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Statistical Testing of Residuals
Published in Janos J. Gertler, Fault Detection and Diagnosis in Engineering Systems, 2017
Straight comparison of likelihoods. The basic likelihood ratio concept calls for the straight comparison of conditional likelihoods obtained under the various hypotheses. The comparison may be performed pairwise, considering two hypotheses at a time, or globally, considering all. Using the conditional log-likelihood functions, the pairwise decision rule is () iflogLi(t)>logLj(t)thenHiisacceptedoverHj
Reasoning on Technology Uncertainties for Enterprise Transformation
Published in Kenneth C. Hoffman, Christopher G. Glazner, William J. Bunting, Leonard A. Wojcik, Anne Cady, Enterprise Dynamics Sourcebook, 2013
LSERA uses probability likelihood ratios to measure the force of individual items of evidence and the influence of evidence across the argument. The likelihood ratio is simply the ratio of the likelihood of a piece of evidence (e∗) existing if something (call it H) occurred, divided by the likelihood of e∗ existing if H did not occur (Hc). Evidential force (shown as Le∗) using the likelihood ratio is Le*=P(e*|H)/P(e*|Hc).
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Published in Alexander D. Poularikas, Stergios Stergiopoulos, Advanced Signal Processing, 2017
The detection problem, that is, the problem of detecting an information-bearing signal in noise, may be viewed as one of hypothesis testing with deep roots in statistical decision theory (Van Trees, 1968). In the statistical formulation of hypothesis testing, there are two criteria of most interest: the Bayes criterion and the Neyman–Pearson criterion. In the Bayes test, we minimize the average cost or risk of the experiment of interest, which incorporates two sets of parameters: (1) a priori probabilities that represent the observer’s information about the source of information before the experiment is conducted; and (2) a set of costs assigned to the various possible courses of action. As such, the Bayes criterion is directly applicable to digital communications. In the Neyman–Pearson test, on the other hand, we maximize the probability of detection subject to the constraint that the probability of false alarm does not exceed some preassigned value. Accordingly, the Neyman–Pearson criterion is directly applicable to radar or sonar. An idea of fundamental importance that emerges in hypothesis testing is that for a Bayes criterion or Neyman–Pearson criterion, the optimum test consists of two distinct operations: (1) processing the observed data to compute a test statistic called the likelihood ratio and (2) computing the likelihood ratio with a threshold to make a decision in favor of one of the two hypotheses. The choice of one criterion or the other merely affects the value assigned to the threshold. Let H1 denote the hypothesis that the observed data consist of noise alone, and let H2 denote the hypothesis that the data consist of signal plus noise. The likelihood ratio is defined as the ratio of two maximum likelihood functions, with the numerator assuming that hypothesis H2 is true and the denominator assuming that hypothesis H1 is true. If the likelihood ratio exceeds the threshold, the decision is made in favor of hypothesis H2; otherwise, the decision is made in favor of hypothesis H1.
LDPC Codes and Digital Forensics – A Perspective Approach
Published in IETE Journal of Research, 2022
Computer forensics deal with the investigation of computer crime pertaining to legal evidence found in computers and digital storage media. The interdisciplinary field of Computer forensics is Computational criminology which defines criminology concepts and generates solutions for the complex phenomena, using the back-up thrust of quantitative approach of computing science methods relating to Computational forensics (CF). The research investigation and problem definition methods of Computer forensics span over computer-based modeling, simulation, and analysis based on pattern evidences, such as tool marks, fingerprints, shoe prints, documents, DNA patterns, digital evidence, and crime scenes. One of the Computational methods is the definition and establishment of likelihood ratio (LR) that can be applied in the forensic sciences to increase the efficiency and effectiveness of forensic casework.
A statistical study on lognormal central tendency estimation in probabilistic seismic assessments
Published in Structure and Infrastructure Engineering, 2020
Mohamad Zarrin, Mohsen Abyani, Behrouz Asgarian
In the simplest case, when the two hypotheses are single distributions with no free parameters the likelihood ratio is equal to Bayes factor (Kass & Raftery, 1995). The Bayes factor is a reliable evidence provided by the data either in favour of one hypothesis or against it, which may have different interpretations (Jeffreys, 1961).
ASDC-Net: Optimized Convolutional Neural Network-Based Automatic Autism Spectrum Disorder Classification Using rs-fMRI Data
Published in IETE Journal of Research, 2023
Anjali Chandra, Shrish Verma, Ajay Singh Raghuvanshi, Narendra Kuber Bodhey
The diagnostic process focuses mainly on the probability of a diseased person rather than the test's Sen and Spe values. Such probabilities are negative and positive predictive values (NPV, PPV). The PPV and NPV are formulated as given in Eq. (31–32): The diagnostic odds ratio is also one of the metrics used to assess a diagnostic test's overall performance [41]. The odds ratio in diagnostic tests is defined as the odds of a test being positive among diseased subjects relative to the odds in subjects without the disease. It is a metric that is not influenced by prevalence and is represented as shown in Eq. (33). For each increase in the odds ratio, the discriminative power also increases. Youden Index (Y.I.) is also a parameter for measuring the diagnostic test's overall performance [41]. It reveals how positive the test results are in the diseased population compared to the healthy populations. The Youden index has a value range of 0–1. As the test gets closer to 0, it has poor discrimination performance, and as it gets closer to 1, it indicates the opposite. It can also compare multiple diagnostic tests given by Eq. (34). In this paper, Y.I. has also been evaluated to compare the performance of the diagnostic model. A likelihood ratio is a test performance metric that combines sensitivity and specificity. The positive likelihood ratio and the negative likelihood ratio are two different measures and are represented as shown in Eq. (35–36) The geometric mean of the problem's regression coefficients and its dual is represented by the MCC [29]. This correlation coefficient ranges between −1 and +1 between the actual and expected instances. A value of −1 denotes a discrepancy between the actual and predicted values, while a value of +1 denotes a perfect prediction, as given in Eq. (37).