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Roots anchor plants in soil, and the failure of anchorage (i.e. root lodging) is a major cause of crop yield loss. Anchorage is often assumed to be driven by root system architecture (RSA). We made use of a natural experiment to measure the overlap between the genetic regulation of RSA and anchorage. After one of the most devastating derechos ever recorded in August 2020, we phenotyped root lodging in a maize (Zea mays) diversity panel consisting of 369 genotypes grown in 6 environments affected by the derecho. Genome-wide and transcriptome-wide association studies identified 118 candidate genes associated with root lodging. Thirty-four percent (40/118) of these were homologs of genes from Arabidopsis (Arabidopsis thaliana) that affect traits such as root morphology and lignin content, expected to affect root lodging. Finally, gene ontology enrichment analysis of the candidate genes and their predicted interaction partners at the transcriptional and translational levels revealed the complex regulatory networks of physiological and biochemical pathways underlying root lodging in maize. Limited overlap between genes associated with lodging resistance and RSA in this diversity panel suggests that anchorage depends in part on factors other than the gross characteristics of RSA.

In the United States, the official database of severe thunderstorm wind reports arguably has more serious deficiencies than those of tornadoes and hail. Roughly 90% of the thunderstorm wind reports in the Storm Events database during the period 2007-2021 are estimates without any nearby measurement, and the fact that 40% of the estimates have a value of exactly 50 knots compared to only 13% of the measurements strongly suggests that many may be overestimates since 50 knots is the minimum threshold to be considered a severe wind. The problems in the database negatively impact development of new forecasting tools and verification. We have tested six different machine learning approaches, training on roughly 20,000 measured reports during 2007-2017 to create a tool that assigns a probability that any severe thunderstorm wind report is due to winds of 50 knots or greater. Training is based on date, time, location, and episode and event narrative data from the Storm Events database along with 31 near-storm weather parameters from the Storm Prediction Center mesoanalysis output. In addition, population density and elevation are used. Land use and radar reflectivity were also tested but found to not improve the performance. The best-performing algorithm, the Stacked Generalized Linear Model has been found to show large skill with Areas Under ROC curves as high as .90 and Brier Scores around 0.1. When a supplemental sub-severe database is added for testing, reliability is shown to be good. Subjective evaluations from testing during three years of NOAA Hazardous Weather Testbed Spring Forecast Experiments have been favorable and will be discussed, along with implications for forecasters. A recent test found that the average probability for estimated 50 knot wind reports is only 57% whereas it is 81% for measured 50 knot reports, supporting the view of many forecasters that overestimates are a large problem among the estimated reports in the database.

Personalized synthetic MRI (syn-MRI) uses MR images of an individual subject acquired at a few design parameters (echo time, repetition time, flip angle) to obtain underlying parametricOur DL enhancements employ a Deep Image Prior (DIP) with a U-net type denoising architecture that includes situations with minimal training data, such as personalized syn-MRI. We provide a general workflow for syn-MRI from three or more training images. Our workflow, called DIPsyn-MRI, uses DIP to enhance training images, then obtains parametric images using LS or MLE before synthesizing images at desired design parameter settings. DIPsyn-MRI is implemented in our publicly available Python package DeepSynMRI available at: https://github.com/StatPal/DeepSynMRI.We demonstrate feasibility and improved performance of DIPsyn-MRI on 3D datasets acquired using the Brainweb interface for spin-echo and FLASH imaging sequences, at different noise levels. Our DL enhancements improve syn-MRI in the presence of different intensity nonuniformity levels of the magnetic field, for all but very low noise levels.This article provides recipes and software to realistically facilitate DL-enhanced personalized syn-MRI.

