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A novel approach for estimating densities of secretive species from road-survey and spatial-movement data
Accurate estimates of population density are a critical component of effective wildlife conservation and management. However, many snake species are so secretive that their density cannot be determined using traditional methods such as capture–mark–recapture. Thus, the status of most terrestrial snake populations remains completely unknown. We developed a novel simulation-based technique for estimating density of secretive snakes that combined behavioural observations of snake road-crossing behaviour (crossing speed), effort-corrected road-survey data, and simulations of spatial movement patterns derived from radio-telemetry, without relying on mark–recapture. Here, we used radio-telemetry data to parameterise individual-based movement models that estimate the frequency with which individual snakes cross roads and used information on survey vehicle speed and snake crossing speed to determine the probability of detecting a snake, given that it crosses the road transect during a survey. Snake encounter frequencies during systematic road surveys were then interpreted in light of detection probabilities and simulation model results to estimate snake densities and to assess various factors likely to affect abundance estimates. We demonstrated the broad applicability of this approach through a case study of the imperiled southern hognose snake (Heterodon simus) in the North Carolina (USA) Sandhills. We estimated that H. simus occurs at average densities of 0.17 ha –1 in the North Carolina Sandhills and explored the sensitivity of this estimate to assumptions and variation in model parameters. Our novel method allowed us to generate the first abundance estimates for H. simus. We found that H. simus exists at low densities relative to congeners and other mid-sized snake species, raising concern that this species may not only have declined in geographic range, but may also occur at low densities or be declining in their strongholds, such as the North Carolina Sandhills. We present a framework for estimating density of species that have traditionally been considered too secretive to study at the population level. This method will greatly enhance our ability to study and manage a wide variety of snake species and could be applied to other secretive wildlife species that are most frequently encountered during road surveys.
Automated fibroglandular tissue segmentation and volumetric density estimation in breast MRI using an atlas-aided fuzzy C-means method
Purpose: Breast magnetic resonance imaging (MRI) plays an important role in the clinical management of breast cancer. Studies suggest that the relative amount of fibroglandular (i.e., dense) tissue in the breast as quantified in MR images can be predictive of the risk for developing breast cancer, especially for high-risk women. Automated segmentation of the fibroglandular tissue and volumetric density estimation in breast MRI could therefore be useful for breast cancer risk assessment. Methods: In this work the authors develop and validate a fully automated segmentation algorithm, namely, an atlas-aided fuzzy C-means (FCM-Atlas) method, to estimate the volumetric amount of fibroglandular tissue in breast MRI. The FCM-Atlas is a 2D segmentation method working on a slice-by-slice basis. FCM clustering is first applied to the intensity space of each 2D MR slice to produce an initial voxelwise likelihood map of fibroglandular tissue. Then a prior learned fibroglandular tissue likelihood atlas is incorporated to refine the initial FCM likelihood map to achieve enhanced segmentation, from which the absolute volume of the fibroglandular tissue (|FGT|) and the relative amount (i.e., percentage) of the |FGT| relative to the whole breast volume (FGT%) are computed. The authors' method is evaluated by a representative dataset of 60 3D bilateral breast MRI scans (120 breasts) that span the full breast density range of the American College of Radiology Breast Imaging Reporting and Data System. The automated segmentation is compared to manual segmentation obtained by two experienced breast imaging radiologists. Segmentation performance is assessed by linear regression, Pearson's correlation coefficients, Student's pairedt-test, and Dice's similarity coefficients (DSC). Results: The inter-reader correlation is 0.97 for FGT% and 0.95 for |FGT|. When compared to the average of the two readers’ manual segmentation, the proposed FCM-Atlas method achieves a correlation ofr = 0.92 for FGT% and r = 0.93 for |FGT|, and the automated segmentation is not statistically significantly different (p = 0.46 for FGT% and p = 0.55 for |FGT|). The bilateral correlation between left breasts and right breasts for the FGT% is 0.94, 0.92, and 0.95 for reader 1, reader 2, and the FCM-Atlas, respectively; likewise, for the |FGT|, it is 0.92, 0.92, and 0.93, respectively. For the spatial segmentation agreement, the automated algorithm achieves a DSC of 0.69 ± 0.1 when compared to reader 1 and 0.61 ± 0.1 for reader 2, respectively, while the DSC between the two readers’ manual segmentation is 0.67 ± 0.15. Additional robustness analysis shows that the segmentation performance of the authors' method is stable both with respect to selecting different cases and to varying the number of cases needed to construct the prior probability atlas. The authors' results also show that the proposed FCM-Atlas method outperforms the commonly used two-cluster FCM-alone method. The authors' method runs at ∼5 min for each 3D bilateral MR scan (56 slices) for computing the FGT% and |FGT|, compared to ∼55 min needed for manual segmentation for the same purpose. Conclusions: The authors' method achieves robust segmentation and can serve as an efficient tool for processing large clinical datasets for quantifying the fibroglandular tissue content in breast MRI. It holds a great potential to support clinical applications in the future including breast cancer risk assessment.
