Statistical Mixture Model Research Articles

On the directional nature of celestial object’s fall on the earth (Part 1: Distribution of fireball shower, meteor fall & crater on earth’s surface)

Abstract This paper investigates the directional distribution of extraterrestrial objects (meteors, fireballs, and craters) impacting Earth’s surface, and introduces a novel directional statistical mixture model to analyze their falls, validated through rigorous testing. First, we address whether these falls follow non-uniform directional patterns by explicitly employing directional statistical tools for analyzing such data. Using projection techniques for longitude and latitude and more importantly, a general spherical statistical approach, we statistically investigate the suitability of the von Mises distribution and its spherical version, the von Mises Fisher distribution, (a maximum entropy distribution for directional data). Moreover, leveraging extensive datasets encompassing meteor falls, fireball showers, and craters, we propose and validate a novel mixture von Mises-Fisher model for comprehensively analyzing extraterrestrial object falls. Our study reveals distinct statistical characteristics across datasets: fireball falls exhibit non-uniformity, while meteor craters suggest a potential for both uniform and von Mises distributions with a preference for the latter after further refinement. Meteor landings deviate from a single directional maximum entropic distribution; we demonstrate the effectiveness of an optimal 13-component mixture von Mises-Fisher distribution for accurate modeling. Similar analyses resulted in 3- and 6-component partitions for fireball and crater datasets. This research presents valuable insights into the spatial patterns and directional statistical distribution models governing extraterrestrial objects’ fall on Earth, useful for various future works.

Learning Disentangled Graph Convolutional Networks Locally and Globally.

Graph convolutional networks (GCNs) emerge as the most successful learning models for graph-structured data. Despite their success, existing GCNs usually ignore the entangled latent factors typically arising in real-world graphs, which results in nonexplainable node representations. Even worse, while the emphasis has been placed on local graph information, the global knowledge of the entire graph is lost to a certain extent. In this work, to address these issues, we propose a novel framework for GCNs, termed LGD-GCN, taking advantage of both local and global information for disentangling node representations in the latent space. Specifically, we propose to represent a disentangled latent continuous space with a statistical mixture model, by leveraging neighborhood routing mechanism locally. From the latent space, various new graphs can then be disentangled and learned, to overall reflect the hidden structures with respect to different factors. On the one hand, a novel regularizer is designed to encourage interfactor diversity for model expressivity in the latent space. On the other hand, the factor-specific information is encoded globally via employing a message passing along these new graphs, in order to strengthen intrafactor consistency. Extensive evaluations on both synthetic and five benchmark datasets show that LGD-GCN brings significant performance gains over the recent competitive models in both disentangling and node classification. Particularly, LGD-GCN is able to outperform averagely the disentangled state-of-the-arts by 7.4% on social network datasets.

Covering Hierarchical Dirichlet Mixture Models on binary data to enhance genomic stratifications in onco-hematology.

Onco-hematological studies are increasingly adopting statistical mixture models to support the advancement of the genomically-driven classification systems for blood cancer. Targeting enhanced patients stratification based on the sole role of molecular biology attracted much interest and contributes to bring personalized medicine closer to reality. In onco-hematology, Hierarchical Dirichlet Mixture Models (HDMM) have become one of the preferred method to cluster the genomics data, that include the presence or absence of gene mutations and cytogenetics anomalies, into components. This work unfolds the standard workflow used in onco-hematology to improve patient stratification and proposes alternative approaches to characterize the components and to assign patient to them, as they are crucial tasks usually supported by a priori clinical knowledge. We propose (a) to compute the parameters of the multinomial components of the HDMM or (b) to estimate the parameters of the HDMM components as if they were Multivariate Fisher's Non-Central Hypergeometric (MFNCH) distributions. Then, our approach to perform patients assignments to the HDMM components is designed to essentially determine for each patient its most likely component. We show on simulated data that the patients assignment using the MFNCH-based approach can be superior, if not comparable, to using the multinomial-based approach. Lastly, we illustrate on real Acute Myeloid Leukemia data how the utilization of MFNCH-based approach emerges as a good trade-off between the rigorous multinomial-based characterization of the HDMM components and the common refinement of them based on a priori clinical knowledge.

