Density Estimation Research Articles

Use of cross-validation Bayes factors to test equality of two densities

We propose a nonparametric, two-sample Bayesian test for checking whether or not two data sets share a common distribution. The test makes use of data splitting ideas and requires only simple priors for the bandwidths of two kernel density estimates. Importantly, it does not require priors for high- or infinite-dimensional parameter vectors, as do other nonparametric Bayesian procedures. We provide evidence that the new procedure leads to more stable Bayes factors than do methods based on Pólya trees. Somewhat surprisingly, the behaviour of the proposed Bayes factors when the two distributions are the same is usually superior to that of Pólya tree Bayes factors. We showcase the effectiveness of the test by proving its consistency, conducting a simulation study and applying the test to Higgs Boson data.

Vertical kinematics of the young Galactic clusters

Abstract The young disc vertical phase is paramount in our understanding of Galaxy evolution. Analysing the vertical kinematics at different galactic regions provides important information about the space-time variations of the Galactic potential. The vertical phase snail-shell structure found after Gaia DR2 release encompasses a wide range of ages. However, the structure of the VZ vs Z diagram appears linear when the analysis is limited to studying objects younger than 30 Ma. Based on the vertical velocity and height-over-disc maps obtained for a sample of young open clusters, this method also allows the matter density in the Solar neighbourhood to be estimated using a completely different approach than previously found in the literature. We use two different catalogues of star clusters to confirm the previous result and study new age ranges. The linear pattern between VZ and Z shows different slopes, ∂VZ/∂Z, for various age groups. The results fit a simple model (harmonic oscillator) of in-plane decoupled vertical dynamics up to a certain age limit, corresponding to ∼ 30 Ma. This work also analyses the relationship between the local volumetric density of matter (ρ0) and the disc vertical kinematics for different age ranges, all below 50 Ma. The best estimates of the effective volumetric mass density in the Solar neighbourhood, 0.09-0.15 M⊙ pc−3, agree with those given by other authors, assessing the reliability of the proposed dynamical model. These values are a minorant of the actual matter density in the region.

ASSESSING COVID-19 SPREAD AND VACCINATION EFFECTIVENESS IN CHAD THROUGH MEAN KERNEL DENSITY ESTIMATION

This study introduces an innovative approach to assess the impact of COVID-19 vaccination on the spread of the virus in Chad by employing mean kernel density (MKD) estimation for non-parametric analysis. Utilizing epidemiological data collected between January 2021 and June 2023, we explore the correlation between vaccination rates and confirmed cases across various regions of Chad. Our analysis demonstrates that the application of MKD provides a smoother and more accurate visualization of infection trends before and after vaccination campaigns. The results reveal a significant reduction in confirmed cases post-vaccination, particularly in areas with higher vaccination rates. Correlation analysis further highlights the effectiveness of vaccination campaigns, showing a strong association between vaccination rates and the decrease in infections. However, the data also suggest a reactive vaccination strategy in regions with initially high infection rates. This innovative application of mean KDE provides new insights into the dynamics of vaccination efforts and their crucial role in reducing the spread of COVID-19 in Chad.

Exploring the role of electrode density in capturing spatiotemporal dynamics of resting-state networks with EEG

Abstract This study investigates the role of electrode density in capturing resting-state brain activity, an area of significant clinical relevance, where electroencephalography (EEG) is favored for its cost-efficiency. We analyze how different electrode configurations affect the precision of cortical current density estimation in EEG recordings. Using exact Low-Resolution Electromagnetic Tomography (eLORETA), we estimated the cortical current density in regions of interest linked to Resting State Networks (RSN). Point process analysis was employed to identify regions of high activity over time, revealing dynamic brain salient activity patterns, or brain maps. We evaluated the impact of electrode density by comparing 64-channel and 20-channel configurations and found that both configurations yielded similar and consistent brain maps. To confirm the robustness of our approach, we assessed the Berger effect in eyes-closed (EC) versus eyes-open (EO) conditions, observing that the functional differences between EC and EO states remained stable regardless of electrode density, aligning with previous research. Conversely, randomization of data or the use of non-homogeneous electrode configurations disrupted the resulting patterns, highlighting the physiological relevance of our methodology. Overall, our results demonstrate that this approach reliably captures the spatiotemporal dynamics of brain activity, even with fewer electrodes, and holds promise for broader clinical applications.

