# Questions tagged [markov-random-field]

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Given the Bayesian network on the left hand side in the following figure, it shows that the random variable $B$ is dependent on $A$ and $C$, and the Bayesian network $G$ can be factorized as: $P(G) = ... 0answers 401 views ### How to implement a Gaussian Markov Random field (GMRF) model in R? I would like to model a (conditional) GMRF using a linear mixed effects model without having grid Data but only a neighbourhood matrix$W$. My model is given by $$Y=X\beta+ \epsilon$$ and the error ... 0answers 23 views ### Discriminative Models with Class Priors In discriminative models, we model$p(Y|X)$directly while in generative models we model$p(X|Y)p(Y)$where$X$is the input and$Y$is the output variable. I am confused when the parameters and ... 0answers 35 views ### How exactly does Gibbs sampling work in Markov Networks? I was going through the Probabilistic Graphical Modelling course by Stanford and they used a network such as this one-https://imgur.com/gallery/k0C8FY2 Now if we want to sample P(A|B), how would we ... 0answers 32 views ### Are self loops allowed in Markov networks? I am studying about Markov networks from Probabilistic Graphical Models: Principles and Techniques Book by Daphne Koller and Nir Friedman. In Bayesian networks, it is clear that, it is a directed ... 0answers 30 views ### References on simulating a raster with spatial dependence I've simulated an N-by-N raster in the following way: define a set$S$containing a finite number$|S| = K$of possible raster values (in my simulation,$K=3$and the elements of$S$are land uses / ... 0answers 519 views ### How to express Bayesian Network or Markov Random Field using deep learning Bayesian Nework and Makov random field are instances of general probabilistic graphical model. Is it possible to express Bayesian Network or Markov Random Field using deep learning? or in general to ... 0answers 12 views ### Models for interdependent finite sequences? I have a large set S of pairs of (short) sequences (, )_i where the first sequence of each pair comes from sequence set A and the second sequence of each pair comes from the sequence set B. Sequences ... 0answers 14 views ### Is every distribution factorizable by an MRF also factorizable via a Bayesian network? And vice versa? This has probably been asked before, so if it has please provide a link to the original question and close this as a duplicate -- I was not able to find the original question myself. Question: Let'... 0answers 21 views ### Is the Markov Network (Markov Random Field) property biconditional? As far as I know, the property of a Markov Random Field is defined as follows: Let$G = (V, E)$be a Markov Network. Let$X, Y, C \subseteq V$. If every path from a vertex in$X$to a vertex in$Y$... 0answers 255 views ### Factorization of a Markov random field Consider the Markov random field in the following figure, some literature and textbooks say that the MRF$G$can be factorized as$P_1(G) = \phi_1(A,B) \times \phi_2(A,C) \times \phi_3(C,D) \times \...
I'm reading the notes here. The formal definiton states A Markov Random Field (MRF) is a probability distribution $p$ over variables $x_1,\ldots,x_n$ defined by an undirected graph $G$ in which ...