Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability matrices are difficult to estimate from sparse sample data and are impractical in representing the complex spatial heterogeneity of states, the transiogram, which is defined as a transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.
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mathematicians often use a Markovchain Monte Carlo (MCMC) sampler. The central idea is to design a judicious Markovchain model with a prescribed stationary...
constraining data. AVA geostatistical inversion software uses leading-edge geostatistical techniques, including Markovchain Monte Carlo (MCMC) sampling...
graphs are special cases of chain graphs, which can therefore provide a way of unifying and generalizing Bayesian and Markov networks. An ancestral graph...
Various other numerical methods based on fixed grid approximations, MarkovChain Monte Carlo techniques, conventional linearization, extended Kalman filters...
Gelfand who had been a pioneer in the development of the Gibbs sampler and Markovchain Monte Carlo algorithms in Bayesian statistics. Banerjee joined the University...
variables. The use of Bayesian hierarchical modeling in conjunction with Markovchain Monte Carlo (MCMC) methods have recently shown to be effective in modeling...
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can also be estimated through the use of simulation techniques such as Markovchain Monte Carlo. A frequentist 95% confidence interval means that with a...
analytic form: in this case, the distribution can be simulated using Markovchain Monte Carlo techniques, while optimization to find its mode(s) may be...
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procedures tend to be computationally expensive and, in the days before Markovchain Monte Carlo computations were developed, approximations for Bayesian...
be approximated, usually using Laplace approximations or some type of Markovchain Monte Carlo method such as Gibbs sampling. A possible point of confusion...
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variable Bernoulli process Continuous or discrete Expected value Variance Markovchain Observed value Random walk Stochastic process Complementary event Joint...
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