First density estimates of the Endangered Claire's mouse lemur Microcebus mamiratra and recommendations for its conservation

Abstract Mouse lemurs Microcebus spp. are small, nocturnal primates endemic to Madagascar. The genus is extraordinarily diverse, with 25 extant species, several of which have been described recently. The Endangered Claire's mouse lemur Microcebus mamiratra was first described in 2006, but, similarly to other newly described mouse lemurs, remains understudied, and estimates of its population size are unavailable, hampering effective conservation management. We conducted line transect distance sampling surveys of M. mamiratra across several habitat types in and around Lokobe National Park on the island of Nosy Be in north-western Madagascar. Using a systematic random design we surveyed 15 transects over a 6-week period in 2023, recording 92 detections from a total survey effort of 46.5 km. We estimate the density of M. mamiratra on Nosy Be to be 125.1 individuals/km2, which extrapolates to an estimate of c. 4,700 individuals across the forested areas of its range on the island. Our results indicate that Nosy Be harbours moderately high densities of M. mamiratra, with the highest encounter rates in the unprotected secondary and degraded forests around Lokobe National Park. Our population estimate will inform future conservation status assessments and conservation planning for this range-restricted species and provide a baseline for monitoring population changes over time. We present recommendations for the conservation of M. mamiratra and highlight the potential for lemur watching, sustained by the strong tourism industry on Nosy Be, to help protect lemur habitat and generate economic opportunities for local communities.

On the sign changes of 𝜓(𝑥)-𝑥

We improve the lower bound for V ( T ) V(T) , the number of sign changes of the error term ψ ( x ) − x \psi (x)-x in the Prime Number Theorem in the interval [ 1 , T ] [1,T] for large T T . We show that \[ lim inf T → ∞ V ( T ) log ⁡ T ≥ γ 0 π + 1 60 , \liminf _{T\to \infty }\frac {V(T)}{\log T}\geq \frac {\gamma _{0}}{\pi }+\frac {1}{60}, \] where γ 0 = 14.13 … \gamma _{0}=14.13\ldots is the imaginary part of the lowest-lying non-trivial zero of the Riemann zeta-function. The result is based on a new density estimate for zeros of the associated k k -function, over 4 ⋅ 10 21 4\cdot 10^{21} times better than previously known estimates of this type.

Measurement and spatiotemporal evolution characteristics of dietary diversity among Chinese residents

PurposeThe purpose of this paper is to measure the dietary diversity and to analyze the regional characteristics, differences, and evolutionary trends of dietary diversity among Chinese residents.MethodsIn this paper, the dietary diversity among Chinese residents was measured using the Shannon index based on the provincial-level food consumption data from 1995 to 2021. On this basis, the paper employs analysis methods such as kernel density estimation, spatial correlation test, and Dagum’s Gini coefficient to analyze the regional characteristics, differences, and trends of change in dietary diversity.ResultsDuring the study period, the dietary diversity among Chinese residents showed an increasing trend. Among the four major geographic regions, the dietary diversity was highest in the southern region, followed by the northern region, northwest region, and Qinghai-Tibet region. Among the three major economic regions, the dietary diversity was highest in the eastern region, followed by the central region and western region. There was a significant positive spatial correlation in the dietary diversity among Chinese residents, and both high-high agglomeration and low-low agglomeration phenomena were strengthened. In terms of the trend of regional differences, whether overall differences, interregional differences, or intraregional differences, they all showed a shrinking trend. However, interregional differences were the main source of overall differences in dietary diversity among Chinese residents.ConclusionThe dietary diversity among Chinese residents shows an overall increasing trend, and there are regional differences in dietary diversity from the perspectives of economic and geographic regions, which have been narrowing over time.

