Paraconsistent Sensitivity Analysis for Bayesian Significance Tests

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed

Paraconsistent probabilities: consistency, contradictions and bayes' theorem

2010/51038-0sem informaçãoThis paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.This paper represents the first steps towards constructing a paraconsistent theory of probability based on the logics of formal inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.189FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICO2010/51038-0sem informaçã

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes

The Rules of Logic Composition for the Bayesian Epistemic e-Values

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectivel

The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

This article gives a conceptual review of the e-value, ev(H|X) – the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory

Performance Evaluation of Network Anomaly Detection Systems

Nowadays, there is a huge and growing concern about security in information and communication technology (ICT) among the scientific community because any attack or anomaly in the network can greatly affect many domains such as national security, private data storage, social welfare, economic issues, and so on. Therefore, the anomaly detection domain is a broad research area, and many different techniques and approaches for this purpose have emerged through the years. Attacks, problems, and internal failures when not detected early may badly harm an entire Network system. Thus, this thesis presents an autonomous profile-based anomaly detection system based on the statistical method Principal Component Analysis (PCADS-AD). This approach creates a network profile called Digital Signature of Network Segment using Flow Analysis (DSNSF) that denotes the predicted normal behavior of a network traffic activity through historical data analysis. That digital signature is used as a threshold for volume anomaly detection to detect disparities in the normal traffic trend. The proposed system uses seven traffic flow attributes: Bits, Packets and Number of Flows to detect problems, and Source and Destination IP addresses and Ports, to provides the network administrator necessary information to solve them. Via evaluation techniques, addition of a different anomaly detection approach, and comparisons to other methods performed in this thesis using real network traffic data, results showed good traffic prediction by the DSNSF and encouraging false alarm generation and detection accuracy on the detection schema. The observed results seek to contribute to the advance of the state of the art in methods and strategies for anomaly detection that aim to surpass some challenges that emerge from the constant growth in complexity, speed and size of today’s large scale networks, also providing high-value results for a better detection in real time.Atualmente, existe uma enorme e crescente preocupação com segurança em tecnologia da informação e comunicação (TIC) entre a comunidade científica. Isto porque qualquer ataque ou anomalia na rede pode afetar a qualidade, interoperabilidade, disponibilidade, e integridade em muitos domínios, como segurança nacional, armazenamento de dados privados, bem-estar social, questões econômicas, e assim por diante. Portanto, a deteção de anomalias é uma ampla área de pesquisa, e muitas técnicas e abordagens diferentes para esse propósito surgiram ao longo dos anos. Ataques, problemas e falhas internas quando não detetados precocemente podem prejudicar gravemente todo um sistema de rede. Assim, esta Tese apresenta um sistema autônomo de deteção de anomalias baseado em perfil utilizando o método estatístico Análise de Componentes Principais (PCADS-AD). Essa abordagem cria um perfil de rede chamado Assinatura Digital do Segmento de Rede usando Análise de Fluxos (DSNSF) que denota o comportamento normal previsto de uma atividade de tráfego de rede por meio da análise de dados históricos. Essa assinatura digital é utilizada como um limiar para deteção de anomalia de volume e identificar disparidades na tendência de tráfego normal. O sistema proposto utiliza sete atributos de fluxo de tráfego: bits, pacotes e número de fluxos para detetar problemas, além de endereços IP e portas de origem e destino para fornecer ao administrador de rede as informações necessárias para resolvê-los. Por meio da utilização de métricas de avaliação, do acrescimento de uma abordagem de deteção distinta da proposta principal e comparações com outros métodos realizados nesta tese usando dados reais de tráfego de rede, os resultados mostraram boas previsões de tráfego pelo DSNSF e resultados encorajadores quanto a geração de alarmes falsos e precisão de deteção. Com os resultados observados nesta tese, este trabalho de doutoramento busca contribuir para o avanço do estado da arte em métodos e estratégias de deteção de anomalias, visando superar alguns desafios que emergem do constante crescimento em complexidade, velocidade e tamanho das redes de grande porte da atualidade, proporcionando também alta performance. Ainda, a baixa complexidade e agilidade do sistema proposto contribuem para que possa ser aplicado a deteção em tempo real

FBST for a Generalized Poisson Distribution.

The Generalized Poisson Distribution (GPD) adds an extra parameter to the usual Poisson distribution. This parameter induces a loss of homogeneity in the stochastic processes modeled by the distribution. Thus, the generalized distribution becomes an useful model for counting processes where the occurrence of events is not homogeneous. This model creates the need for an inferential procedure, to test for the value of this extra parameter. The FBST (Full Bayesian Significance Test) is a Bayesian hypotheses test procedure, capable of providing an evidence measure on sharp hypotheses (where the dimension of the parametric space under the null hypotheses is smaller than that of the full parametric space). The goal of this work is study the empirical properties of the FBST for testing the nullity of extra parameter of the generalized Poisson distribution. Numerical experiments show a better performance of FBST with respect to the classical likelihood ratio test, and suggest that FBST is an efficient and robust tool for this application

Testing Significance in Bayesian Classifiers.

The Fully Bayesian Significance Test (FBST) is a coherent Bayesian significance test for sharp hypotheses. This paper explores the FBST as a model selection tool for general mixture models, and gives some computational experiments for Multinomial-Dirichlet-Normal-Wishart models