Minimum local distance density estimation
We present a local density estimator based on first-order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to define the density estimate at $x$. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.
UNVEILING THE NATURE OF THE UNIDENTIFIED GAMMA-RAY SOURCES. V. ANALYSIS OF THE RADIO CANDIDATES WITH THE KERNEL DENSITY ESTIMATION
Nearly one-third of the γ-ray sources detected by Fermi are still unidentified, despite significant recent progress in this area. However, all of the γ-ray extragalactic sources associated in the second Fermi-LAT catalog have a radio counterpart. Motivated by this observational evidence, we investigate all the radio sources of the major radio surveys that lie within the positional uncertainty region of the unidentified γ-ray sources (UGSs) at a 95% level of confidence. First, we search for their infrared counterparts in the all-sky survey performed by the Wide-field Infrared Survey Explorer (WISE) and then we analyze their IR colors in comparison with those of the known γ-ray blazars. We propose a new approach, on the basis of a two-dimensional kernel density estimation technique in the single [3.4] – [4.6] – [12] μm WISE color-color plot, replacing the constraint imposed in our previous investigations on the detection at 22 μm of each potential IR counterpart of the UGSs with associated radio emission. The main goal of this analysis is to find distant γ-ray blazar candidates that, being too faint at 22 μm, are not detected by WISE and thus are not selected by our purely IR-based methods. We find 55 UGSs that likely correspond to radio sources with blazar-like IR signatures. An additional 11 UGSs that have blazar-like IR colors have been found within the sample of sources found with deep recent Australia Telescope Compact Array observations.
Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators: Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators
Forecasts of available wind power are critical in key electric power systems operations planning problems, including economic dispatch and unit commitment. Such forecasts are necessarily uncertain, limiting the reliability and cost effectiveness of operations planning models based on a single deterministic or “point” forecast. A common approach to address this limitation involves the use of a number of probabilistic scenarios, each specifying a possible trajectory of wind power production, with associated probability. We present and analyze a novel method for generating probabilistic wind power scenarios, leveraging available historical information in the form of forecasted and corresponding observed wind power time series. We estimate non-parametric forecast error densities, specifically using epi-spline basis functions, allowing us to capture the skewed and non-parametric nature of error densities observed in real-world data. We then describe a method to generate probabilistic scenarios from these basis functions that allows users to control for the degree to which extreme errors are captured.We compare the performance of our approach to the current state-of-the-art considering publicly available data associated with the Bonneville Power Administration, analyzing aggregate production of a number of wind farms over a large geographic region. Finally, we discuss the advantages of our approach in the context of specific power systems operations planning problems: stochastic unit commitment and economic dispatch. Here, our methodology is embodied in the joint Sandia – University of California Davis Prescient software package for assessing and analyzing stochastic operations strategies.
Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities
Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.
eFESTA: Ensemble Feature Exploration with Surface Density Estimates
We propose surface density estimate (SDE) to model the spatial distribution of surface features-isosurfaces, ridge surfaces, and streamsurfaces-in 3D ensemble simulation data. The inputs of SDE computation are surface features represented as polygon meshes, and no field datasets are required (e.g., scalar fields or vector fields). The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.