Estimated baseline density of a spotted hyaena population in a post-war landscape

Abstract The spotted hyaena Crocuta crocuta is relatively understudied across its range despite evidence of widespread declines. It is therefore essential that robust baseline population density assessments are conducted to inform current management and future conservation policy. In Mozambique this is urgent as decades of armed conflict followed by unchecked poaching have resulted in large-scale wildlife declines and extirpations. We conducted the first robust population density estimate for a spotted hyaena population in Mozambique using spatially explicit capture–recapture methodologies. We recorded a relatively low population density of 0.8–2.1 hyaenas/100 km2 in the wildlife management area Coutada 11 in the Zambezi Delta of central Mozambique in 2021. These densities are well below the estimated carrying capacity for the landscape and are comparable to published densities in high human-impact, miombo woodland-dominated and arid environments. The combination of historical armed conflict, marginal trophy hunting and bushmeat poaching using wire snares and gin traps (with physical injuries evident in 9% of identified individuals) presents persistent anthropogenic pressure, limiting the post-war recovery of this resident hyaena population. We provide insights into the dynamics of hyaena population status and recovery in such post-war landscapes, adding to mounting evidence that the species is less resilient to severe anthropogenic disturbances than previously believed. We recommend long-term monitoring of this and other carnivore populations in post-war landscapes to ascertain demographic trends and implement effective conservation interventions for population recovery.

Selective Scale-Aware Network for Traffic Density Estimation and Congestion Detection in ITS

Selective Scale-Aware Network for Traffic Density Estimation and Congestion Detection in ITS

Machine Learning-Based Approaches for Breast Density Estimation from Mammograms: A Comprehensive Review

Breast cancer, as of 2022, is the most prevalent type of cancer in women. Breast density—a measure of the non-fatty tissue in the breast—is a strong risk factor for breast cancer that can be estimated from mammograms. The importance of studying breast density is twofold. First, high breast density can be a factor in lowering mammogram sensitivity, as dense tissue can mask tumors. Second, higher breast density is associated with an increased risk of breast cancer, making accurate assessments vital. This paper presents a comprehensive review of the mammographic density estimation literature, with an emphasis on machine-learning-based approaches. The approaches reviewed can be classified as visual, software-, machine learning-, and segmentation-based. Machine learning methods can be further broken down into two categories: traditional machine learning and deep learning approaches. The most commonly utilized models are support vector machines (SVMs) and convolutional neural networks (CNNs), with classification accuracies ranging from 76.70% to 98.75%. Major limitations of the current works include subjectivity and cost-inefficiency. Future work can focus on addressing these limitations, potentially through the use of unsupervised segmentation and state-of-the-art deep learning models such as transformers. By addressing the current limitations, future research can pave the way for more reliable breast density estimation methods, ultimately improving early detection and diagnosis.

Ecological Efficiency Evaluation and Development Trend Prediction of Marine Aquaculture Industry: A Case Study of Weihai City, China

The marine aquaculture industry holds a significant position in the development of Weihai City’s fishing industry, with its ecological efficiency having a direct impact on the sustainable progress of the regional fishing sector. Utilizing a three-stage DEA model as an unexpected output model, this study systematically assessed the ecological efficiency of Weihai City’s marine aquaculture industry. By employing kernel density estimation, we analyzed the temporal dynamic evolution of ecological efficiency within the marine aquaculture industry. The results indicate that the overall ecological efficiency of marine aquaculture in Weihai City has improved to some extent, influenced by environmental factors such as government support, urbanization level, and regional economic development level. After removing environmental and random factors, it was found that the overall ecological efficiency of the marine aquaculture industry in Weihai City shows a more stable upward trend. Furthermore, using a gray dynamic model, GM (1, 1), we predicted the trend of ecological efficiency in the marine aquaculture industry. The findings indicate that, with the progressive adoption of advanced aquaculture technologies, the ecological efficiency of Weihai City’s marine aquaculture is anticipated to continue growing in the future. However, the pace of growth has decelerated. To maximize ecological efficiency, it is imperative to optimize resource allocation, foster technological innovation, and elevate awareness regarding ecological and environmental preservation. By assessing the ecological efficiency of Weihai City’s marine aquaculture industry, this article aims to shed light on the industry’s progress, thereby promoting its high-quality and sustainable development.