The symbiotic relationship between soybean [Glycine max L. (Merr.)] roots and bacteria (Bradyrhizobium japonicum) lead to the development of nodules, important legume root structures where atmospheric nitrogen (N2) is fixed into bio-available ammonia (NH3) for plant growth and development. With the recent development of the Soybean Nodule Acquisition Pipeline (SNAP), nodules can more easily be quantified and evaluated for genetic diversity and growth patterns across unique soybean root system architectures. We explored six diverse soybean genotypes across three field year combinations in three early vegetative stages of development and report the unique relationships between soybean nodules in the taproot and non-taproot growth zones of diverse root system architectures of these genotypes. We found unique growth patterns in the nodules of taproots showing genotypic differences in how nodules grew in count, size, and total nodule area per genotype compared to non-taproot nodules. We propose that nodulation should be defined as a function of both nodule count and individual nodule area resulting in a total nodule area per root or growth regions of the root. We also report on the relationships between the nodules and total nitrogen in the seed at maturity, finding a strong correlation between the taproot nodules and final seed nitrogen at maturity. The applications of these findings could lead to an enhanced understanding of the plant-Bradyrhizobium relationship, and exploring these relationships could lead to leveraging greater nitrogen use efficiency and nodulation carbon to nitrogen production efficiency across the soybean germplasm.Core IdeasThe growth and development of soybean nodules on the taproot and non-taproots have unique growth and development patterns.In general, taproot nodules increase in area, while non-taproot nodules increase in count and area.Nodulation should be defined by the total nodule area as a function of both nodule count and individual nodule size.Genotypes adjust their nodulation through either increasing nodule count or nodule size to increase the total nodule area per root between each growth stage.There is a strong correlation between early growth stage taproot nodules and final seed nitrogen content.

HighlightsA calibration procedure was conducted using a Kinect V2 to convert image pixels to physical measurements.A total of 61 sows were observed, and their static and dynamic space usage was measured from depth images.Equations were developed to predict the length, width, and height of sow space usage.Abstract. The amount of space provided to individually housed sows has both financial and animal welfare implications. Many U.S. swine producers use stall dimensions based on recommendations published in the 1980s (length × width × height: 2.13 m × 0.61 m × 1.00 m). Limited empirical data are available concerning the space allocation needed to accommodate modern sows housed in stalls during breeding, gestation, or farrowing. This study used a time-of-flight depth sensor to quantify static and dynamic space usage of 61 modern sows in late gestation. A calibration equation was developed to convert image pixels to physical dimensions. Statistical models were developed to relate the length, width, and height of sow space usage to body weight. The dimensions of sow space usage were then predicted. Results showed that free choice space usage of average (228 kg) sows was 1.96 m × 1.15 m × 0.93 m (length × width × height). For 95th percentile (267 kg) sows, space usage was 2.04 m × 1.12 m × 0.95 m. The width of space usage was primarily attributed to sow body depth when lying recumbent and the dynamic space used for transitioning between postures. These results help to inform future gestating and farrowing sow housing designs. Further work is needed to understand how restrictions on sow space usage may impact sow welfare and production performance, as well as the space needed to perform behaviors such as defecating, feeding, and turning around. Keywords: Animal welfare, Computer vision, Farrowing stall, Gestation stall, Kinect V2, Space allowance.

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators and a control group., Comment: 10 pages, 5 figures, 4 tables

This large-scale field study evaluated the effects farrowing stall environment on piglet productivity and behavior. Three farrowing stall layouts were tested (T – traditional, C – expanded creep area, S – expanded sow area) in conjunction with one or two heat lamps (1HL or 2HL). Production data were collected on the number of piglets live at birth, percent stillborn, percent preweaning piglet mortality, percent over-lay (crushing), number of piglets weaned, average daily weight gain, and litter uniformity. The only productivity difference found was in percent stillborn (p = 0.045); however, it was of small magnitude and not of practical significance. Piglet behavior data were collected and processed with a custom imaging system. Each farrowing stall was divided into three regions: heated region directly below the heat lamp (Rheated), unheated regions of the creep (Rcreep), and sow stall region (Rsow). The proportion of piglets within each farrowing stall region were analyzed and compared on select days of lactation. Piglets in the 2HL treatment spent a significantly greater amount of time in Rheated compared to the 1Hl treatment (p

Background: Chronic environmental exposure to manganese (Mn) can cause debilitating damage to the central nervous system. However, its potential toxic effects on the enteric nervous system (ENS) have yet to be assessed. Objective: We examined the effect of Mn on the ENS using both cell and animal models. Method: Rat enteric glial cells (EGCs) and mouse primary enteric cultures were exposed to increasing concentrations of Mn and cell viability and mitochondrial health were assessed using various morphological and functional assays. C57BL/6 mice were exposed daily to a sublethal dose of Mn (15mg/kg/d) for 30 d. Gut peristalsis, enteric inflammation, gut microbiome profile, and fecal metabolite composition were assessed at the end of exposure. Results: EGC mitochondria were highly susceptible to Mn neurotoxicity, as evidenced by lower mitochondrial mass, adenosine triphosphate–linked respiration, and aconitase activity as well as higher mitochondrial superoxide, upon Mn exposure. Minor differences were seen in the mouse model: specifically, longer intestinal transit times and higher levels of colonic inflammation. Conclusion: Based on our findings from this study, Mn preferentially induced mitochondrial dysfunction in a rat EGC line and in vivo resulted in inflammation in the ENS. https://doi.org/10.1289/EHP7877