Mixed infections in genotypic drug-resistant Mycobacterium tuberculosis

Tuberculosis disease (TB), caused by Mycobacterium tuberculosis, is a major global public health problem, resulting in more than 1 million deaths each year. Drug resistance (DR), including multi-drug (MDR-TB), is making TB control difficult and accounts for 16% of new and 48% of previously treated cases. To further complicate treatment decision-making, many clinical studies have reported patients harbouring multiple distinct strains of M. tuberculosis across the main lineages (L1 to L4). The extent to which drug-resistant strains can be deconvoluted within mixed strain infection samples is understudied. Here, we analysed M. tuberculosis isolates with whole genome sequencing data (n = 50,723), which covered the main lineages (L1 9.1%, L2 27.6%, L3 11.8%, L4 48.3%), with genotypic resistance to isoniazid (HR-TB; n = 9546 (29.2%)), rifampicin (RR-TB; n = 7974 (24.4%)), and at least MDR-TB (n = 5385 (16.5%)). TB-Profiler software revealed 531 (1.0%) isolates with potential mixed sub-lineage infections, including some with DR mutations (RR-TB 21/531; HR-TB 59/531; at least MDR-TB 173/531). To assist with the deconvolution of such mixtures, we adopted and evaluated a statistical Gaussian Mixture model (GMM) approach. By simulating 240 artificial mixtures of different ratios from empirical data across L1 to L4, a GMM approach was able to accurately estimate the DR profile of each lineage, with a low error rate for the estimated mixing proportions (mean squared error 0.012) and high accuracy for the DR predictions (93.5%). Application of the GMM model to the clinical mixtures (n = 531), found that 33.3% (188/531) of samples consisted of DR and sensitive lineages, 20.2% (114/531) consisted of lineages with only DR mutations, and 40.6% (229/531) consisted of lineages with genotypic pan-susceptibility. Overall, our work demonstrates the utility of combined whole genome sequencing data and GMM statistical analysis approaches for providing insights into mono and mixed M. tuberculosis infections, thereby potentially assisting diagnosis, treatment decision-making, drug resistance and transmission mapping for infection control.

Unraveling the palindromic and nonpalindromic motifs of retroviral integration site sequences by statistical mixture models.

A weak palindromic nucleotide motif is the hallmark of retroviral integration site alignments. Given that the majority of target sequences are not palindromic, the current model explains the symmetry by an overlap of the nonpalindromic motif present on one of the half-sites of the sequences. Here, we show that the implementation of multicomponent mixture models allows for different interpretations consistent with the existence of both palindromic and nonpalindromic submotifs in the sets of integration site sequences. We further show that the weak palindromic motifs result from freely combined site-specific submotifs restricted to only a few positions proximal to the site of integration. The submotifs are formed by either palindrome-forming nucleotide preference or nucleotide exclusion. Using the mixture models, we also identify HIV-1-favored palindromic sequences in Alu repeats serving as local hotspots for integration. The application of the novel statistical approach provides deeper insight into the selection of retroviral integration sites and may prove to be a valuable tool in the analysis of any type of DNA motifs.

Characterising the AGB bump and its potential to constrain mixing processes in stellar interiors

Context. In the 1990s, theoretical studies motivated the use of the asymptotic giant branch bump (AGBb) as a standard candle given the weak dependence between its luminosity and stellar metallicity. Because of the small size of observed asymptotic giant branch (AGB) samples, detecting the AGBb is not an easy task. However, this has now been made possible thanks to the wealth of data collected by the CoRoT, Kepler, and TESS space-borne missions. Aims. It is well-known that the AGB bump provides valuable information on the internal structure of low-mass stars, particularly on mixing processes such as core overshooting during the core He-burning phase. Here, we investigate the dependence of the AGBb position on stellar parameters such as the stellar mass and metallicity based on the calibration of stellar models to observations. Methods. In this context, we analysed ∼4000 evolved giants observed by Kepler and TESS, including red giant branch (RGB) stars and AGB stars, for which asteroseismic and spectrometric data are available. By using statistical mixture models, we detected the AGBb both in frequency at maximum oscillation power, νmax, and in effective temperature, Teff. Then, we used the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code to model AGB stars and match the AGBb occurrence with observations. Results. From the observations, we were able to derive the AGBb location in 15 bins of mass and metallicity. We noted that the higher the mass, the later the AGBb occurs in the evolutionary track, which agrees with theoretical works. Moreover, we found a slight increase in the luminosity at the AGBb when the metallicity increases. By fitting those observations with stellar models, we noticed that low-mass stars (M ≤ 1.0 M⊙) require a small core overshooting region during the core He-burning phase. This core overshooting extent increases toward high mass; however, above M ≥ 1.5 M⊙, we found that the AGBb location cannot be reproduced with a realistic He-core overshooting alone. Thus, additional mixing processes have to be invoked instead. Conclusions. The observed dependence on metallicity complicates the application of the AGBb as a standard candle. Moreover, different mixing processes may occur according to stellar mass. At low mass (M ≤ 1.5 M⊙), the AGBb location can be used to constrain the He-core overshooting. At high mass (M ≥ 1.5 M⊙), an additional mixing induced, for instance, by rotation is needed to reproduce what is seen in observations.

