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Cross-Domain Analysis of Social Data and the Effect of Valence Shifters
Published in Balwinder Raj, Brij B. Gupta, Jeetendra Singh, Advanced Circuits and Systems for Healthcare and Security Applications, 2023
Naïve-Bayesian is a classification algorithm based on the Bayes theorem. The Bayes theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. In Naïve-Bayesian, no relatedness is considered between two features that is why it is called naïve. This algorithm is considered best for text classification and is capable of giving tough competition to much more complex methods such as support vector machines. In Naïve-Bayesian, we calculate posterior probability. It can be simply defined with the following equation: PCX=PX(C)P(C)p(X)
Tracking Regime Changes Using Directional Change Indicators
Published in Jun Chen, Edward P K Tsang, Detecting Regime Change in Computational Finance, 2020
In statistics, the Bayes’ theorem is used to describe the probability of an event, based on prior knowledge of conditions that might be related to the event. Based on the Bayes’ theorem, the NBC allows us to calculate the conditional probability of the current market being in a particular regime, based on the information of previous regime changes. Using Bayes’ theorem, the NBC is established as follows: p(Ck|x)=p(Ck)p(x|Ck)p(x), where p(Ck) is the prior probability of class k, p(x|Ck) is the conditional probability of each input data given the class label, and p(x) is the prior probability of the data.
Significance of Greenhouse Gas Measurement for Carbon Management Technologies
Published in Subhas K Sikdar, Frank Princiotta, Advances in Carbon Management Technologies, 2020
Bayesian inference methods are applied to estimation of GHG fluxes and their dynamics across global, continental, regional, or urban modeling domains. The observed quantity is the GHG concentration. Statistical optimization methods are based on Bayes’ concept that the probability associated with an event, or initial data set, can be updated by additional information. Stated more formally, Bayesian inference is a method of statistical inference based upon Bayes’ theorem,8 where it is assumed that the probability for a hypothesis can be modified or updated as more evidence or information becomes available. In the case of evidence-based GHG flux estimation, an initial estimate, termed a prior, is updated by additional observations in order to inform or refine the prior estimate with more information and construct a posterior flux estimate. In estimating urban source and sink fluxes, the hypothesis is based upon emissions inventory data for the region of interest. In some cases, an analysis may begin with a so-called “flat prior” that might be derived from a whole-city emission estimate which is then sub-divided equally among the surface grid cells of the NWP applied domain, as illustrated in Figure 4.
Bayesian estimate of the elastic modulus of concrete box girders from dynamic identification: a statistical framework for the A24 motorway in Italy
Published in Structure and Infrastructure Engineering, 2021
Angelo Aloisio, Dag Pasquale Pasca, Rocco Alaggio, Massimo Fragiacomo
Bayes’ theorem describes the probability of an event, based on prior knowledge of conditions possibly related to the event (Aloisio, Battista, Alaggio, Antonacci, & Fragiacomo, 2020; Gelman et al., 2013). The probability of having the EM below a given value indicated as updated to the experimental evidence from dynamic tests can be written as: where is the posterior probability, that is, the probability of observing if the expected first natural frequency f is below the measured one is the likelihood distribution, that is, the probability of observing natural frequencies f below is the prior distribution, that is, the probability of observing E below is the marginal likelihood.
Dynamic reliability analysis for residual life assessment of corroded subsea pipelines
Published in Ships and Offshore Structures, 2021
Reza Aulia, Henry Tan, Srinivas Sriramula
Bayesian network modelling is a probabilistic approach representing the relationships between causes and consequences, and their conditional interdependencies through a directed acyclic graph. Whereas Bayesian inference is a statistical method in which Bayes’ theorem is utilised to update the probability for a hypothesis as more evidence or observed data information becomes available. This method is very effective for modelling situations where some information is uncertain or partially unavailable and incoming data is already known. Figure 1 shows a simple Bayesian network consisting of three nodes, i.e. H2S concentration and CO2 partial pressure as the parent nodes and internal corrosion causes as the child node. Each node represents a probability distribution, which may in principle be continuous or discrete, and captures the probability distribution conditional on its direct predecessors (parents), also known as conditional probability table (CPT). The CPT is defined as a set of discrete (not independent) random variables to demonstrate marginal probabilities of each variable with respect to the others. According to Shabarchin and Tesfamariam (2016), the conditional probabilities can be quantified by using information obtained from the field data, expert opinion, analytical model or a combination of all.
Assuring design using Bayesian Networks to support quantifying knowledge and evidence
Published in Australian Journal of Multi-Disciplinary Engineering, 2019
The basis of Bayes Theorem is the updating of output estimates based upon new and updated information. When developing our knowledge of systems, we are looking to obtain new and updated information as a matter of course. Bayes Theorem is a probabilistic modelling paradigm that allows the incorporation of this information into the model as new information is obtained, which in turn supports making more informed decisions. That is, the gap between what is unknown and what is known is reduced based upon updated information. This process is variously known as Bayesian inference, Bayesian analysis, Bayesian statistics, Bayesian modelling, and is also sometimes referred to simply as Common Sense Reasoning (Stone 2013).