Fractional Gaussian fields provide a rich class of spatial models and have a long history of applications in multiple branches of science. However, estimation and inference for fractional Gaussian fields present significant challenges. This book chapter investigates the use of the fractional Laplacian differencing on regular lattices to approximate to continuum fractional Gaussian fields. Emphasis is given on model based geostatistics and likelihood based computations. For a certain range of the fractional parameter, we demonstrate that there is considerable agreement between the continuum models and their lattice approximations. For that range, the parameter estimates and inferences about the continuum fractional Gaussian fields can be derived from the lattice approximations. Interestingly, regular lattice approximations facilitate fast matrix-free computations and enable anisotropic representations. We illustrate the usefulness of lattice approximations via simulation studies and by analyzing sea-surface temperature on the Indian Ocean.

Prion diseases are transmissible spongiform encephalopathies (TSEs) characterized by fatal, progressive neurologic diseases with prolonged incubation periods and an accumulation of infectious misfolded prion proteins. Antemortem diagnosis is often difficult due to a long asymptomatic incubation period, differences in the pathogenesis of different prions, and the presence of very low levels of infectious prion in easily accessible samples. Chronic wasting disease (CWD) is a TSE affecting both wild and captive populations of cervids, including mule deer, white-tailed deer, elk, moose, muntjac, and most recently, wild reindeer. This study represents a well-controlled evaluation of a newly developed real-time quaking-induced conversion (RT-QuIC) assay as a potential CWD diagnostic screening test using rectal biopsy sections from a depopulated elk herd. We evaluated 69 blinded samples of recto-anal mucosa-associated lymphoid tissue (RAMALT) obtained from USDA Veterinary Services. The results were later un-blinded and statistically compared to immunohistochemical (IHC) results from the USDA National Veterinary Services Laboratories (NVSL) for RAMALT, obex, and medial retropharyngeal lymph node (MRPLN). Comparison of RAMALT RT-QuIC assay results with the IHC results of RAMALT revealed 92% relative sensitivity (95% confidence limits: 61.52–99.8%) and 95% relative specificity (95% confidence limits: 85.13–99%). Collectively, our results show a potential utility of the RT-QuIC assay to advance the development of a rapid, sensitive, and specific prion diagnostic assay for CWD prions.

Gastrointestinal (GI) disturbances are one of the earliest symptoms affecting most patients with Parkinson’s disease (PD). In many cases, these symptoms are observed years before motor impairments become apparent. Hence, the molecular and cellular underpinnings that contribute to this early GI dysfunction in PD have actively been explored using a relevant animal model. The MitoPark model is a chronic, progressive mouse model recapitulating several key pathophysiological aspects of PD. However, GI dysfunction and gut microbiome changes have not been categorized in this model. Herein, we show that decreased GI motility was one of the first non-motor symptoms to develop, evident as early as 8 weeks with significantly different transit times from 12 weeks onwards. These symptoms were observed well before motor symptoms developed, thereby paralleling PD progression in humans. At age 24 weeks, we observed increased colon transit time and reduced fecal water content, indicative of constipation. Intestinal inflammation was evidenced with increased expression of iNOS and TNFα in the small and large intestine. Specifically, iNOS was observed mainly in the enteric plexi, indicating enteric glial cell activation. A pronounced loss of tyrosine hydroxylase-positive neurons occurred at 24 weeks both in the mid-brain region as well as the gut, leading to a corresponding decrease in dopamine (DA) production. We also observed decreased DARPP-32 expression in the colon, validating the loss of DAergic neurons in the gut. However, the total number of enteric neurons did not significantly differ between the two groups. Metabolomic gas chromatography-mass spectrometry analysis of fecal samples showed increased sterol, glycerol, and tocopherol production in MitoPark mice compared to age-matched littermate controls at 20 weeks of age while 16 s microbiome sequencing showed a transient temporal increase in the genus Prevotella. Altogether, the data shed more light on the role of the gut dopaminergic system in maintaining intestinal health. Importantly, this model recapitulates the chronology and development of GI dysfunction along with other non-motor symptoms and can become an attractive translational animal model for pre-clinical assessment of the efficacy of new anti-Parkinsonian drugs that can alleviate GI dysfunction in PD.

