Here we present a dataset, MNIST4OD, of large size (number of dimensions and number of instances) suitable for Outliers Detection task.The dataset is based on the famous MNIST dataset (http://yann.lecun.com/exdb/mnist/).We build MNIST4OD in the following way:To distinguish between outliers and inliers, we choose the images belonging to a digit as inliers (e.g. digit 1) and we sample with uniform probability on the remaining images as outliers such as their number is equal to 10% of that of inliers. We repeat this dataset generation process for all digits. For implementation simplicity we then flatten the images (28 X 28) into vectors.Each file MNIST_x.csv.gz contains the corresponding dataset where the inlier class is equal to x.The data contains one instance (vector) in each line where the last column represents the outlier label (yes/no) of the data point. The data contains also a column which indicates the original image class (0-9).See the following numbers for a complete list of the statistics of each datasets ( Name | Instances | Dimensions | Number of Outliers in % ):MNIST_0 | 7594 | 784 | 10MNIST_1 | 8665 | 784 | 10MNIST_2 | 7689 | 784 | 10MNIST_3 | 7856 | 784 | 10MNIST_4 | 7507 | 784 | 10MNIST_5 | 6945 | 784 | 10MNIST_6 | 7564 | 784 | 10MNIST_7 | 8023 | 784 | 10MNIST_8 | 7508 | 784 | 10MNIST_9 | 7654 | 784 | 10

ABSTRACT The considerable volume of data generated by sensors in the field presents systematic errors; thus, it is extremely important to exclude these errors to ensure mapping quality. The objective of this research was to develop and test a methodology to identify and exclude outliers in high-density spatial data sets, determine whether the developed filter process could help decrease the nugget effect and improve the spatial variability characterization of high sampling data. We created a filter composed of a global, anisotropic, and an anisotropic local analysis of data, which considered the respective neighborhood values. For that purpose, we used the median to classify a given spatial point into the data set as the main statistical parameter and took into account its neighbors within a radius. The filter was tested using raw data sets of corn yield, soil electrical conductivity (ECa), and the sensor vegetation index (SVI) in sugarcane. The results showed an improvement in accuracy of spatial variability within the data sets. The methodology reduced RMSE by 85 %, 97 %, and 79 % in corn yield, soil ECa, and SVI respectively, compared to interpolation errors of raw data sets. The filter excluded the local outliers, which considerably reduced the nugget effects, reducing estimation error of the interpolated data. The methodology proposed in this work had a better performance in removing outlier data when compared to two other methodologies from the literature.

There has been a tremendous increase in the volume of sensor data collected over the last decade for different monitoring tasks. For example, petabytes of earth science data are collected from modern satellites, in-situ sensors and different climate models. Similarly, huge amount of flight operational data is downloaded for different commercial airlines. These different types of datasets need to be analyzed for finding outliers. Information extraction from such rich data sources using advanced data mining methodologies is a challenging task not only due to the massive volume of data, but also because these datasets are physically stored at different geographical locations with only a subset of features available at any location. Moving these petabytes of data to a single location may waste a lot of bandwidth. To solve this problem, in this paper, we present a novel algorithm which can identify outliers in the entire data without moving all the data to a single location. The method we propose only centralizes a very small sample from the different data subsets at different locations. We analytically prove and experimentally verify that the algorithm offers high accuracy compared to complete centralization with only a fraction of the communication cost. We show that our algorithm is highly relevant to both earth sciences and aeronautics by describing applications in these domains. The performance of the algorithm is demonstrated on two large publicly available datasets: (1) the NASA MODIS satellite images and (2) a simulated aviation dataset generated by the ‘Commercial Modular Aero-Propulsion System Simulation’ (CMAPSS).

Cylindrical data are bivariate data formed from the combination of circular and linear variables. Identifying outliers is a crucial step in any data analysis work. This paper proposes a new distribution-free procedure to detect outliers in cylindrical data using the Mahalanobis distance concept. The use of Mahalanobis distance incorporates the correlation between the components of the cylindrical distribution, which had not been accounted for in the earlier papers on outlier detection in cylindrical data. The threshold for declaring an observation to be an outlier can be obtained via parametric or non-parametric bootstrap, depending on whether the underlying distribution is known or unknown. The performance of the proposed method is examined via extensive simulations from the Johnson-Wehrly distribution. The proposed method is applied to two real datasets, and the outliers are identified in those datasets.

