To P or not to P: on the evidential nature of P-values and their place in scientific inference

The customary use of P-values in scientific research has been attacked as being ill-conceived, and the utility of P-values has been derided. This paper reviews common misconceptions about P-values and their alleged deficits as indices of experimental evidence and, using an empirical exploration of the properties of P-values, documents the intimate relationship between P-values and likelihood functions. It is shown that P-values quantify experimental evidence not by their numerical value, but through the likelihood functions that they index. Many arguments against the utility of P-values are refuted and the conclusion is drawn that P-values are useful indices of experimental evidence. The widespread use of P-values in scientific research is well justified by the actual properties of P-values, but those properties need to be more widely understood.Comment: 31 pages, 9 figures and R cod

A method of classification for multisource data in remote sensing based on interval-valued probabilities

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method

Evidential Label Propagation Algorithm for Graphs

Community detection has attracted considerable attention crossing many areas as it can be used for discovering the structure and features of complex networks. With the increasing size of social networks in real world, community detection approaches should be fast and accurate. The Label Propagation Algorithm (LPA) is known to be one of the near-linear solutions and benefits of easy implementation, thus it forms a good basis for efficient community detection methods. In this paper, we extend the update rule and propagation criterion of LPA in the framework of belief functions. A new community detection approach, called Evidential Label Propagation (ELP), is proposed as an enhanced version of conventional LPA. The node influence is first defined to guide the propagation process. The plausibility is used to determine the domain label of each node. The update order of nodes is discussed to improve the robustness of the method. ELP algorithm will converge after the domain labels of all the nodes become unchanged. The mass assignments are calculated finally as memberships of nodes. The overlapping nodes and outliers can be detected simultaneously through the proposed method. The experimental results demonstrate the effectiveness of ELP.Comment: 19th International Conference on Information Fusion, Jul 2016, Heidelber, Franc

Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models

Land cover classification using fuzzy rules and aggregation of contextual information through evidence theory

Land cover classification using multispectral satellite image is a very challenging task with numerous practical applications. We propose a multi-stage classifier that involves fuzzy rule extraction from the training data and then generation of a possibilistic label vector for each pixel using the fuzzy rule base. To exploit the spatial correlation of land cover types we propose four different information aggregation methods which use the possibilistic class label of a pixel and those of its eight spatial neighbors for making the final classification decision. Three of the aggregation methods use Dempster-Shafer theory of evidence while the remaining one is modeled after the fuzzy k-NN rule. The proposed methods are tested with two benchmark seven channel satellite images and the results are found to be quite satisfactory. They are also compared with a Markov random field (MRF) model-based contextual classification method and found to perform consistently better.Comment: 14 pages, 2 figure

BPEC: Belief-Peaks Evidential Clustering

International audienceThis paper introduces a new evidential clustering method based on the notion of "belief peaks" in the framework of belief functions. The basic idea is that all data objects in the neighborhood of each sample provide pieces of evidence that induce belief on the possibility of such sample to become a cluster center. A sample having higher belief than its neighbors and located far away from other local maxima is then characterized as cluster center. Finally, a credal partition is created by minimizing an objective function with the fixed cluster centers. An adaptive distance metric is used to fit for unknown shapes of data structures. We show that the proposed evidential clustering procedure has very good performance with an ability to reveal the data structure in the form of a credal partition, from which hard, fuzzy, possibilistic and rough partitions can be derived. Simulations on synthetic and real-world datasets validate our conclusions