Kernel Density Estimation (KDE) with adaptive bandwidth selection for environmental contours of extreme sea states.
Abstract not provided.
Regularized Differentiation for Bioburden Density Estimation in Planetary Protection
In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.
DENSITY ESTIMATION FOR PROJECTED EXOPLANET QUANTITIES
Exoplanet searches using radial velocity (RV) and microlensing (ML) produce samples of 'projected' mass and orbital radius, respectively. We present a new method for estimating the probability density distribution (density) of the unprojected quantity from such samples. For a sample of n data values, the method involves solving n simultaneous linear equations to determine the weights of delta functions for the raw, unsmoothed density of the unprojected quantity that cause the associated cumulative distribution function (CDF) of the projected quantity to exactly reproduce the empirical CDF of the sample at the locations of the n data values. We smooth the raw density using nonparametric kernel density estimation with a normal kernel of bandwidth {sigma}. We calibrate the dependence of {sigma} on n by Monte Carlo experiments performed on samples drawn from a theoretical density, in which the integrated square error is minimized. We scale this calibration to the ranges of real RV samples using the Normal Reference Rule. The resolution and amplitude accuracy of the estimated density improve with n. For typical RV and ML samples, we expect the fractional noise at the PDF peak to be approximately 80 n{sup -log2}. For illustrations, we apply the new method to 67 RV values given a similar treatment by Jorissen et al. in 2001, and to the 308 RV values listed at exoplanets.org on 2010 October 20. In addition to analyzing observational results, our methods can be used to develop measurement requirements-particularly on the minimum sample size n-for future programs, such as the microlensing survey of Earth-like exoplanets recommended by the Astro 2010 committee.
Raccoon density estimation from camera traps for raccoon rabies management
Abstract Density estimation for unmarked animals is particularly challenging, yet density estimates are often necessary for effective wildlife management. Raccoons ( Procyon lotor ) are the primary terrestrial wildlife reservoir for Lyssavirus rabies within the United States. The raccoon rabies variant (RRVV) is actively managed at landscape scales using oral rabies vaccination (ORV) within the eastern United States. To effectively manage RRVV, it is important to know the density of raccoons to appropriately scale the density of ORV baits distributed on the landscape. We compared methods to estimate raccoon densities from camera‐trap data versus more intensive capture‐mark‐recapture (CMR) estimates across 2 land cover types (upland pine and bottomland hardwood) in the southeastern United States during 2019 and 2020. We evaluated the effect of alternative camera configurations and durations of camera trapping on density estimates and used an N‐mixture model to estimate raccoon densities, including covariates on abundance and detection. We further compared different methods of scaling camera‐based counts, with the maximum number of raccoons seen on any given image within a day best explaining density. Camera‐trap density estimates were moderately correlated with CMR estimates ( r = 0.56). However, densities from camera‐trap data were more reliable when classifying category of density as an index used to inform management (83% correct when compared to CMR estimates), although the densities in our study fell into the 2 lowest density classes only. Using more cameras reduced bias and uncertainty around density estimates; however, if ≤6 camera traps were used at a site, a line transect approach proved less biased than a grid design. Camera trapping should be conducted for at least 3 weeks for more accurate estimates of raccoon population density in our study area (<5% bias). We show that camera‐trap data can be used to assign raccoon densities to management‐relevant density index bins, but more studies are needed to ensure reliability across a greater range of environmental conditions and raccoon densities.
GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations
Kernel Density Estimators (KDEs) are a non-parametric density estimation technique that has recently been applied to Monte Carlo radiation transport simulations. Kernel density estimators are an alternative to histogram tallies for obtaining global solutions in Monte Carlo tallies. With KDEs, a single event, either a collision or particle track, can contribute to the score at multiple tally points with the uncertainty at those points being independent of the desired resolution of the solution. Thus, KDEs show potential for obtaining estimates of a global solution with reduced variance when compared to a histogram. Previously, KDEs have been applied to neutronics for one-group reactor physics problems and fixed source shielding applications. However, little work was done to obtain reaction rates using KDEs. This paper introduces a new form of the MFP KDE that is capable of handling general geometries. Furthermore, extending the MFP KDE to 2-D problems in continuous energy introduces inaccuracies to the solution. An ad-hoc solution to these inaccuracies is introduced that produces errors smaller than 4% at material interfaces.