Farrowing stalls are used in the United States swine industry to reduce pre-weaning piglet mortality, enable efficient individual animal management, and decrease facility construction and operating costs. The quantity and quality of space provided for sows and piglets in farrowing stalls are important economic and welfare considerations. To further explore the impacts of farrowing stall space allocation, a large-scale field study was conducted to compare sow and piglet behavior when housed in three farrowing stall layouts (TSL – traditional stall layout, ECSL – expanded creep area stall layout, ESCSL – expanded sow and creep area stall layout) with either one or two heat lamps (1HL and 2HL, respectively). A computer vision system classified posture budgets and behaviors of 322 sows and piglet location for 324 litters. Linear mixed models were developed to compare behavior and piglet pre-weaning mortality metrics between experimental treatments. Results show sows in ESCSL spent more time lying compared to sows in ECSL (p = 0.028) and less time sitting compared to sows in TSL and ECSL (p 0.05). Results can guide producers to consider wider sow areas in farrowing stalls to better meet sow behavioral needs and to include larger heated areas to meet piglet behavioral needs during lactation.

Despite the important roles of microorganisms in soil organic matter (SOM) decomposition and nutrient cycling, how their biomass, community composition and function are driven by a joint effect of edaphic and environmental factors at a large spatial scale remains unclear. Moreover, a mechanistic understanding of the associations among microbial communities and SOM chemistry as a key indicator of substrate availability over large spatial scales has been lacking until now. To fill this knowledge gap, we examined how soil microbial community abundance and composition (via phospholipid fatty acid (PLFA) analysis) and function (via enzyme activities and net N mineralization) were associated with the edaphic and environmental factors from six oriental oak (Quercus variabilis) forest sites arranged across a 11° latitudinal gradient in East China. We found strong relationships between SOM chemistry as indicated by 13C nuclear magnetic resonance (NMR) spectroscopy and microbial community composition and function along this gradient. For example, the ratio of fungi to bacteria (F/B) decreased with increasing carboxyl C percentage; the lower abundance of arbuscular mycorrhizal fungi (AMF) and decreased invertase activity in the southern sites were possibly related to higher ratio of alkyl to O alkyl (A/O); urease activity increased with carboxyl C percentage. Microbial biomass (total PLFAs) had positive relationships with urease activity, net N mineralization rate, and soil pH. Mean annual precipitation (MAP) and pH were important for overall microbial community composition. Overall, our results indicate that SOM chemistry is closely related to microbial community composition and function along the latitudinal gradient and should be considered in future studies. Our study contributes to a better prediction of microbial responses to possible substrate changes brought by future environmental changes, which is urgently needed under the context of accelerating global change.

Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the items are ranked. In this paper we analyze rank data using a purely probabilistic model where the observed ranks are assumed to be perturbed versions of the true rank and each perturbation has a specific probability of occurring. We consider the general case when covariate information is present and has an impact on the rankings. An empirical Bayes approach is taken for estimating the model parameters. The Gibbs sampler is shown to converge very slowly to the target posterior distribution and we show that some of the widely used empirical convergence diagnostic tools may fail to detect this lack of convergence. We propose a novel, fast mixing sandwich algorithm for exploring the posterior distribution. An EM algorithm based on Markov chain Monte Carlo (MCMC) sampling is developed for estimating prior hyperparameters. A real life rank data set is analyzed using the methods developed in the paper. The results obtained indicate the usefulness of these methods in analyzing rank data with covariate information.

We discuss a numerical algorithm for calculating a large class of analytically intractable theoretical variogram functions that arise in studies of random fields on regular lattices. Examples of these random fields include conditional and intrinsic autoregressions, fractional Laplacian differenced random fields, and regular block averages of continuum random fields. Typically, the variogram functions for these random fields appear in the form of multi-dimensional integrals, often with singularities at the origin, and the algorithm laid out to evaluate these integrals invoke certain quadrature rules and regression formulas based on the asymptotic expansions of these integrals. This is so that singularities at the origin can be accounted for in a straightforward manner. This numerical algorithm opens new avenues to advancing geostatistical data analysis, solving kriging and estimation problems and exploring properties for various lattice-based random fields. The usefulness of this numerical method is illustrated by fitting certain theoretical variogram functions to ocean color and the Walker Lake data. Copyright © 2016 John Wiley & Sons, Ltd.

This paper discusses models for circular responses with a spike at zero. Maximum likelihood estimation for the underlying parameters and a test for checking a spike are also carried out. Simulations and a real data example are considered for illustrations.