A Ship Detection and Imagery Scheme for Airborne Single-Channel SAR in Coastal Regions

Ship detection and management in coastal regions are challenging tasks due to the complex appearances of ships and the background. For further applications in the context of fisheries monitoring and vessel traffic services, a single-channel synthetic aperture radar (SAR) is mounted on a number of maneuvering and inexpensive rotor platforms, which are utilized according to the consideration of flexible observation, cost savings, weight, and space constraints. In this paper, a hierarchical scheme of ship detection, ship imaging, and classification is proposed. It mainly includes three parts. First, a mixture statistical model of semi-parametric K-lognormal distribution based on adaptive background windows with a constant false alarm rate (CFAR) is proposed for ship prescreening in SAR imagery. Then, the discrimination stage, combined with ship imaging via the difference between the true ship targets and the false ones in the aspects of micro-Doppler motion properties, is performed. Finally, the simulation and field data processing results are presented to validate the proposed scheme.

Capacity and Allocation across Sensory and Short-Term Memories.

Human memory consists of sensory memory (SM), short-term memory (STM), and long-term memory (LTM). SM enables a large capacity, but decays rapidly. STM has limited capacity, but lasts longer. The traditional view of these memory systems resembles a leaky hourglass, the large top and bottom portions representing the large capacities of SM and LTM, whereas the narrow portion in the middle represents the limited capacity of STM. The “leak” in the top part of the hourglass depicts the rapid decay of the contents of SM. However, recently, it was shown that major bottlenecks for motion processing exist prior to STM, and the “leaky hourglass” model was replaced by a “leaky flask” model with a narrower top part to capture bottlenecks prior to STM. The leaky flask model was based on data from one study, and the first goal of the current paper was to test if the leaky flask model would generalize by using a different set of data. The second goal of the paper was to explore various block diagram models for memory systems and determine the one best supported by the data. We expressed these block diagram models in terms of statistical mixture models and, by using the Bayesian information criterion (BIC), found that a model with four components, viz., SM, attention, STM, and guessing, provided the best fit to our data. In summary, we generalized previous findings about early qualitative and quantitative bottlenecks, as expressed in the leaky flask model and showed that a four-process model can provide a good explanation for how visual information is processed and stored in memory.

Spatial analysis of damage evolution in cyclic-loaded reinforced concrete shear walls

This paper introduces a probabilistic framework to quantify the spatial distribution of cracking and crushing in rectangular reinforced concrete shear walls at different drift ratios. In this research, a comprehensive probabilistic spatial analysis is conducted on an extensive collected database of reinforced concrete shear walls tested under the quasi-static cyclic loading. The database includes 235 images of 72 damaged walls with various geometry and material properties at different drift ratios between 0.0 and 4.0%. Various image processing filters are implemented to the images to highlight the wall areas that are more prone to cracking and crushing. Then, advanced statistical analysis is carried out at the post-processing phase in order to quantify the spatial distribution of the damage. The results of the probabilistic analysis are presented for three major classes based on the variation of the wall aspect ratio. The damage heat maps are produced for each class, which show the concentration and severity of the occurred damages. In the following, statistical mixture models have been used to formulate the spatial variation of the damage over the 2D space of the concrete shear walls. A set of nonlinear predictive equations are also proposed to predict the probability of cracking at any specific zones of the walls based on the wall drift ratio. A major contribution of this study is to propose a visual benchmark for the inspectors to predict the peak-experienced drift ratio of a damaged wall (especially after a terminated cyclic-load) based only on the ultimate spatial distribution of damages. Therefore, the presented framework plays a crucial role in determining the post-hazard status of reinforced concrete shear walls based on the prediction of the peak drift ratio.

