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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.
Different Machine Learning Models
Published in Neeraj Kumar, Aaisha Makkar, Machine Learning in Cognitive IoT, 2020
Bayesian methods use the data analysis process to reduce the property of the underlying probability distribution. Bayes theorem is used to update the probability of a hypothesis as information becomes more available. Sequential analysis is used to update the data. The equation is stated as below: P(x|y)=P(y|x)P(x)P(y)
Bayesian optimisation of part orientation in additive manufacturing
Published in International Journal of Computer Integrated Manufacturing, 2021
Steven Goguelin, Vimal Dhokia, Joseph M. Flynn
Bayes theorem, a representation of which is shown in (4), is the key to optimising an objective function. Bayes theorem states that the posterior probability of a model, , given evidence, , is proportional to the likelihood of given , multiplied by the prior probability of . The prior represents the belief relating to the feasible space of the objective function. Although this is unknown, it is possible to make assumptions about its nature, which makes some solutions more feasible than others.
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.