Grain yield progress over 50 years of spring wheat breeding at the International Maize and Wheat Improvement Center (CIMMYT) was determined in field trials conducted during five crop seasons (2013–2017) at Norman E. Borlaug research station near Ciudad Obregon, Mexico. The trials included 30 varieties (24 bread wheat and 6 durum wheat) released between 1965–2014 and were sown under managed optimum, drought, and heat stress conditions. The optimum irrigated environment had 3 management systems, flat sowing with weekly drip irrigation (FDI), bed sowing with flood irrigation (BFI), and flat sowing with flood irrigation (FFI). The drought environment had 2 management systems, flat sowing with reduced irrigation (FRI) and flat sowing under severe drought stress (FSD). The heat stress environment was sown in beds (HFI) three months later than the normally sown irrigated and drought environments. The rate of grain yield progress was estimated relative to Sonalika released in 1965 and Mexicali C75 released in 1975 for bread and durum wheat, respectively. Grain yield progress per year for bread wheat was, 31.2 kg ha−1, 35.3 kg ha−1, and 24.7 kg ha−1 in irrigated environments FDI, BFI, and FFI, respectively. In the stress environments, bread wheat grain yield progress was estimated as 25.6 kg ha−1, 17.7 kg ha−1, and 18.1 kg ha−1 per year in FRI, FSD, and HFI, respectively. For durum wheat, the grain yield progress was estimated as 29.6 kg ha−1, 48.1 kg ha−1, 18.8 kg ha−1, and 29.8 kg ha−1, per year in FDI, BFI, FFI, and HFI, respectively. Trait linkage graph analysis using LASSO regularized graphical model estimated that biomass, harvest index, and grains per meter square (GNM) were linked to grain yield progress in all environments. Thousand kernel weight was associated with grain yield progress under optimum and heat stress conditions, whereas grain weight per tiller (GWT) associated with progress under drought. Results also show that the highest yielding varieties in each environment however, had different trait attributes, with some varieties having higher GNM and tillers per meter square compensating for low GWT, while others had high GWT to compensate for reduced GNM. In conclusion, CIMMYT’s wheat breeding program has continued to show progress in grain yield in different environments/management systems, and while certain traits have consistently improved over the years, the varieties developed have employed different trait strategies to achieve final grain yield.

This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genomic prediction, spatial effects often affect phenotypic measurements of plants. We consider a Gaussian random field model with an additive covariance structure that incorporates genotype effects, spatial effects and subpopulation effects. An empirical study shows the existence of spatial effects and heterogeneity across different subpopulation families, while simulations illustrate the improvement in selecting genotypically superior plants by adjusting for spatial effects in genomic prediction., Comment: 22 pages, 6 figures, 10 tables

Summary We consider sparse spatial mixed linear models, particularly those described by Besag and Higdon, and develop an h-likelihood method for their statistical inference. The method proposed allows for singular precision matrices, as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model. Furthermore, we generalize the h-likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between Gaussian intrinsic Markov random fields on regular arrays and the de Wijs process. Keeping various applications of spatial mixed linear models in mind, we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix-free statistical computations. We provide two applications. The first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation. The second application concerns an analysis of a large cotton field which gives a focus to matrix-free computations. The paper closes with some further considerations, such as applications to irregularly spaced data, use of the parametric bootstrap and some generalizations to the Gaussian Matérn mixed effect models.

Response-adaptive designs are used in phase III clinical trials to allocate a larger proportion of patients to the better treatment. Circular data is a natural outcome in many clinical trial setup, e.g., some measurements in opthalmologic studies, degrees of rotation of hand or waist, etc. There is no available work on response-adaptive designs for circular data. With reference to a dataset on cataract surgery we provide some response-adaptive designs where the responses are of circular nature and propose some test statistics for treatment comparison under adaptive data allocation procedure. Detailed simulation study and the analysis of the dataset, including redesigning the cataract surgery data, are carried out.