Technical Note: Cortical thickness and density estimation from clinical CT using a prior thickness-density relationship
Purpose: Cortical thickness and density are critical components in determining the strength of bony structures. Computed tomography (CT) is one possible modality for analyzing the cortex in 3D. In this paper, a model-based approach for measuring the cortical bone thickness and density from clinical CT images is proposed. Methods: Density variations across the cortex were modeled as a function of the cortical thickness and density, location of the cortex, density of surrounding tissues, and imaging blur. High resolution micro-CT data of cadaver proximal femurs were analyzed to determine a relationship between cortical thickness and density. This thickness-density relationship was used as prior information to be incorporated in the model to obtain accurate measurements of cortical thickness and density from clinical CT volumes. The method was validated using micro-CT scans of 23 cadaver proximal femurs. Simulated clinical CT images with different voxel sizes were generated from the micro-CT data. Cortical thickness and density were estimated from the simulated images using the proposed method and compared with measurements obtained using the micro-CT images to evaluate the effect of voxel size on the accuracy of the method. Then, 19 of the 23 specimens were imaged using a clinical CT scanner. Cortical thickness and density were estimated from the clinical CT images using the proposed method and compared with the micro-CT measurements. Finally, a case-control study including 20 patients with osteoporosis and 20 age-matched controls with normal bone density was performed to evaluate the proposed method in a clinical context. Results: Cortical thickness (density) estimation errors were 0.07 ± 0.19 mm (−18 ± 92 mg/cm{sup 3}) using the simulated clinical CT volumes with the smallest voxel size (0.33 × 0.33 × 0.5 mm{sup 3}), and 0.10 ± 0.24 mm (−10 ± 115 mg/cm{sup 3}) using the volumes with the largest voxel size (1.0 × 1.0 × 3.0 mm{sup 3}). A trend for the cortical thickness and density estimation errors to increase with voxel size was observed and was more pronounced for thin cortices. Using clinical CT data for 19 of the 23 samples, mean errors of 0.18 ± 0.24 mm for the cortical thickness and 15 ± 106 mg/cm{sup 3} for the density were found. The case-control study showed that osteoporotic patients had a thinner cortex and a lower cortical density, with average differences of −0.8 mm and −58.6 mg/cm{sup 3} at the proximal femur in comparison with age-matched controls (p-value < 0.001). Conclusions: This method might be a promising approach for the quantification of cortical bone thickness and density using clinical routine imaging techniques. Future work will concentrate on investigating how this approach can improve the estimation of mechanical strength of bony structures, the prevention of fracture, and the management of osteoporosis.
Uncertainty Quantification Techniques for Population Density Estimates Derived from Sparse Open Source Data
The Population Density Tables (PDT) project at the Oak Ridge National Laboratory (www.ornl.gov) is developing population density estimates for specific human activities under normal patterns of life based largely on information available in open source. Currently, activity based density estimates are based on simple summary data statistics such as range and mean. Researchers are interested in improving activity estimation and uncertainty quantification by adopting a Bayesian framework that considers both data and sociocultural knowledge. Under a Bayesian approach knowledge about population density may be encoded through the process of expert elicitation. Due to the scale of the PDT effort which considers over 250 countries, spans 40 human activity categories, and includes numerous contributors, an elicitation tool is required that can be operationalized within an enterprise data collection and reporting system. Such a method would ideally require that the contributor have minimal statistical knowledge, require minimal input by a statistician or facilitator, consider human difficulties in expressing qualitative knowledge in a quantitative setting, and provide methods by which the contributor can appraise whether their understanding and associated uncertainty was well captured. This paper introduces an algorithm that transforms answers to simple, non-statistical questions into a bivariate Gaussian distribution as the prior for the Beta distribution. Based on geometric properties of the Beta distribution parameter feasibility space and the bivariate Gaussian distribution, an automated method for encoding is developed that responds to these challenging enterprise requirements. Though created within the context of population density, this approach may be applicable to a wide array of problem domains requiring informative priors for the Beta distribution.