The "Amsterdam Library of Object Images" is a collection of 110250 images of 1000 small objects, taken under various light conditions and rotation angles. All objects were placed on a black background. Thus the images are taken under rather uniform conditions, which means there is little uncontrolled bias in the data set (unless mixed with other sources). They do however not resemble a "typical" image collection. The data set has a rather unique property for its size: there are around 100 different images of each object, so it is well suited for clustering. By downsampling some objects it can also be used for outlier detection. For multi-view research, we offer a number of different feature vector sets for evaluating this data set.

We present a set of novel algorithms which we call sequenceMiner, that detect and characterize anomalies in large sets of high-dimensional symbol sequences that arise from recordings of switch sensors in the cockpits of commercial airliners. While the algorithms we present are general and domain-independent, we focus on a specific problem that is critical to determining system-wide health of a fleet of aircraft. The approach taken uses unsupervised clustering of sequences using the normalized length of he longest common subsequence (nLCS) as a similarity measure, followed by a detailed analysis of outliers to detect anomalies. In this method, an outlier sequence is defined as a sequence that is far away from a cluster. We present new algorithms for outlier analysis that provide comprehensible indicators as to why a particular sequence is deemed to be an outlier. The algorithm provides a coherent description to an analyst of the anomalies in the sequence when compared to more normal sequences. The final section of the paper demonstrates the effectiveness of sequenceMiner for anomaly detection on a real set of discrete sequence data from a fleet of commercial airliners. We show that sequenceMiner discovers actionable and operationally significant safety events. We also compare our innovations with standard HiddenMarkov Models, and show that our methods are superior

Dataset Card for "cifar10-outlier"

📚 This dataset is an enriched version of the CIFAR-10 Dataset. The workflow is described in the medium article: Changes of Embeddings during Fine-Tuning of Transformers.

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The open source data curation tool Renumics Spotlight allows you to explorer this dataset. You can find a Hugging Face Spaces running Spotlight with this dataset here:

Full Version (High hardware requirement)… See the full description on the dataset page: https://huggingface.co/datasets/renumics/cifar10-outlier.

Usage notes

The objects are numbered. The Y-variable are boiling points. Other features are structural features of molecules. In the outlier column the outliers are assigned with a value of 1.

The data is derived from a published chemical dataset on boiling point measurements [1] and from public data [2]. Features were generated by means of the RDKit Python library [3]. The dataset was infused with known outliers (~5%) based on significant structural differences, i.e. polar and non-polar molecules.

1. Cherqaoui D., Villemin D. Use of a Neural Network to determine the Boiling Point of Alkanes. J CHEM SOC FARADAY TRANS. 1994;90(1):97–102.
2. https://pubchem.ncbi.nlm.nih.gov/
3. RDKit: Open-source cheminformatics; http://www.rdkit.org

The Multi-Domain Outlier Detection Dataset contains datasets for conducting outlier detection experiments for four different application domains:

1. Astrophysics - detecting anomalous observations in the Dark Energy Survey (DES) catalog (data type: feature vectors)
2. Planetary science - selecting novel geologic targets for follow-up observation onboard the Mars Science Laboratory (MSL) rover (data type: grayscale images)
3. Earth science: detecting anomalous samples in satellite time series corresponding to ground-truth observations of maize crops (data type: time series/feature vectors)
4. Fashion-MNIST/MNIST: benchmark task to detect anomalous MNIST images among Fashion-MNIST images (data type: grayscale images)

Each dataset contains a "fit" dataset (used for fitting or training outlier detection models), a "score" dataset (used for scoring samples used to evaluate model performance, analogous to test set), and a label dataset (indicates whether samples in the score dataset are considered outliers or not in the domain of each dataset).

To read more about the datasets and how they are used for outlier detection, or to cite this dataset in your own work, please see the following citation:

Kerner, H. R., Rebbapragada, U., Wagstaff, K. L., Lu, S., Dubayah, B., Huff, E., Lee, J., Raman, V., and Kulshrestha, S. (2022). Domain-agnostic Outlier Ranking Algorithms (DORA)-A Configurable Pipeline for Facilitating Outlier Detection in Scientific Datasets. Under review for Frontiers in Astronomy and Space Sciences.