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based Markov chain Monte Carlo (TMCMC). One of the remarkable advantages of our proposal is that even if the underlying target distribution is very high-dimensional, deterministic transformation of a one-dimensional random variable is sufficient to generate an appropriate Markov chain that is guaranteed to converge to the high-dimensional target distribution. Apart from clearly leading to massive computational savings, this idea of deterministically transforming a single random variable very generally leads to excellent acceptance rates, even though all the random variables associated with the high-dimensional target distribution are updated in a single block. Since it is well-known that joint updating of many random variables using Metropolis-Hastings (MH) algorithm generally leads to poor acceptance rates, TMCMC, in this regard, seems to provide a significant advance. We validate our proposal theoretically, establishing the convergence properties. Furthermore, we show that TMCMC can be very effectively adopted for simulating from doubly intractable distributions. TMCMC is compared with MH using the well-known Challenger data, demonstrating the effectiveness of of the former in the case of highly correlated variables. Moreover, we apply our methodology to a challenging posterior simulation problem associated with the geostatistical model of Diggle et al. (1998), updating 160 unknown parameters jointly, using a deterministic transformation of a one-dimensional random variable. Remarkable computational savings as well as good convergence properties and acceptance rates are the results., 28 pages, 3 figures; Longer abstract inside article

Independence screening methods such as the two sample $t$-test and the marginal correlation based ranking are among the most widely used techniques for variable selection in ultrahigh dimensional data sets. In this short note, simple examples are used to demonstrate potential problems with the independence screening methods in the presence of correlated predictors. Also, an example is considered where all important variables are independent among themselves and all but one important variables are independent with the unimportant variables. Furthermore, a real data example from a genome wide association study is used to illustrate inferior performance of marginal correlation screening compared to another screening method.

Testing of various classes of life distributions has been a subject of investigation for more than four decades. In this study, we restrict ourselves to the problem of testing exponentiality (which essentially means no aging) against positive aging, which is captured by the class of increasing failure rate alternatives. Recent tests are discussed and compared. The empirical size of the tests is obtained by simulation. Power computations, using simulations, are done for each test procedure. These comparisons are done both for small and large sample sizes. Suggestions are made regarding the choice of the test when a particular alternative is suspected.

We present a new matrix-free residual maximum likelihood (REML) analysis for irregularly spaced spatial data, where observations usually represent average values over very small regions that are interpreted as points. The REML analysis is obtained after embedding the sampling locations in a fine scale rectangular lattice, treating unobserved sites as missing data. The spatial random fields considered here are based on fractional Laplacian differencing on the lattice and they are unique in approximating continuum intrinsic Matern dependence. Here, using the h-likelihood method, we derive REML estimating equations that allow for singular precision matrices, estimation of covariate effects, prediction of unobserved spatial effects and REML estimation of precision parameters as a solution to an explicit gamma non-linear model. Furthermore, we devise a sophisticated computational algorithm that enables us to achieve scalable matrix-free statistical computations. In particular, these matrix-free computations include the use of (1) the two-dimensional discrete cosine transformation that arises in the spectral decomposition of the precision matrix of our spatial random fields and that allows fast matrix-free matrix-vector multiplication, (2) a matrix-free pre-conditioned Lanczos algorithm that solves non-sparse matrix equations with linear constraints, (3) a matrix-free Hutchinson’s trace estimator that stochastically approximates the trace of a matrix, (4) a robust trust region method that always finds a local maximum of the non-concave residual log-likelihood function and (5) some preliminary computations of the log REML likelihood function based on Taylor series approximation. Using computer experiments, we provide further understanding on not just the number and values but also the basins of attraction of the local and global maxima of the REML function. This understanding significantly simplifies the problem of finding global maxima. We further demonstrate through computer experiments that our matrix-free REML estimators attain both efficiency and geostatistical inference, and surpass the widely used INLA methods in computational times. We provide an extensive application on mapping ground water arsenic concentration in Bangladesh, indicating numeric consistency of results and robustness of inference to changes of lattice spacing. The paper closes with some discussions that include computations in the stationary case, conditional simulations and matrix-free MCMC computations.

Circular data are a natural outcome in many biomedical studies, e.g. some measurements in ophthalmologic studies, degrees of rotation of hand or waist, etc. With reference to a real data set on astigmatism induced in two types of cataract surgeries we carry out some two-sample testing problems with the possibility of common or different concentration parameters in the circular set up. Detailed simulation study and the analysis of the data set, including redesigning the cataract surgery data, are carried out.

In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov chain Monte Carlo literature. The associated kernel is shown to have standard properties like irreducibility, aperiodicity and Harris recurrence under some mild assumptions. These ensure basic convergence (ergodicity) of the kernel. Further the kernel is shown to be geometric ergodic for a large class of target densities on $\mathbb{R}$. This class even contains realistic target densities for which random walk or Langevin MH are not geometrically ergodic. Three simulation studies are given to demonstrate the mixing property and superiority of RDMH to standard MH algorithms on real line. A share-price return data is also analyzed and the results are compared with those available in the literature.