The theory on Feynman-Kac particle methodologies and related particle filter algorithms was developed in 2000 and 2004 in the books. These abstract probabilistic models encapsulate genetic type algorithms, particle, and bootstrap filters, interacting Kalman filters (a.k.a. Rao–Blackwellized particle filter), importance sampling and resampling style particle filter techniques, including genealogical tree-based and particle backward methodologies for solving filtering and smoothing problems. Other classes of particle filtering methodologies include genealogical tree-based models, backward Markov particle models, adaptive mean-field particle models, island-type particle models, particle Markov chain Monte Carlo methodologies, Sequential Monte Carlo samplers and Sequential Monte Carlo Approximate Bayesian Computation methods and Sequential Monte Carlo ABC based Bayesian Bootstrap.