Causal Discovery and Reasoning for Continuous Variables with an Improved Bayesian Network Constructed by Locality Sensitive Hashing and Kernel Density Estimation

The structure learning of a Bayesian network (BN) is a crucial process that aims to unravel the complex dependencies relationships among variables using a given dataset. This paper proposes a new BN structure learning method for data with continuous attribute values. As a non-parametric distribution-free method, kernel density estimation (KDE) is applied in the conditional independence (CI) test. The skeleton of the BN is constructed utilizing the test based on mutual information and conditional mutual information, delineating potential relational connections between parents and children without imposing any distributional assumptions. In the searching stage of BN structure learning, the causal relationships between variables are achieved by using the conditional entropy scoring function and hill-climbing strategy. To further enhance the computational efficiency of our method, we incorporate a locality sensitive hashing (LSH) function into the KDE process. The method speeds up the calculations of KDE while maintaining the precision of the estimates, leading to a notable decrease in the time required for computing mutual information, conditional mutual information, and conditional entropy. A BN classifier (BNC) is established by using the computationally efficient BN learning method. Our experiments demonstrated that KDE using LSH has greatly improved the speed compared to traditional KDE without losing fitting accuracy. This achievement underscores the effectiveness of our method in balancing speed and accuracy. By giving the benchmark networks, the network structure learning accuracy with the proposed method is superior to other traditional structure learning methods. The BNC also demonstrates better accuracy with stronger interpretability compared to conventional classifiers on public datasets.

Accounting for spatiotemporal patterns of long‐term recursion in estimating local‐scale step selection

Abstract Step‐selection analysis (SSA) is ubiquitous for assessing local‐scale habitat selection by comparing relocations from telemetry data (used steps) to potential relocations given the movement of the animal (available steps). The case–control design of SSA is intended to estimate selection at the spatiotemporal scale of these steps. However, long‐term behaviour associated with recurring use of certain locations or resources may additionally impact movement decisions, potentially impacting the estimates produced by SSA. To determine the impact of recursive behaviour on local selection, we simulated movement trajectories in which animals exhibited patterns of recursion. Based on these simulated trajectories, we evaluated the impact of long‐term behaviour on estimates of step‐selection. Then, we developed a new approach to identify recursion points based on a time‐dependent kernel density estimate including latitude, longitude and time of day. Based on this information, we accounted for recursive behaviour by including the relationship between available steps to recursion points or using recursion points to adjust our sample of available steps. Finally, we apply this approach to estimate the response of white‐tailed deer (Odocoileus virginianus) to sources of risk. Recursive movement resulted in biased estimates of selection when using previously established step‐selection methods. However, we found that our correction models were able to produce accurate estimates across differing recursion scenarios. When applied to an empirical deer data set, these methods revealed a pattern of selection and avoidance for human modified areas that was masked by previous approaches. Our results suggest that long‐term recursive behaviour may have unappreciated effects on estimates from SSA. Specifically, since the used and available steps in SSA are associated with specific places and times, covariates must account for variation in spatial and temporal patterns of long‐term behaviour. Unless properly accounted for, the effects of long‐term recursive behaviour will inhibit the ability of SSA to characterize fine‐scale behaviours such as predator response or foraging ecology.

