Fundamentals of Probability Theory
Plamen Parvanov Angelov · 2012
Probability theory is one of the methodologies to represent and tackle some types of uncertainties. The frequentistic approach considers the probability as a frequency of occurrence of an event. Obviously, the belief-based approach is more subjective, epistemiological, while the frequentistic approach is rooted in statistics. Probabilities are non-negative (since they represent frequencies) and are represented by probability densities. Kernel density estimation (KDE) is a generic approach where the conclusions apply to the whole data distribution but the kernels are drawn from a finite set of representative data samples. The recursive expressions of the recursive density estimation (RDE) are exact and apply for both global and local density. There is a solid body of literature concerning statistical approaches for novelty (respectively, anomalies, outliers) detection, but the approaches are predominantly offline or require expert knowledge. Controlled Vocabulary Terms probability; probability theory; recursive estimation