Regionalisation of flood frequencies based on flood type-specific mixture distributions

The regionalisation of flood frequencies is a precondition for the estimation of flood statistics for ungauged basins. It is often based on either the concept of hydrological similarity of catchments or spatial proximity. Similarity is usually defined by comparing catchment attributes or distances. Here, we apply flood types in regionalisation directly to consider the type-specific aspects of similarity. The different flood types are classified according to their meteorological causes and hydrographs. Their probability distributions are modelled by type-specific distribution functions which are combined into one statistical annual mixture model afterwards. For regionalisation, we specified the parameters of each type-specific probability distribution separately with hierarchical clustering and regressions from catchment attributes. By selection of most relevant features, depending on the flood type, the specifics of flood-generating processes and meteorological causes were considered. The results demonstrate how this consideration of deterministic aspects can improve the transferability of distribution parameters to ungauged catchments. The type-specific regionalisation approach offers a higher degree of freedom for regionalisation as it describes the relationships between catchment characteristics, meteorological causes of floods and response of watersheds.

Correction of overlapping peaks of Pb and As spectrum based on a chaotic particle swarm optimization–Gaussian mixture statistical model

AbstractEnergy‐dispersive X‐ray fluorescence spectroscopy has been effectively applied to detect heavy metals in soil because of its fast detection speed, low cost, and high accuracy. However, overlapping peaks appear in the detection of some heavy metals, such as Pb and As, resulting in significant errors in the detection. Therefore, it is impossible to accurately predict the content of heavy metals in soil. To solve this problem, a Gaussian mixture statistical model (GMSM) is applied based on physical characteristics randomly formed by X‐rays combined with statistical ideas. Subsequently, when estimating the parameters of the GMSM, performing particle swarm optimization (PSO) causes the parameters to fall into the local optima easily. Chaos theory is introduced to the PSO algorithm to promote its weight update strategy, and the chaotic PSO (CPSO) with an anti‐premature mechanism is proposed to achieve global convergence. When using CPSO‐GMSM to analyze the overlapping peaks, the relative error compared with the actual single metal sample is less than 0.0693, and the error compared with the actual characteristic peak position is less than 0.0133. The overlapping peaks are corrected effectively, providing a foundation for the accurate quantitative analysis of heavy metals in soil.

Location Based Generalized Akash Distribution: Properties and Applications

In recent years, several statistical finite mixture models have been proposed to model the lifetime data with heterogeneity. The Lindley distribution has been highlighted by many authors for these types of lifetime data analysis. This paper introduces a new Lindley family distribution called location-based generalized Akash distribution (NGAD) with monotonic increasing and bathtub failure rates. The density function of NGAD is flexible to cover the left-skewed, right-skewed and symmetrical shapes with different tail-weights. Its fundamental structural properties and its ability to provide a suitable statistical model for various types of data sets are studied. The maximum likelihood (ML) method is used to estimate its unknown parameters and the performance of ML estimates are examined by a simulation study. Finally, several real-data sets with different characteristics are used to illustrate its flexibility. It is observed that NGAD provides a better fit than some other existing modified Lindley distributions.

Energy Consumption Analysis for Adaptive Transmission of Big Data Over Fading Channels: A Statistical Characterization

We study the energy consumption of the adaptive transmission of big data over fading channels. Transmission of big data usually lasts over multiple channel coherence time periods. With adaptive transmission, the transmission rate and/or power is adaptively adjusted according to the channel realization. The energy comsumption varies with channel realizations. We propose a novel analytical framework to statistically evaluate the energy consumption of adaptive big data transmission. For the slow fading scenario, we derive the exact probability density function (PDF) and cumulative distribution function (CDF) of energy consumed over Markov channels. For the fast fading cases, we apply the statistical mixture model to estimate the PDF of energy consumption for wireless transmission of big data adaptively. Selected numerical results are presented to illustrate and to validate the mathematical formulations. These analytical results will greatly benefit the study of big data applications in the wireless environment.

