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Syntax. A Markov logic network consists of a collection of formulas from first-order logic, to each of which is assigned a real number, the weight. The underlying idea is that an interpretation is more likely if it satisfies formulas with positive weights and less likely if it satisfies formulas with negative weights. [6]
For example, in the infinite ferromagnetic Ising model below the critical temperature, there are two pure states, the "mostly-up" and "mostly-down" states, which are interchanged under the model's symmetry. Markov property. An example of the Markov property can be seen in the Gibbs measure of the Ising model.
The Swiss cheese model of accident causation is a model used in risk analysis and risk management, including aviation safety, engineering, healthcare, emergency service organizations, and as the principle behind layered security, as used in computer security and defense in depth. It likens human systems to multiple slices of Swiss cheese, which ...
P (¬H) = 1−P (H) 1. Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem : where.
Hamiltonian Monte Carlo. The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples which converge to being distributed according to a target probability distribution for which direct sampling is difficult. This sequence can be used to estimate ...
The original derivation of the equations by Kolmogorov starts with the Chapman–Kolmogorov equation (Kolmogorov called it fundamental equation) for time-continuous and differentiable Markov processes on a finite, discrete state space. [2] In this formulation, it is assumed that the probabilities are continuous and differentiable functions of ...
Markovian arrival process. In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process ( MAP or MArP [1]) is a mathematical model for the time between job arrivals to a system. The simplest such process is a Poisson process where the time between each arrival is exponentially distributed.
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. HMM models are widely used in speech recognition, for translating a time series of spoken words into text.