An Improved Gaussian Mixture Model-Based Data Normalization Method for Removing Environmental Effects on Damage Detection of Structures

In structural health monitoring, effectively eliminating the influence of variable environmental conditions on modal frequencies remains a critical challenge for accurate damage identification. Nonstationary and nonlinear variations in modal frequencies, commonly induced by environmental changes, tend to overshadow the effects caused by structural damage. An improved Gaussian mixture model (GMM) is proposed in this paper to normalize nonlinear and nonstationary frequency data, enabling effective structural damage detection under variable environmental conditions. As the effectiveness of the GMM is highly influenced by the initial parameter values used in the expectation-maximization (EM) algorithm, a subdomain division strategy is first presented to determine the unique initial values of the GMM parameters. Through the application of the EM algorithm, the GMM is constructed simply and efficiently through the determined initial parameters. Next, on the basis of the constructed GMM, the modal frequency data are normalized to extract damage features that remain unaffected by environmental variations. Subsequently, Hotelling’s T2 statistic and its cumulative form are calculated for the damage features and designated as the damage indicators; meanwhile, the corresponding damage thresholds are also calculated according to the kernel density estimation technique. To validate the proposed method, two case studies are conducted: one with a numerical mass-spring system and the other with a real bridge structure. Results show that environmental influences no longer impact the normalized frequency data, and the cumulative statistic demonstrates outstanding accuracy in identifying structural damage.

Empirical Insights into Centroid Optimization in Transportation Planning: A Novel Approach

In complex urban environments, sophisticated analytical techniques are essential to improve the accuracy of transportation modeling and the precision of travel time predictions. This research endeavors to critically examine various multi-zone centroid positioning strategies, with the goal of unveiling the method that most authentically represents the dynamics of urban travel. Anchored by a comprehensive case study of the city of Istanbul in Turkey, the investigation utilizes various analytical tools meticulously tailored to account for the intricate interplay of demographic and geographic variables. This methodical approach enables the identification of optimal centroid locations by evaluating various methods, including a novel approach called kernel density estimation (KDE), as well as five other established other methods. The results are then aligned with real-world travel time data through rigorous statistical analysis to ensure accurate predictions of travel times. The KDE method demonstrated its more acceptable correlation coefficient and lower mean absolute error, root mean square error, and mean absolute percentage error metrics, establishing its superiority in model performance. By highlighting the paramount importance of accurately placed centroids within urban transportation models, this research’s findings contribute significantly to the evolution of transportation planning methodologies and the advancement of urban mobility models through a comparative analysis of optimal methods.

Trap density estimation for TDDB testing in SiC power MOSFETs

Abstract The trap density estimation of SiC power MOSFET in time-dependent dielectric breakdown (TDDB) was investigated by using experiment and TCAD simulation. The gate leakage current (IGSS) under negative voltage was measured and a current spike was found which was linearly shifted with TDDB stress. Based on four-state nonradiative multi phonon (NMP) defect capture model, the mechanism and modeling of IGSS current spike was studied. Based on TCAD simulation, the characteristics of gate oxygen donor traps including trap energy level, trap density, and position distribution were estimated, and the trap density model in TDDB experiment was proposed and verified. This study may contribute to the estimation of trap density in SiC MOSFET.

Invasive control and native restoration: Directing ecosystem transformation through purposeful food web manipulations

ABSTRACT Ecosystems are abruptly changing due to invasive species and global climate change. In lakes, invasive Rainbow Smelt Osmerus mordax can cause negative ecosystem effects through competitive and predatory interactions with native species leading to food web shifts away from native species dominance, altered zooplankton communities, and the decline or extirpation of native cool and coldwater fishes. We conducted two whole-lake removals of invasive Rainbow Smelt and simultaneous introductions of native Cisco Coregonus artedi through stocking. About 327 and 1.6 adult Rainbow Smelt/ha were removed and about 45 adult Cisco/ha were stocked over 4 years into the two experimental lakes. In one system, native Yellow Perch Perca flavscens relative abundance and density significantly increased by 556% and 143% post-manipulation, respectively. In the other system, native Walleye Sander vitreus relative abundance increased by 26% and became consistently present in the pelagic zone post-manipulation (allowing for density estimation). Rainbow Smelt relative abundance and density decreased by >85% in both experimental lakes. The two ecosystems shifted to native species dominance while invasive Rainbow Smelt became insignificant components of the food webs. In these two intensive whole-lake manipulations, we applied the Resist–Accept–Direct (RAD) climate adaptation framework to test an applicable ecological adaptation strategy and used panarchy theory as an ecologically grounded pathway to purposefully direct ecosystem transformation. We used this holistic management framework to better understand and manage undesired ecological change—“food web thinking.” In the context of our study, two ecosystems were purposefully directed towards native food web structures, species interactions, and processes, which mitigated Rainbow Smelt driven negative effects.