1. NCCTG Lung cancer datasetSurvival in patients with advanced lung cancer from the North Central Cancer Treatment Group. Performance scores rate how well the patient can perform usual daily activities.2.CNV measurements of CNV of GBM This dataset records the information about copy number variation of Glioblastoma (GBM).Abstract:In biology and medicine, conservative patient and data collection malpractice can lead to missing or incorrect values in patient registries, which can affect both diagnosis and prognosis. Insufficient or biased patient information significantly impedes the sensitivity and accuracy of predicting cancer survival. In bioinformatics, making a best guess of the missing values and identifying the incorrect values are collectively called “imputation”. Existing imputation methods work by establishing a model based on the data mechanism of the missing values. Existing imputation methods work well under two assumptions: 1) the data is missing completely at random, and 2) the percentage of missing values is not high. These are not cases found in biomedical datasets, such as the Cancer Genome Atlas Glioblastoma Copy-Number Variant dataset (TCGA: 108 columns), or the North Central Cancer Treatment Group Lung Cancer (NCCTG) dataset (NCCTG: 9 columns). We tested six existing imputation methods, but only two of them worked with these datasets: The Last Observation Carried Forward (LOCF) and K-nearest Algorithm (KNN). Predictive Mean Matching (PMM) and Classification and Regression Trees (CART) worked only with the NCCTG lung cancer dataset with fewer columns, except when the dataset contains 45% missing data. The quality of the imputed values using existing methods is bad because they do not meet the two assumptions.In our study, we propose a Restricted Boltzmann Machine (RBM)-based imputation method to cope with low randomness and the high percentage of the missing values. RBM is an undirected, probabilistic and parameterized two-layer neural network model, which is often used for extracting abstract information from data, especially for high-dimensional data with unknown or non-standard distributions. In our benchmarks, we applied our method to two cancer datasets: 1) NCCTG, and 2) TCGA. The running time, root mean squared error (RMSE) of the different methods were gauged. The benchmarks for the NCCTG dataset show that our method performs better than other methods when there is 5% missing data in the dataset, with 4.64 RMSE lower than the best KNN. For the TCGA dataset, our method achieved 0.78 RMSE lower than the best KNN.In addition to imputation, RBM can achieve simultaneous predictions. We compared the RBM model with four traditional prediction methods. The running time and area under the curve (AUC) were measured to evaluate the performance. Our RBM-based approach outperformed traditional methods. Specifically, the AUC was up to 19.8% higher than the multivariate logistic regression model in the NCCTG lung cancer dataset, and the AUC was higher than the Cox proportional hazard regression model, with 28.1% in the TCGA dataset.Apart from imputation and prediction, RBM models can detect outliers in one pass by allowing the reconstruction of all the inputs in the visible layer with in a single backward pass. Our results show that RBM models have achieved higher precision and recall on detecting outliers than other methods.

There has been a tremendous increase in the volume of Earth Science data over the last decade from modern satellites, in-situ sensors and different climate models. All these datasets need to be co-analyzed for finding interesting patterns or for searching for extremes or outliers. Information extraction from such rich data sources using advanced data mining methodologies is a challenging task not only due to the massive volume of data, but also because these datasets are physically stored at different geographical locations. Moving these petabytes of data over the network to a single location may waste a lot of bandwidth, and can take days to finish. To solve this problem, in this paper, we present a novel algorithm which can identify outliers in the global data without moving all the data to one location. The algorithm is highly accurate (close to 99%) and requires centralizing less than 5% of the entire dataset. We demonstrate the performance of the algorithm using data obtained from the NASA MODerate-resolution Imaging Spectroradiometer (MODIS) satellite images.

There are three files containing Stata data, and do and log-files. These are associated with the empirical models reported in the replication study, “Outlier Analysis: Natural Resources and Immigration Policy,” POLS ONE. Questions or comments regarding these materials should be directed to Seung-Whan Choi, Department of Political Science, University of Illinois at Chicago. His email address is whanchoi@uic.edu and his homepage address is https://whanchoi.people.uic.edu/.