Fully Automated Computer-Assisted Diagnostic Method for Mitosis Detection on Histology Slide Images of Breast Cancer

Background: Nowadays, advances in the field of medical science, especially the branch of histology, have made it possible to detect cancer, its growth rate, type, and extent of cancer malignancy. According to GLOBOCAN 2012, breast cancer ranks second in terms of prevalence and mortality [1]. The number of mitoses in histology slide images is considered as one of the three significant factors in grading breast cancer. The mitosis count is done manually by pathologists but automating the mitosis count process can decrease its time and costs. Different automatic techniques have been proposed in the literature for breast cancer mitotic counting [2-5]. Objectives: In this paper, we propose an automated method for accurate mitotic cell detection in breast cancer histology slide images. Methods: To evaluate experiments, we used the Mitos-ICPR 2012 dataset consisting of 50 HPFs with the train-to-test ratio of 70% to 30%, accounting for 35 images for training and 15 images for testing. These 50 HPFs were obtained by analyzing the texture of five different patients. Each slide was stained with standard Hematoxylin and Eosin (H&E) stains and two expert pathologists marked the mitotic cells with labels in 10 selected distinct microscopic HPFs at 40x magnification. The slides were scanned by two slide scanners, including Aperio Scanscope XT and Hamamatsu Nano-zoomer. Totally, there were 326 mitotic cells in this dataset [6]. As shown in Figure 1, the proposed fully automated system consisted of the following stages: segmentation and extraction of mitosis candidates using statistical Gaussian Mixture Model (GMM), feature extraction, and classification using SVM classifier (with different kernels) and decision tree classifier. After candidate extraction using GMM, to identify candidates as mitoses or non-mitoses, it was necessary to extract discriminant and reliable features. In the proposed feature extraction stage, we focused on the extraction of textural features including GLCM, CLBP, and statistical moments of filtered images by the Gabor filter in the RGB color space. Moreover, several shape features were proposed to achieve a better distinction of mitosis from non-mitosis candidates. The proposed shape features were based on calculating the Euclidean distance of boundary pixels from the center of each cell. Two types of textural and shape features were combined with each other to provide the final feature vector with a length of 214. Results: The visual results of the proposed automated mitosis detection system for a sample histopathology slide image are shown in Figure 2. Conclusion: The detailed experimental results demonstrated the promising performance of the proposed fully automated method for mitosis detection with F-measure (91.49%).

A soft computing model based on asymmetric Gaussian mixtures and Bayesian inference

A novel unsupervised Bayesian learning framework based on asymmetric Gaussian mixture (AGM) statistical model is proposed since AGM is shown to be more effective compared to the classic Gaussian mixture model. The Bayesian learning framework is developed by adopting sampling-based Markov chain Monte Carlo (MCMC) methodology. More precisely, the fundamental learning algorithm is a hybrid Metropolis–Hastings within Gibbs sampling solution which is integrated within a reversible jump MCMC learning framework, a self-adapted sampling-based implementation, that enables model transfer throughout the mixture parameters learning process and therefore automatically converges to the optimal number of data groups. Furthermore, in order to handle high-dimensional vectors of features, a dimensionality reduction algorithm based on mixtures of distributions is included to tackle the irrelevant and extraneous features. The performance comparison between AGM and other popular models is given, and both synthetic and real datasets extracted from challenging applications such as intrusion detection, spam filtering and image categorization are evaluated to show the merits of the proposed approach.

Clustering in the wireless channel with a power weighted statistical mixture model in indoor scenario

Cluster-based channel model is the main stream of fifth generation mobile communications, thus the accuracy of clustering algorithm is important. Traditional Gaussian mixture model (GMM) does not consider the power information which is important for the channel multipath clustering. In this paper, a normalized power weighted GMM (PGMM) is introduced to model the channel multipath components (MPCs). With MPC power as a weighted factor, the PGMM can fit the MPCs in accordance with the cluster-based channel models. Firstly, expectation maximization (EM) algorithm is employed to optimize the PGMM parameters. Then, to further increase the searching ability of EM and choose the optimal number of components without resort to cross-validation, the variational Bayesian (VB) inference is employed. Finally, 28 GHz indoor channel measurement data is used to demonstrate the effectiveness of the PGMM clustering algorithm.

