Related papers: Sensitivity Analysis of the MCRF Model to Differen…

The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies…

Models of spatial transition probabilities, or equivalently, transiogram models have been recently proposed as spatial continuity measures in categorical fields. In this paper, properties of transiogram models are examined analytically, and…

This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…

Key challenges in the analysis of highly multivariate large-scale spatial stochastic processes, where both the number of components (p) and spatial locations (n) can be large, include achieving maximal sparsity in the joint precision…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

The application of the Markov chain to modeling agricultural succession is well known. In most cases, the main problem is the inference of the model, i.e. the estimation of the transition matrix. In this work we present methods to estimate…

The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and…

I consider the use of Markov random fields (MRFs) on a fine grid to represent latent spatial processes when modeling point-level and areal data, including situations with spatial misalignment. Point observations are related to the grid cell…

Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov Chain Monte Carlo (rjMCMC), it is possible to vary this…

MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…

Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and…

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer…

Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical…

For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important…

Metric graphs are useful tools for describing spatial domains like road and river networks, where spatial dependence act along the network. We take advantage of recent developments for such Gaussian Random Fields (GRFs), and consider joint…

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighbourhood structure of the model, and a precision, or…

The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…