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Picometer Detection by Adaptive Holographic Interferometry
Published in Klaus D. Sattler, Fundamentals of PICOSCIENCE, 2013
The Bayesian probability used in Bayesian inference is an interpretation of the probability. It is conceptually different from the common frequency probability interpretation, whose value is determined only after an infinite number of trials and is therefore independent of the limitation of knowledge we can use at a certain moment. Bayesian probability takes into account the limitation of knowledge, and hence it can sometimes treat an object that is usually treated as non-probabilistic. For example, based on the Bayesian probability interpretation, Laplace said that the mass of Saturn is 1/3512 that of the Sun and that the odds are 1:11,000 that his estimate is off by more than 1% of the computed mass of Saturn [9]. Although the mass of Saturn is a fixed value, 1/3499 of the mass of the Sun, the uncertainty due to the limitation of his knowledge was treated as the probability distribution in the Bayesian probability interpretation. Another characteristic example is distorted dice. Think about a distorted six-sided die. What is the probability of getting six? When we use the frequency probability, we can say nothing based on only this information. When we use the Bayesian probability, the probability is one-sixth. This value is refined when we obtain additional information.
Machine Learning Basics
Published in Fei Hu, Qi Hao, Intelligent Sensor Networks, 2012
Krasimira Kapitanova, Sang H. Son
Bayesian probability interprets the concept of probability as degree of belief. A Bayesian classifier analyzes the feature vector describing a particular input instance and assigns the instance to the most likely class. A Bayesian classifier is based on applying Bayes’ theorem to evaluate the likelihood of particular events. Bayes’ theorem gives the relationship between the prior and posterior beliefs for two events. In Bayes’ theorem, P(A) is the prior initial belief in A. P(A∣B) is the posterior belief in A, after B has been encountered, i.e., the conditional probability of A given B. Similarly for B, P(B) is the prior initial belief in A, and P(B∣A) is the posterior belief in B given A. Assuming that P(B)≠0,Bayes′theoremstatesthatP(A|B)=P(B|A)P(A)P(B)
Adaptation of fan motor and VFD efficiency correlations using Bayesian inference
Published in Science and Technology for the Built Environment, 2019
Lisa Rivalin, Marco Pritoni, Pascal Stabat, Dominique Marchio
Bayesian inference is a method to update a knowledge-based model with experimental observations (Gregory 2005). The Bayesian probability is seen as a “degree of belief” of the phenomena (O’Hagan 2004) which is revised if new information (observation) is provided. Thus, “uncertainty” in the Bayesian paradigm can describe both the lack of knowledge of a parameter and its variability. In practice, to set a Bayesian calibration, a model linking data to parameters is build. Then, a formulation of uncertainty knowledge about the parameters is provided “a priori”. The model is combined with experimental values through the Bayes formula to obtain the “a posteriori” distribution (Parent and Bernier 2007). Bayesian inference can be seen as an inversion problem as it permits to understand the causes through the effects given by the observation (Robert 2007).