to estimate the effect of adherence to antiretroviral medications on virologic failure in HIV positive individuals.     

Smoothness selection for penalized quantile regression splines

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods.     

Confidence Limits for the Onset and Duration of Treatment Effect

Studies of biological variables such as those based on blood chemistry often have measurements taken over time at closely spaced intervals for groups of individuals. Natural scientific questions may then relate to the first time that the underlying population curve crosses a threshold (onset) and to how long it stays above the threshold (duration). In this paper we give general confidence regions for these population quantities. The regions are based on the intersection-union principle and may be applied to totally nonparametric, semiparametric, or fully parametric models where level-α tests exist pointwise at each time point. A key advantage of the approach is that no modeling of the correlation over time is required.     

Linking small desert mammal distribution to habitat structure in a protected and grazed landscape of the Monte, Argentina

Interpretation of landscape patterns from the perspective of different species allows knowing the way in which they perceive landscape, and how their perception varies with scale. We examined distribution of four small mammal species at different scales over a landscape including protected and grazed areas, and associated species distribution with landscape structure. The study was conducted in the central Monte Desert (Reserve of Ñacuñán). Trap grids were set in both areas at two scales, varying their grain and extent. To determine whether spatial patterns are random, clumped or regular, we used a point pattern analysis. Logistic regressions were performed to relate the presence-absence of small mammals to environmental variables. Intensity of the point pattern was not constant, either in the Reserve or the grazed area. Small mammal abundance exhibited a heterogeneous distribution, and the existence of a first-order effect was detected for all species. No second-order effects were detected, the point pattern was random for all species in both areas. Both areas were differently perceived by rodent species. Habitat structure in both conditions and its variations with scale appear to be important factors affecting distribution patterns.     

Efficient Monte Carlo method for simulation of fluctuating conformations of native proteins

A powerful Monte Carlo method is described to simulate thermal conformational fluctuations in native proteins by using an empirical conformational energy function in which bond lengths and bond angles are kept fixed and only dihedral angles are independent variables. In this method, collective variables corresponding to eigenvectors of the second-derivative matrix of the energy function at its minimum point are scaled according to corresponding eigenvalues in such a way that the energy function in terms of the scaled collective variables is isotropic at the minimum point. Simulation is carried out with an isotropic step size in the space of these scaled collective variables. This simulation method is applied to a small protein, bovine pancreatic trypsin inhibitor (BPTI), and its model harmonic system defined by a quadratic energy function with the same second-derivative matrix as that of BPTI at its minimum point. Efficiency of the simulation method with an isotropic step size in the space of the scaled collective variables is found to be about 500–50 times greater than the conventional method with with an isotropic step in the space of the usual nonscaled variables. One step of this new method generates conformational changes that occur in the real-time range of 0.05 ps. In a record of 5 × 10⁵ step simulation, the BPTI molecule is observed to migrate beyond a single minimum-energy region.     

Causality and persistence in ecological systems: a nonparametric spectral granger causality approach

Abstract Directionality in coupling, defined as the linkage relating causes to their effects at a later time, can be used to explain the core dynamics of ecological systems by untangling direct and feedback relationships between the different components of the systems. Inferring causality from measured ecological variables sampled through time remains a formidable challenge further made difficult by the action of periodic drivers overlapping the natural dynamics of the system. Periodicity in the drivers can often mask the self-sustained oscillations originating from the autonomous dynamics. While linear and direct causal relationships are commonly addressed in the time domain, using the well-established machinery of Granger causality (G-causality), the presence of periodic forcing requires frequency-based statistics (e.g., the Fourier transform), able to distinguish coupling induced by oscillations in external drivers from genuine endogenous interactions. Recent nonparametric spectral extensions of G-causality to the frequency domain pave the way for the scale-by-scale decomposition of causality, which can improve our ability to link oscillatory behaviors of ecological networks to causal mechanisms. The performance of both spectral G-causality and its conditional extension for multivariate systems is explored in quantifying causal interactions within ecological networks. Through two case studies involving synthetic and actual time series, it is demonstrated that conditional G-causality outperforms standard G-causality in identifying causal links and their concomitant timescales.     

Early Warnings of Regime Shift When the Ecosystem Structure Is Unknown

Abrupt changes in dynamics of an ecosystem can sometimes be detected using monitoring data. Using nonparametric methods that assume minimal knowledge of the underlying structure, we compute separate estimates of the drift (deterministic) and diffusion (stochastic) components of a general dynamical process, as well as an indicator of the conditional variance. Theory and simulations show that nonparametric conditional variance rises prior to critical transition. Nonparametric diffusion rises also, in cases where the true diffusion function involves a critical transition (sometimes called a noise-induced transition). Thus it is possible to discriminate noise-induced transitions from other kinds of critical transitions by comparing time series for the conditional variance and the diffusion function. Monte Carlo analysis shows that the indicators generally increase prior to the transition, but uncertainties of the indicators become large as the ecosystem approaches the transition point.     

A Finding of the Crab Planes marinus Rathbun, 1914 (Decapoda: Grapsidae) in Peter the Great Bay,Sea of Japan

A crab Planes marinus Rathbun, 1914 was found on a drifting buoy in Peter the Great Bay (Sea of Japan). The crab probably arrived in the bay with subtropical waters penetrating into this area during the summer period.     

Bayesian lasso for semiparametric structural equation models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model.