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A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6]
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution.Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution.
These models can also be seen as the evolution of the law of the random states of a nonlinear Markov chain. [10] [11] A natural way to simulate these sophisticated nonlinear Markov processes is to sample multiple copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical ...
GNU MCSim is a suite of simulation software. It allows one to design one's own statistical or simulation models, perform Monte Carlo simulations, and Bayesian inference through (tempered) Markov chain Monte Carlo simulations. The latest version allows parallel computing of Monte Carlo or MCMC simulations.
The simplest Markov model is the Markov chain.It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state.
One natural way to approximate these evolution equations is to reduce sequentially the state space using a mean field particle model. One of the simplest mean field simulation scheme is defined by the Markov chain = ((,),, (,))
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix.
A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.