LD-SMOTE: A Novel Local Density Estimation-Based Oversampling Method for Imbalanced Datasets

Imbalanced data have become an essential stumbling block in the field of machine learning. In this paper, a novel oversampling method based on local density estimation, namely LD-SMOTE, is presented to address constraints of the popular rebalance technique SMOTE. LD-SMOTE initiates with k-means clustering to quantificationally measure the classification contribution of each feature. Subsequently, a novel distance metric grounded in Jaccard similarity is defined, which accentuates the features that are more intricately linked to the minority class. Utilizing this metric, we estimate the local density with a Gaussian-like function to control the quantity of synthetic samples around every minority sample, thus simulating the distribution of the minority class. Additionally, the generation of synthetic samples occurs within a triangular region constructed by this minority sample and its two chosen neighbors in LD-SMOTE, instead of on the line connecting the minority sample and one of its neighbors. Experimental comparisons between LD-SMOTE and 16 existing resampling methods on 19 datasets reveal a significant average increase in LD-SMOTE with 6.4% in accuracy, 4.4% in the F-measure, 5.4% in the G-mean, and 4.0% in AUC. This result indicates that LD-SMOTE can be an alternative oversampling method for imbalanced datasets.

A Novel Ultra-High Voltage Direct Current Line Fault Diagnosis Method Based on Principal Component Analysis and Kernel Density Estimation

As renewable energy resources are increasingly deployed on a large scale in remote areas, their share within the power grid continues to expand, rendering direct current (DC) transmission essential to the stability and efficiency of power systems. However, existing transmission line protection principles are constrained by limited fault feature quantities and insufficient correlation exploration among features, leading to operational refusals under remote and high-resistance fault conditions. To address these limitations in traditional protection methods, this study proposes an innovative single-ended protection principle based on Principal Component Analysis (PCA) and Kernel Density Estimation (KDE). Initially, PCA is employed for multidimensional feature extraction from fault data, followed by KDE to construct a joint probability density function of the multidimensional fault features, allowing for fault type identification based on the joint probability density values of new samples. In comparison to conventional methods, the proposed approach effectively uncovers intrinsic correlations among multidimensional features, integrating them into a comprehensive feature set for fault diagnosis. Simulation results indicate that the method exhibits robustness across various transition resistances and fault distances, demonstrates insensitivity to sampling frequency, and achieves 100% accuracy in fault identification across sampling time windows of 0.5 ms, 1 ms, and 2 ms.

Bayesian Optimization of insect trap distribution for pest monitoring efficiency in agroecosystems

Insect trap networks targeting agricultural pests are commonplace but seldom optimized to improve precision or efficiency. Trap site selection is often driven by user convenience or predetermined trap densities relative to sensitive host crop abundance in the landscape. Monitoring for invasive pests often requires expedient decisions based on dispersal potential and ecology to inform trap placement. Optimization of trap networks using contemporary analytical approaches can help users determine the distribution of traps as information accumulates and priorities change. In this study, a Bayesian optimization (BO) algorithm was used to learn more about the optimal distribution of a fine-scale trap network targeting Helicoverpa zea (Boddie), a significant agricultural pest across North America. Four years of pheromone trap monitoring was conducted at the same 21 locations distributed across ~7,000 square kilometers in a five-county area in North Carolina, USA. Three years of data were used to train a BO model with a fourth year designated for testing. For any quantity of trap locations, the approach identified those that provide the most information, allowing optimization of trapping efficiency given either a constraint on the number of locations, or a set precision required for pest density estimation. Results suggest that BO is a powerful approach to enable optimized trap placement decisions by practitioners given finite resources and time.