Mixture of Species Sampling Models

We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an exchangeable sequence to the classes of a latent exchangeable random partition. Using this representation, we give an explicit expression of the Exchangeable Partition Probability Function of the partition generated by an mSSS. Some special cases are discussed in detail—in particular, species sampling sequences with general base measures and a mixture of species sampling sequences with Gibbs-type latent partition. Finally, we give explicit expressions of the predictive distributions of an mSSS.

Study on Data Partition for Delimitation of Masses in Mammography

Mammography is the primary medical imaging method used for routine screening and early detection of breast cancer in women. However, the process of manually inspecting, detecting, and delimiting the tumoral massess in 2D images is a very time-consuming task, subject to human errors due to fatigue. Therefore, integrated computer-aided detection systems have been proposed, based on modern computer vision and machine learning methods. In the present work, mammogram images from the publicly available Inbreast dataset are first converted to pseudo-color and then used to train and test a Mask R-CNN deep neural network. The most common approach is to start with a dataset and split the images into train and test set randomly. However, since there are often two or more images of the same case in the dataset, the way the dataset is split may have an impact on the results. Our experiments show that random partition of the data can produce unreliable training, so the dataset must be split using case-wise partition for more stable results. In experimental results, the method achieves an average true positive rate of 0.936 with 0.063 standard deviation using random partition and 0.908 with 0.002 standard deviation using case-wise partition, showing that case-wise partition must be used for more reliable results.

Selection of Best Test Cases using Support Vector Machine for ARPT

Software testing is an essential activity in software industries for quality assurance; subsequently, it can be effectively removing defects before software deployment. Mostly good software testing strategy is to accomplish the fundamental testing objective while solving the trade-offs between effectiveness and efficiency testing issues. Adaptive and Random Partition software Testing (ARPT) approach was a combination of Adaptive Testing (AT) and Random Partition Approach (RPT) used to test software effectively. It has two variants they are ARPT-1 and ARPT-2. In ARPT-1, AT was used to select a certain number of test cases and then RPT was used to select a number of test cases before returning to AT. In ARPT-2, AT was used to select the first m test cases and then switch to RPT for the remaining tests. The computational complexity for random partitioning in ARPT was solved by cluster the test cases using a different clustering algorithm. The parameters of ARPT-1 and ARPT-2 needs to be estimated for different software, it leads to high computation overhead and time consumption. It was solved by Improvised BAT optimization algorithms and this approach is named as Optimized ARPT1 (OARPT1) and OARPT2. By using all test cases in OARPT will leads to high time consumption and computational overhead. In order to avoid this problem, OARPT1 with Support Vector Machine (OARPT1-SVM) and OARPT2- SVM are introduced in this paper. The SVM is used for selection of best test cases for OARPT-1 and OARPT-2 testing strategy. The SVM constructs hyper plane in a multi-dimensional space which is used to separate test cases which have high code and branch coverage and test cases which have low code and branch coverage. Thus, the SVM selects the best test cases for OARPT-1 and OARPT-2. The selected test cases are used in OARPT-1 and OARPT-2 to test software. In the experiment, three different software is used to prove the effectiveness of proposed OARPT1- SVM and OARPT2-SVM testing strategies in terms of time consumption, defect detection efficiency, branch coverage and code coverage.

Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization

This paper considers a method of the calculation of probability of the exit from a band of the solution of a stochastic differential equation. The method is based on the approximation of the solution of the considered equation by a process which is received as a concatenation of Gauss processes, random partition of the interval, Girsanov transform and Wiener-Hopf factorization, and the Monte-Carlo method. The errors of approximation are estimated. The proposed method is illustrated by numerical examples.