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by principal component analysis (PCA), which in its basic form is not robust to outliers. Much research has focused on handling rowwise outliers, that is, rows that deviate from the majority of the rows in the data (e.g., they might belong to a different population). In recent years also cellwise outliers are receiving attention. These are suspicious cells (entries) that can occur anywhere in the table. Even a relatively small proportion of outlying cells can contaminate over half the rows, which causes rowwise robust methods to break down. In this article, a new PCA method is constructed which combines the strengths of two existing robust methods to be robust against both cellwise and rowwise outliers. At the same time, the algorithm can cope with missing values. As of yet it is the only PCA method that can deal with all three problems simultaneously. Its name MacroPCA stands for PCA allowing for Missingness And Cellwise & Rowwise Outliers. Several simulations and real datasets illustrate its robustness. New residual maps are introduced, which help to determine which variables are responsible for the outlying behavior. The method is well-suited for online process control.

Abstract: Building health management is an important part in running an efficient and cost-effective building. Many problems in a building’s system can go undetected for long periods of time, leading to expensive repairs or wasted resources. This project aims to help detect and diagnose the building‘s health with data driven methods throughout the day. Orca and IMS are two state of the art algorithms that observe an array of building health sensors and provide feedback on the overall system’s health as well as localize the problem to one, or possibly two, components. With this level of feedback the hope is to quickly identify problems and provide appropriate maintenance while reducing the number of complaints and service calls. Introduction: To prepare these technologies for the new installation, the proposed methods are being tested on a current system that behaves similarly to the future green building. Building 241 was determined to best resemble the proposed building 232 and therefore was chosen for this study. Building 241 is currently outfitted with 34 sensors that monitor the heating & cooling temperatures for the air and water systems as well as other various subsystem states. The daily sensor recordings were logged and sent to the IDU group for analysis. The period of analysis was focused from July 1st through August 10th 2009. Methodology: The two algorithms used for analysis were Orca and IMS. Both methods look for anomalies using a distanced based scoring approach. Orca has the ability to use a single data set and find outliers within that data set. This tactic was applied to each day. After scoring each time sample throughout a given day the Orca score profiles were compared by computing the correlation against all other days. Days with high overall correlations were considered normal however days with lower overall correlations were more anomalous. IMS, on the other hand, needs a normal set of data to build a model, which can be applied to a set of test data to asses how anomaly the particular data set is. The typical days identified by Orca were used as the reference/training set for IMS, while all the other days were passed through IMS resulting in an anomaly score profile for each day. The mean of the IMS score profile was then calculated for each day to produce a summary IMS score. These summary scores were ranked and the top outliers were identified (see Figure 1). Once the anomalies were identified the contributing parameters were then ranked by the algorithm. Analysis: The contributing parameters identified by IMS were localized to the return air temperature duct system. -7/03/09 (Figure 2 & 3) AHU-1 Return Air Temperature (RAT) Calculated Average Return Air Temperature -7/19/09 (Figure 3 & 4) AHU-2 Return Air Temperature (RAT) Calculated Average Return Air Temperature IMS identified significantly higher temperatures compared to other days during the month of July and August. Conclusion: The proposed algorithms Orca and IMS have shown that they were able to pick up significant anomalies in the building system as well as diagnose the anomaly by identifying the sensor values that were anomalous. In the future these methods can be used on live streaming data and produce a real time anomaly score to help building maintenance with detection and diagnosis of problems.

