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Basic Approaches of Artificial Intelligence and Machine Learning in Thermal Image Processing
Published in U. Snekhalatha, K. Palani Thanaraj, Kurt Ammer, Artificial Intelligence-Based Infrared Thermal Image Processing and Its Applications, 2023
U. Snekhalatha, K. Palani Thanaraj, Kurt Ammer
This algorithm is based on the Bayes theorem which is based on the concept of conditional probability. Conditional probability is the estimation of the probability of one event, given that another one has already occurred. The Naïve Bayes is the fastest algorithm when compared to other algorithm techniques and is also relatively simple and easy to implement. This algorithm needs a small amount of training data to evaluate the necessary parameters. The Bayes algorithm is a supervised learning algorithm. It is possible to apply it in both binary and multiclass classifications. The Bayes algorithm can be mathematically represented as follows: Pa|y=py|apa/Py where p(y|a) = Likelihood, p(a) = Class prior probability, P(a|y) = Posterior probability, and P(y) = Predictor probability.
Basics of probability and statistics
Published in Amit Kumar Gorai, Snehamoy Chatterjee, Optimization Techniques and their Applications to Mine Systems, 2023
Amit Kumar Gorai, Snehamoy Chatterjee
Conditional probability is the probability of occurrence of one event with some relationship to (conditioning to) one or more other events. For two events A and B with P(B)>0, the conditional probability of A and B, P(A|B) is defined as P(A|B)=P(A∩B)P(B),P(B)>0
Basics of Probability
Published in Aliakbar Montazer Haghighi, Indika Wickramasinghe, Probability, Statistics, and Stochastic Processes for Engineers and Scientists, 2020
Aliakbar Montazer Haghighi, Indika Wickramasinghe
Bayes’ theorem may be interpreted as the relationship between the probability of the hypothesis, say an event A, before obtaining an evidence, E, that is, P(A), the prior probability, and the probability of the hypothesis after obtaining the evidence, that is, the conditional probability of A, given E, P(A|E), the posterior probability, which is as follows: P(A|E)=P(E|A)P(E)⋅P(A).
Towards the cognitive and psychological perspectives of crowd behaviour: a vision-based analysis
Published in Connection Science, 2021
Elizabeth B. Varghese, Sabu M. Thampi
Bayesian approaches are based on the prominent theorem in probability known as the Bayes' theorem which states that the probability of the occurrence of an event depends on the conditional probability of the prior knowledge of the event. For a given hypothesis H, and event E, the Bayes' theorem is stated as: where and are conditional probabilities. The theorem is analogous to human mind that consists of conditional probabilities and statistical correlations that can predict an event based on statistical representations and probability calculations (Jiang et al., 2017). The Bayesian theorem was utilised in analysing crowd behaviour in the field of computer vision and is discussed below.
Improved calibration of building models using approximate Bayesian calibration and neural networks
Published in Journal of Building Performance Simulation, 2023
Statistical inference is about trying to learn what we cannot easily observe through what we can observe. Statistical inference can be performed using Bayesian modelling, which integrates prior knowledge that gets conditioned on observations in a statistically consistent manner. Bayesian modelling is founded on Bayes' theorem, which is based on conditional probability: the likelihood of an event happening due to the occurrence of a separate event or outcome. Bayes' theorem is stated mathematically as: In this generic case, θ is a parameter, or set of parameters of a model and D is observed data. Hereinafter, the term is referred to as the posterior, the term is referred to as the likelihood, the term is referred to as the evidence, and the term is referred to as the prior. In the context of building energy model calibration, the parameters are characteristics of the building that are difficult to ascertain. The likelihood is the probability to obtain the data D with the parameters θ. The priors incorporate the existing knowledge of the parameters before inference, usually from a combination of subject matter expertise, existing drawings or reports, or previously measured or inferred data. The evidence takes the form of a scaling factor which is used to ensure the posterior is a proper probability distribution with a summation of 1 (van de Schoot et al. 2021).
A computerized hybrid Bayesian-based approach for modelling the deterioration of concrete bridge decks
Published in Structure and Infrastructure Engineering, 2019
Eslam Mohammed Abdelkader, Tarek Zayed, Mohamed Marzouk
DAGs are graphs, where the links have directions and do not form cycles, whereas the nodes represent the random variables of interest, and each node is associated with several possible states. The relationships between the nodes in the BBN are demonstrated in the form of family relationships, whereas and are regarded as parents of and is considered as the child of both and if a link goes from to and to The steps of formulating the BBN are as follows (Siraj et al., 2015): Identifying the random variables that are needed to model the problem of interest such asEstablishing the casual interrelationships between the nodes, whereas is dependent on both and as shown in Figure 2. A link between two variables indicates that there is direct dependence between the two variables, whereas one of them is called a ‘parent’ while the other is called a ‘child’.Assigning a set of mutually exclusive states to each variable as well as the probability of each state such as very poor, poor, medium, and good. For instance, if random variable is associated with four states, the sum of the probabilities equals to one.Quantifying the conditional probability, which is the probability of occurrence of a certain event given that another event has occurred. The conditional probability allows the quantification of the influence of the parent node on the desired node. For the parent nodes, there are no conditional probabilities and they are only given marginal probabilities.