2016
DOI: 10.1007/s11222-016-9685-7
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Approximate computations for binary Markov random fields and their use in Bayesian models

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Cited by 9 publications
(8 citation statements)
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“…The first training image, shown in Figure 3(a), is a mortality map for liver and gallbladder cancers for white males between 1950 and 1959 in the eastern United States, analyzed by Riggan et al (1987). This data set is previously considered by Sherman et al (2006), Liang (2010) and Austad and Tjelmeland (2016) using Markov random field models, see also Liang et al (2011). In Figure 3(a) the black (y v = 1) and white (y v = 0) pixels represent counties with high and low cancer mortality rates, respectively.…”
Section: Methodsmentioning
confidence: 99%
“…The first training image, shown in Figure 3(a), is a mortality map for liver and gallbladder cancers for white males between 1950 and 1959 in the eastern United States, analyzed by Riggan et al (1987). This data set is previously considered by Sherman et al (2006), Liang (2010) and Austad and Tjelmeland (2016) using Markov random field models, see also Liang et al (2011). In Figure 3(a) the black (y v = 1) and white (y v = 0) pixels represent counties with high and low cancer mortality rates, respectively.…”
Section: Methodsmentioning
confidence: 99%
“…Still for HMRF, Friel et al (2009) proposed an algorithm for computing the likelihood which relies on the merging of exact computations on small sub-lattices of the original lattice. More recently, Austad & Tjelmeland (2017) applied variable elimination on an approximation of the pseudo Boolean expression of a MRF distribution.…”
Section: The Treewidth To Characterise Variable Elimination Complexitymentioning
confidence: 99%
“…In our algorithm for simulating from p(x 1:t |y 1:t ) we combine single site Gibbs updates of each element in x 1:t with a one-block Metropolis-Hastings update of all elements in x 1:t . To get a reasonable acceptance rate for the one-block proposals we adopt the approximation procedure introduced in Austad and Tjelmeland (2017) to obtain a partially ordered Markov model (Cressie and Davidson, 1998) approximation to p(x 1:t |y 1:t ), propose potential new values for x 1:t from this approximate posterior, and accept or reject the proposed values according to the usual Metropolis-Hastings acceptance probability. For each value of t we run the Metropolis-Hastings algorithm for a large number of iterations and discard a burn-in period.…”
Section: Specification Of Simulation Examplementioning
confidence: 99%