Human Intention Understanding From Multiple Demonstrations and Behavior Generalization in Dynamic Movement Primitives Framework

Human’s interference in the process of skill learning can improve the performance of the robot greatly. However, learning from demonstration to generate a new action with human behavioral characteristics in the varying situation is challenging. Generally, dynamic movement primitives (DMPs) method can generalize the trajectory imitating the demonstration, but cannot integrate the feature of multiple trajectories of different targets. In this paper, the proposed method contains two aspects of learning and generating. The statistical method Gaussian mixture model and Gaussian mixture regression (GMM-GMR) is used to extract the common characteristic and eliminate the uncertainty of the multiple demonstrations. To exert the ability of DMPs to generate a human-like motion to a new goal, and we model the shape parameter with locally weighted regression (LWR) method. To enhance the ability of DMPs in multiple trajectories learning, we propose the multivariate Gaussian process regression (MV-GPR) method to construct the regression model of shape parameters to reflect the human intentions, with respect to the target position. To verify the feasibility of the proposed method, we design a peg-in-hole experiment with proving generalization and obstacle avoidance performance. The results have shown that the strategy integrated the generalization of DMPs and feature regeneration ability of MV-GPR method, and the generated valid trajectory could achieve the peg-in-hole task with 6-DOF whole-arm avoidance.

Deriving Probabilistic SVM Kernels From Flexible Statistical Mixture Models and its Application to Retinal Images Classification

This paper aims to propose a robust hybrid probabilistic learning approach that combines appropriately the advantages of both the generative and discriminative models for the challenging problem of diabetic retinopathy classification in retinal images. We build new probabilistic kernels based on information divergences and Fisher score from the mixture of scaled Dirichlet distributions for support vector machines (SVMs). We also investigate the incorporation of a minimum description length criterion into the learning model to deal with the common problems of determining suitable components and also selecting the best model that describes the dataset. The developed hybrid model is introduced in this paper as an effective SVM kernel able to incorporate prior knowledge about the nature of data involved in the problem at hand and, therefore, permits a good data discrimination. Our approach has been shown to be a better alternative to other methods, which is able to describe the intrinsic nature of datasets and to be of a significant value in a variety of applications involving data classification. We demonstrate the flexibility and the merits of the proposed framework for the problem of diabetic retinopathy detection in eye images.

Climate change or climate regimes? Examining multi-annual variations in the frequency of precipitation extremes over the Argentine Pampas

A recent period of increased precipitation over the Argentinian Pampas expanded the boundary of rain-fed agriculture. However, such changes may not be sustainable if they arose from transient climate regime shifts. Considerable research exists on trends and cycles in sub-daily to annual precipitation metrics including the frequency and intensity of extreme precipitation. However, efforts to identify wetter and drier phases (or regimes) in this region are scant. This article aims to bridge that gap and advance our understanding of the multi-annual behavior of regional precipitation extremes, which can have the greatest impacts. It is unlikely that all extreme events are drawn from a single probability distribution or generated by the same physical processes. Hence, hidden mixtures of Poisson distributions are fitted to several precipitation frequency metrics to explore whether the annual to decadal variations in extreme precipitation frequency are greater than anticipated from a single system, and representative of regime shifts. Statistically significant improvements in the fit over single distributions were found for statistical mixture models of the frequency of very wet days, and the frequency of wet spells. This supports the hypothesis that multiple weather regimes exist giving rise to wetter or drier epochs. Posterior probabilities of hidden states from the fitted mixture distributions were used to identify wetter and drier years for comparison with sea surface temperature anomalies. This confirmed the presence of two distinct regimes, supporting other research, into the dynamical influences of precipitation behavior in the Argentine Pampas.

CONDEL: Detecting Copy Number Variation and Genotyping Deletion Zygosity from Single Tumor Samples Using Sequence Data.

Characterizing copy number variations (CNVs) from sequenced genomes is a both feasible and cost-effective way to search for driver genes in cancer diagnosis. A number of existing algorithms for CNV detection only explored part of the features underlying sequence data and copy number structures, resulting in limited performance. Here, we describe CONDEL, a method for detecting CNVs from single tumor samples using high-throughput sequence data. CONDEL utilizes a novel statistic in combination with a peel-off scheme to assess the statistical significance of genome bins, and adopts a Bayesian approach to infer copy number gains, losses, and deletion zygosity based on statistical mixture models. We compare CONDEL to six peer methods on a large number of simulation datasets, showing improved performance in terms of true positive and false positive rates, and further validate CONDEL on three real datasets derived from the 1000 Genomes Project and the EGA archive. CONDEL obtained higher consistent results in comparison with other three single sample-based methods, and exclusively identified a number of CNVs that were previously associated with cancers. We conclude that CONDEL is a powerful tool for detecting copy number variations on single tumor samples even if these are sequenced at low-coverage.