Abstract: Building health management is an important part in running an efficient and cost-effective building. Many problems in a building’s system can go undetected for long periods of time, leading to expensive repairs or wasted resources. This project aims to help detect and diagnose the building‘s health with data driven methods throughout the day. Orca and IMS are two state of the art algorithms that observe an array of building health sensors and provide feedback on the overall system’s health as well as localize the problem to one, or possibly two, components. With this level of feedback the hope is to quickly identify problems and provide appropriate maintenance while reducing the number of complaints and service calls. Introduction: To prepare these technologies for the new installation, the proposed methods are being tested on a current system that behaves similarly to the future green building. Building 241 was determined to best resemble the proposed building 232 and therefore was chosen for this study. Building 241 is currently outfitted with 34 sensors that monitor the heating & cooling temperatures for the air and water systems as well as other various subsystem states. The daily sensor recordings were logged and sent to the IDU group for analysis. The period of analysis was focused from July 1st through August 10th 2009. Methodology: The two algorithms used for analysis were Orca and IMS. Both methods look for anomalies using a distanced based scoring approach. Orca has the ability to use a single data set and find outliers within that data set. This tactic was applied to each day. After scoring each time sample throughout a given day the Orca score profiles were compared by computing the correlation against all other days. Days with high overall correlations were considered normal however days with lower overall correlations were more anomalous. IMS, on the other hand, needs a normal set of data to build a model, which can be applied to a set of test data to asses how anomaly the particular data set is. The typical days identified by Orca were used as the reference/training set for IMS, while all the other days were passed through IMS resulting in an anomaly score profile for each day. The mean of the IMS score profile was then calculated for each day to produce a summary IMS score. These summary scores were ranked and the top outliers were identified (see Figure 1). Once the anomalies were identified the contributing parameters were then ranked by the algorithm. Analysis: The contributing parameters identified by IMS were localized to the return air temperature duct system. -7/03/09 (Figure 2 & 3) AHU-1 Return Air Temperature (RAT) Calculated Average Return Air Temperature -7/19/09 (Figure 3 & 4) AHU-2 Return Air Temperature (RAT) Calculated Average Return Air Temperature IMS identified significantly higher temperatures compared to other days during the month of July and August. Conclusion: The proposed algorithms Orca and IMS have shown that they were able to pick up significant anomalies in the building system as well as diagnose the anomaly by identifying the sensor values that were anomalous. In the future these methods can be used on live streaming data and produce a real time anomaly score to help building maintenance with detection and diagnosis of problems.

Patterns of multi-locus differentiation (i.e., genomic clines) often extend broadly across hybrid zones and their quantification can help diagnose how species boundaries are shaped by adaptive processes, both intrinsic and extrinsic. In this sense, the transitioning of loci across admixed individuals can be contrasted as a function of the genome-wide trend, in turn allowing an expansion of clinal theory across a much wider array of biodiversity. However, computational tools that serve to interpret and consequently visualize ‘genomic clines’ are limited.

Here, we introduce the ClinePlotR R-package for visualizing genomic clines and detecting outlier loci using output generated by two popular software packages, bgc and Introgress.

ClinePlotR bundles both input generation (i.e, filtering datasets and creating specialized file formats) and output processing (e.g., MCMC thinning and burn-in) with functions that directly facilitate interpretation and hypothesis testing. Tools are also p...

OSU_SnowCourse Summary: Manual snow course observations were collected over WY 2012-2014 from four paired forest-open sites chosen to span a broad elevation range. Study sites were located in the upper McKenzie (McK) River watershed, approximately 100 km east of Corvallis, Oregon, on the western slope of the Cascade Range and in the Middle Fork Willamette (MFW) watershed, located to the south of the McKenzie. The sites were designated based on elevation, with a range of 1110-1480 m. Distributed snow depth and snow water equivalent (SWE) observations were collected via monthly manual snow courses from 1 November through 1 April and bi-weekly thereafter. Snow courses spanned 500 m of forested terrain and 500 m of adjacent open terrain. Snow depth observations were collected approximately every 10 m and SWE was measured every 100 m along the snow courses with a federal snow sampler. These data are raw observations and have not been quality controlled in any way. Distance along the transect was estimated in the field. OSU_SnowDepth Summary: 10-minute snow depth observations collected at OSU met stations in the upper McKenzie River Watershed and the Middle Fork Willamette Watershed during Water Years 2012-2014. Each meterological tower was deployed to represent either a forested or an open area at a particular site, and generally the locations were paired, with a meterological station deployed in the forest and in the open area at a single site. These data were collected in conjunction with manual snow course observations, and the meterological stations were located in the approximate center of each forest or open snow course transect. These data have undergone basic quality control. See manufacturer specifications for individual instruments to determine sensor accuracy. This file was compiled from individual raw data files (named "RawData.txt" within each site and year directory) provided by OSU, along with metadata of site attributes. We converted the Excel-based timestamp (seconds since origin) to a date, changed the NaN flags for missing data to NA, and added site attributes such as site name and cover. We replaced positive values with NA, since snow depth values in raw data are negative (i.e., flipped, with some correction to use the height of the sensor as zero). Thus, positive snow depth values in the raw data equal negative snow depth values. Second, the sign of the data was switched to make them positive. Then, the smooth.m (MATLAB) function was used to roughly smooth the data, with a moving window of 50 points. Third, outliers were removed. All values higher than the smoothed values +10, were replaced with NA. In some cases, further single point outliers were removed. OSU_Met Summary: Raw, 10-minute meteorological observations collected at OSU met stations in the upper McKenzie River Watershed and the Middle Fork Willamette Watershed during Water Years 2012-2014. Each meterological tower was deployed to represent either a forested or an open area at a particular site, and generally the locations were paired, with a meterological station deployed in the forest and in the open area at a single site. These data were collected in conjunction with manual snow course observations, and the meteorological stations were located in the approximate center of each forest or open snow course transect. These stations were deployed to collect numerous meteorological variables, of which snow depth and wind speed are included here. These data are raw datalogger output and have not been quality controlled in any way. See manufacturer specifications for individual instruments to determine sensor accuracy. This file was compiled from individual raw data files (named "RawData.txt" within each site and year directory) provided by OSU, along with metadata of site attributes. We converted the Excel-based timestamp (seconds since origin) to a date, changed the NaN and 7999 flags for missing data to NA, and added site attributes such as site name and cover. OSU_Location Summary: Location Metadata for manual snow course observations and meteorological sensors. These data are compiled from GPS data for which the horizontal accuracy is unknown, and from processed hemispherical photographs. They have not been quality controlled in any way.