Monte Carlo Estimates of Eigenvalue Sensitivity to System Dimensions using Kernel Density Estimators
In the last decade there has been an increasing interest in calculating sensitivity coefficients in order to quantify the impact of uncertainty in material properties and system parameters on quantities of interest. Extensive work has been done developing Monte Carlo methods to estimate eigenvalue sensitivity to material properties. While deterministic methods exist for determining the eigenvalue sensitivity to system dimensions, the use of Monte Carlo methods to efficiently calculate eigenvalue sensitivity coefficients to system dimensions is still an open topic. Current Monte Carlo methods for calculating eigenvalue sensitivity coefficients to system dimensions are inefficient. Direct Monte Carlo perturbations require two additional simulations of high statistical precision in order to determine the eigenvalue sensitivity to the location of a single boundary. If the sensitivity to the location of multiple surfaces are desired, two additional simulations must be run for each surface. Kiedrowski and Favorite extended continuous energy Monte Carlo methods for sensitivities of nuclear cross sections to calculate sensitivities to interface boundaries or system dimensions to create the only current alternative to direct Monte Carlo calculations. However this method relies on the simulation of additional random walks launched at each surface crossing event. The present method extends upon Kiedrowski's work and eliminates the inefficient portions of the calculation through the use of Kernel Density Estimators (KDEs). The new method efficiently estimates eigenvalue sensitivities to the uniform expansion or contraction of material interface boundaries or system dimensions, negligibly impacting the runtime performance of the Monte Carlo code. The new estimator is tested on bare and reflected critical configurations in spherical geometry and is compared to estimates obtained from direct Monte Carlo perturbations.
GPU Acceleration of Kernel Density Estimators in Monte Carlo Neutron Transport Simulations
Kernel Density Estimators (KDEs) have recently been explored for use in Monte Carlo radiation transport simulations as an alternative to histogram tallies for capturing spatially-resolved quantities such as neutron flux and reaction rates. Histogram tallies suffer from large uncertainties when detailed spatial resolution of the quantity of interest is required; increasing the resolution of the underlying mesh increases the uncertainty in each histogram bin. KDEs obtain estimates of underlying densities on user-defined points, with the uncertainty at those points being independent of the spatial resolution desired since collisions and particle-track segments are allowed to contribute to the score at multiple tally points. Thus, KDEs show potential for obtaining estimates of a smoother spatially-resolved with reduced variance when compared to a histogram. However, this ability that enables KDEs to obtain lower uncertainties per particle history is more computationally expensive than using a traditional histogram bins on a structured mesh. While KDEs are capable of producing lower tally uncertainties compared to histogram binning for a given number of histories, their increased computational cost may make them less efficient. Even so, it is possible to reduce this additional cost by exporting the KDE tally routines onto Graphics Processing Units (GPUs). GPUs are commonly found on high-performance computing machines as a means of increasing performance without adding additional compute nodes. While it is difficult for existing Monte Carlo radiation transport codes to take advantage of GPUs without rewriting large portions of the code, it is possible to leverage GPUs through heterogeneous computing. This work uses a modified version of OpenMC and exports the KDE tally routines onto a GPU to obtain problem-dependent speedups ranging between 1.6 and 5.0 for the problem studied in this paper. While this methodology is applied to KDEs, the same ideas can be applied to other computationally expensive vectorizable portions of Monte Carlo algorithms. (authors)
A Non-Parametric Density Estimation Approach to Measuring Beam Cooling in MICE
The goal of the international Muon Ionization Cooling Experiment (MICE) is to demonstrate muon beam ionization cooling for the first time. It constitutes a key part of the R&D towards a future neutrino factory or muon collider. The intended MICE precision requires the development of analysis tools that can account for any effects (e.g., optical aberrations) which may lead to inaccurate cooling measurements. Non-parametric density estimation techniques, in particular, kernel density estimation (KDE), allow very precise calculations of the muon beam phase-space density and its increase as a result of cooling. In this study, kernel density estimation technique and its application to measuring the reduction in MICE muon beam phase-space volume is investigated.