This dataset builds upon "Financial Statement Data Sets" by incorporating several key improvements to enhance the accuracy and usability of US-GAAP financial data from SEC filings of U.S. exchange-listed companies. Drawing on submissions from January 2009 onward, the enhanced dataset aims to provide analysts with a cleaner, more consistent dataset by addressing common challenges found in the original data.

Key Enhancements:

1. Outlier Detection and Correction: Outliers in the original dataset have been systematically identified and corrected, providing more reliable financial figures.
2. Amendment Adjustments: In cases where SEC rules allow amendment filings to only include delta figures, full figures from the original submissions have been carried over for consistency, facilitating more straightforward analysis.
3. Missing Figure Estimation: Using calculation arcs from the US-GAAP taxonomy, missing financial figures have been computed where possible, ensuring greater completeness.
4. Data Structuring: Financial figures that previously appeared as separate rows have been consolidated into single rows with new columns, offering a cleaner structure.

Scope:

• Data Scope: The dataset is restricted to figures reported under US-GAAP standards, with the exception of EntityCommonStockSharesOutstanding and EntityPublicFloat.
• Currency and Units: The dataset exclusively includes figures reported in USD or shares, ensuring uniformity and comparability. It excludes ratios and non-financial metrics to maintain focus on financial data.
• Company Selection: The dataset is limited to companies with U.S. exchange tickers, providing a concentrated analysis of publicly traded firms within the United States.
• Submission Types: The dataset only incorporates data from 10-Q, 10-K, 10-Q/A, and 10-K/A filings, ensuring consistency in the type of financial reports analyzed.

Dataset Features:

• Refined Financial Data: Accurate and consistent figures by addressing reporting issues, corrections for outliers, and data consolidation.
• Enhanced Usability: By handling amendment submissions and leveraging GAAP taxonomies, the dataset offers a more analysis-friendly structure.
• Improved Completeness: Where original submissions had gaps in reporting, this dataset fills those gaps using calculated figures based on accounting principles.

The source code for data extraction is available here

BackgroundThe recent advent of high-throughput SNP genotyping technologies has opened new avenues of research for population genetics. In particular, a growing interest in the identification of footprints of selection, based on genome scans for adaptive differentiation, has emerged.Methodology/Principal FindingsThe purpose of this study is to develop an efficient model-based approach to perform Bayesian exploratory analyses for adaptive differentiation in very large SNP data sets. The basic idea is to start with a very simple model for neutral loci that is easy to implement under a Bayesian framework and to identify selected loci as outliers via Posterior Predictive P-values (PPP-values). Applications of this strategy are considered using two different statistical models. The first one was initially interpreted in the context of populations evolving respectively under pure genetic drift from a common ancestral population while the second one relies on populations under migration-drift equilibrium. Robustness and power of the two resulting Bayesian model-based approaches to detect SNP under selection are further evaluated through extensive simulations. An application to a cattle data set is also provided.Conclusions/SignificanceThe procedure described turns out to be much faster than former Bayesian approaches and also reasonably efficient especially to detect loci under positive selection.